From 62bbc1934dd7718a285584fd3a02780d30f91866 Mon Sep 17 00:00:00 2001 From: alexander Date: Sat, 7 Feb 2026 11:26:05 +0100 Subject: [PATCH 01/51] Added correction --- src/cheatsheets/Schaltungstheorie.typ | 22 +++++++++++----------- 1 file changed, 11 insertions(+), 11 deletions(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index 961a94c..cd5e7ba 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -775,17 +775,17 @@ $bold(B) : bold(u_b) -> text("Zweigspannungsbilanz") = 0$ \ $bold(B^T) : bold(i_m) -> i_b$ - $ - bold(B) = quad mannot.mark( - mat( - b_11, b_12, ..., b_(1m); - b_21, b_22, ..., b_(2m); - dots.v, dots.v, dots.down, dots.v; - b_(n 1), b_(n 2), ..., b_(n m) - ), tag: #<1> - ) - #mannot.annot(<1>, pos: left, text(rgb("#404296"))[#rotate(-90deg)[$<-$ Maschen]], dx: 6mm) - #mannot.annot(<1>, pos: bottom, text(rgb("#404296"))[Zweige $->$], dy: -0.5mm) + $ + bold(B) = quad mannot.mark(mat( + b_11, b_12, ..., b_(1m); + b_21, b_22, ..., b_(2m); + dots.v, dots.v, dots.down, dots.v; + b_(n 1), b_(n 2), ..., b_(n m) + ), tag: #<1>) + + #mannot.annot(<1>, pos:left, text(rgb("#404296"))[#rotate(-90deg)[$<-$ Maschen]], dx: 6mm) + #mannot.annot(<1>, pos:bottom, text(rgb("#404296"))[Zweige $->$], dy: -0.5mm) + b in {-1, 0, 1} $ From 06d365f8caad7dbea853a8565497a913d51688b1 Mon Sep 17 00:00:00 2001 From: levi Date: Sat, 7 Feb 2026 12:41:24 +0100 Subject: [PATCH 02/51] Bauelemente schmente (Eintore bald fertig) --- src/cheatsheets/Schaltungstheorie.typ | 457 ++++++++++++++++---------- 1 file changed, 275 insertions(+), 182 deletions(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index 961a94c..f8b5128 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -412,7 +412,280 @@ columns: (1fr, 1fr, 1fr), stroke: none, align: center, - table.header([*Zeichen*], [*Gleichung*], [*Abbildung*]), + table.header([*Zeichen*], [*Gleichungen*], [*Abbildung*]), + + // Nullator + [ + Nullator + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + + })) + ], + [ + $u = 0$ + + $i = 0$ + ], + [ + #scale(x: 75%, y: 75%, cetz.canvas({ + import cetz.draw: * + import cetz-plot: * + + let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) + + plot.plot(axis-style: "school-book", ..opts, name: "plot", { + + plot.add(((0,0), (0,0)), + mark-style: (stroke: red, fill: red), mark: "o", ) + }) + })) + ], + + // Norator + [ + Norator + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + + })) + ], + [ + u = beliebig + i = beliebig + ], + [ + #scale(x: 75%, y: 75%, cetz.canvas({ + import cetz.draw: * + import cetz-plot: * + + let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) + + plot.plot(axis-style: "school-book", ..opts, name: "plot", { + plot.add-contour(x-domain: (-3, 3), y-domain: (-3, 3), + style: (fill: rgb("#f7000832"), stroke: none), + fill: true, + op: "<", // Find contours where data < z + z: (0,100000), // Z values to find contours for + (x, y) => calc.sqrt(x*x + y * y)) + }) + })) + ], + + table.hline(), + + // Kurzschluss + [ + Kurzschluss + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + + node("n1", (0, 0)) + node("n2", (1, 0)) + wire((0,0), (1,0)) + wire((-0.25,0), (0,0)) + wire((1,0), (1.25,0)) + + })) + ], + [ + $u = 0$ + + i = beliebig + ], + [ + #scale(x: 75%, y: 75%, cetz.canvas({ + import cetz.draw: * + import cetz-plot: * + + let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) + + plot.plot(axis-style: "school-book", ..opts, name: "plot", { + + plot.add(((0, -1), (0, 1)), style: (stroke: red)) + }) + })) + ], + + // Leerlauf + [ + Leerlauf + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + node("n1", (0, 0)) + node("n2", (1, 0)) + + wire((-0.25,0), (0,0)) + wire((1,0), (1.25,0)) + })) + ], + [ + u = beliebig + $i = 0$ + ], + [ + #scale(x: 75%, y: 75%, cetz.canvas({ + import cetz.draw: * + import cetz-plot: * + + let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) + + plot.plot(axis-style: "school-book", ..opts, name: "plot", { + + plot.add(((-1, 0), (1, 0)), style: (stroke: red)) + }) + })) + ], + + table.hline(), + // Quellen: // + // Spannungs-quelle + [ + Spannungs-quelle + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + vsource( + "b1", + (0, 0), + (1.75, 0), + ) + })) + ], + [ + $u = U_0$ + + i = beliebig + ], + [ + #scale(x: 75%, y: 75%, cetz.canvas({ + import cetz.draw: * + import cetz-plot: * + + let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) + + plot.plot(axis-style: "school-book", ..opts, name: "plot", { + + plot.add(((1, -1), (1, 1)), style: (stroke: red)) + plot.add-anchor("pt",(1,0)) + }) + content("plot.pt", [$U_0$], anchor: "north-west", padding: .1) + })) + ], + + // Strom-quelle + [ + Strom-quelle + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + isource( + "b1", + (0, 0), + (1.75, 0), + ) + })) + ], + [ + u = beliebig + + $i = I_0$ + ], + [ + #scale(x: 75%, y: 75%, cetz.canvas({ + import cetz.draw: * + import cetz-plot: * + + let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) + + plot.plot(axis-style: "school-book", ..opts, name: "plot", { + + plot.add(((-1, 1), (1, 1)), style: (stroke: red)) + plot.add-anchor("pt",(0,1)) + }) + content("plot.pt", [$I_0$], anchor: "south-east", padding: .1) + })) + ], + + table.hline(), + +// Wiederstand + [ + Wiederstand + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + resistor( + "b1", + (0, 0), + (2, 0), + ) + })) + ], + [ + $u = r * i$ + $i = u/r$ + ], + [ + #scale(x: 75%, y: 75%, cetz.canvas({ + import cetz.draw: * + import cetz-plot: * + + let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) + + plot.plot(axis-style: "school-book", ..opts, name: "plot", { + + plot.add(((-1, -1), (1, 1)), style: (stroke: red)) + }) + })) + ], + + // Induktivität + [ + Induktivität + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + inductor( + "b1", + (0, 0), + (2, 0), + variant: "ieee", + ) + })) + ], + [ + + ], + [ + + ], + + // Kapazität + [ + Kapazität + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + capacitor( + "b1", + (0, 0), + (2, 0), + ) + })) + ], + [ + + ], + [ + + ], + + table.hline(), // Dioden :// // @@ -547,187 +820,7 @@ ], - // Quellen: // - // Spannungs-quelle - [ - Spannungs-quelle - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - vsource( - "b1", - (0, 0), - (1.75, 0), - ) - })) - ], - [ - - ], - [ - - ], - - // Strom-quelle - [ - Strom-quelle - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - isource( - "b1", - (0, 0), - (1.75, 0), - ) - })) - ], - [ - - ], - [ - - ], - - // Wiederstand - [ - Wiederstand - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - resistor( - "b1", - (0, 0), - (2, 0), - ) - })) - ], - [ - - ], - [ - - ], - - // Induktivität - [ - Induktivität - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - inductor( - "b1", - (0, 0), - (2, 0), - variant: "ieee", - ) - })) - ], - [ - - ], - [ - - ], - - // Kapazität - [ - Kapazität - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - capacitor( - "b1", - (0, 0), - (2, 0), - ) - })) - ], - [ - - ], - [ - - ], - - // Kurzschluss - [ - Kurzschluss - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - capacitor( - "b1", - (0, 0), - (2, 0), - ) - })) - ], - [ - - ], - [ - - ], - - // Leerlauf - [ - Leerlauf - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - capacitor( - "b1", - (0, 0), - (2, 0), - ) - })) - ], - [ - - ], - [ - - ], - - // Nullator - [ - Nullator - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - capacitor( - "b1", - (0, 0), - (2, 0), - ) - })) - ], - [ - - ], - [ - - ], - - // Norator - [ - Norator - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - capacitor( - "b1", - (0, 0), - (2, 0), - ) - })) - ], - [ - - ], - [ - - ], + ); From 6b5eda7c05afa09e119741d801df0d53e02d2760 Mon Sep 17 00:00:00 2001 From: levi Date: Sat, 7 Feb 2026 13:04:20 +0100 Subject: [PATCH 03/51] Bauelemente schmente Norator, Nullator Zeichen added --- src/cheatsheets/Schaltungstheorie.typ | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index 7312582..e4c2a47 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -420,7 +420,7 @@ #scale(x: 100%, y: 100%, zap.circuit({ import zap: * import cetz.draw: content, line - + joham.nullator("nullator1",(0,0), (-1.75,0)) })) ], [ @@ -449,7 +449,7 @@ #scale(x: 100%, y: 100%, zap.circuit({ import zap: * import cetz.draw: content, line - + joham.norator("norator1",(0,0), (-1.75,0)) })) ], [ From 72abc106573c320f15bed7dcd5a0c0fc37f45c95 Mon Sep 17 00:00:00 2001 From: alexander Date: Sat, 7 Feb 2026 16:44:46 +0100 Subject: [PATCH 04/51] Component List --- src/cheatsheets/Schaltungstheorie.typ | 402 ++++++++++++++++++++++++-- 1 file changed, 379 insertions(+), 23 deletions(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index e4c2a47..e66ec2e 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -178,6 +178,8 @@ ) ] + // + // Quell Wandlung #bgBlock(fill: colorEineTore)[ #subHeading(fill: colorEineTore)[Ein-Tor] @@ -1304,7 +1306,7 @@ ], [], [ - $Phi(t) = integral_(-infinity)^(t) u(tau) d tau = \ + $ if calc.rem(y, 2) == 1 { tableFillLow } else { tableFillHigh }, - [], [*$Y = U/I$*], [*$Z = I/U$*], [*$phi$*], - [], [*$Omega$*], [*$S$*], [*rad*], + [], [*$Z = U/I$*], [*$Y = I/U$*], [*$phi$*], + [], [*$I -> U$*], [*$U -> I$*], [*$phi$*], + [], [*$Omega space (R)$*], [*$S space (G)$*], [*rad*], zap.circuit({ import zap: * resistor("R", (0, 0), (0.6, 0), width: 3mm, height: 2mm, fill: none) }), - $R$, - $1/G = R$, + $R = 1/G$, + $G = 1/R$, $0$, zap.circuit({ @@ -1537,36 +1540,389 @@ ) } -#bgBlock(fill: colorAnalyseVerfahren)[ - #subHeading(fill: colorAnalyseVerfahren)[Knotenpotenzial-Analyse Komponetent] - #import mannot: * - #let ImageHeight = 3.0cm +#columns(2)[ + #bgBlock(fill: colorAnalyseVerfahren)[ + #subHeading(fill: colorAnalyseVerfahren)[Knotenpotenzial-Analyse Komponetent] + #import mannot: * - #table( - columns: (1fr, 1fr, 1fr, 1fr), - fill: (x, y) => if calc.rem(y, 2) == 0 { tableFillHigh } else { tableFillLow }, - align(center, image("../images/schaltungstheorie/knotenpotenzial/schaltKontenPotenziell3-1.png", height: ImageHeight, fit: "contain")), + #let ImageHeight = 3.0cm - align(center, image("../images/schaltungstheorie/knotenpotenzial/schaltKontenPotenziell4.png", height: ImageHeight, fit: "contain")), + #table( + columns: (1fr, 1fr), + fill: (x, y) => if calc.rem(y, 2) == 0 { tableFillHigh } else { tableFillLow }, + align(center, image("../images/schaltungstheorie/knotenpotenzial/schaltKontenPotenziell3-1.png", height: ImageHeight, fit: "contain")), - align(center, image("../images/schaltungstheorie/knotenpotenzial/schaltKontenPotenziell5.png", height: ImageHeight, fit: "contain")), + align(center, image("../images/schaltungstheorie/knotenpotenzial/schaltKontenPotenziell4.png", height: ImageHeight, fit: "contain")), - align(center, image("../images/schaltungstheorie/knotenpotenzial/schaltKontenPotenziell6.png", height: ImageHeight, fit: "contain")), + align(center, image("../images/schaltungstheorie/knotenpotenzial/schaltKontenPotenziell5.png", height: ImageHeight, fit: "contain")), - align(center, image("../images/schaltungstheorie/knotenpotenzial/schaltKontenPotenziell7.png", height: ImageHeight, fit: "contain")), + align(center, image("../images/schaltungstheorie/knotenpotenzial/schaltKontenPotenziell6.png", height: ImageHeight, fit: "contain")), - align(center, image("../images/schaltungstheorie/knotenpotenzial/schaltKontenPotenziell8.png", height: ImageHeight, fit: "contain")), + align(center, image("../images/schaltungstheorie/knotenpotenzial/schaltKontenPotenziell7.png", height: ImageHeight, fit: "contain")), - align(center, image("../images/schaltungstheorie/knotenpotenzial/schaltKontenPotenziell9.png", height: ImageHeight, fit: "contain")), + align(center, image("../images/schaltungstheorie/knotenpotenzial/schaltKontenPotenziell8.png", height: ImageHeight, fit: "contain")), - align(center, image("../images/schaltungstheorie/knotenpotenzial/schaltKontenPotenziell10.png", height: ImageHeight, fit: "contain")), + align(center, image("../images/schaltungstheorie/knotenpotenzial/schaltKontenPotenziell9.png", height: ImageHeight, fit: "contain")), - align(center, image("../images/schaltungstheorie/knotenpotenzial/schaltKontenPotenziell1.png", height: ImageHeight, fit: "contain")), + align(center, image("../images/schaltungstheorie/knotenpotenzial/schaltKontenPotenziell10.png", height: ImageHeight, fit: "contain")), - align(center, image("../images/schaltungstheorie/knotenpotenzial/schaltKontenPotenziell2.png", height: ImageHeight, fit: "contain")), + align(center, image("../images/schaltungstheorie/knotenpotenzial/schaltKontenPotenziell1.png", height: ImageHeight, fit: "contain")), - ) + align(center, image("../images/schaltungstheorie/knotenpotenzial/schaltKontenPotenziell2.png", height: ImageHeight, fit: "contain")), + + ) + ] + + #colbreak() + + // Bauelemente + #bgBlock(fill: colorEineTore)[ + #subHeading(fill: colorEineTore)[Bauelemente] + #table( + columns: (1fr, 1fr, 1fr), + stroke: none, + align: center, + fill: (x, y) => if (calc.rem(y, 2) == 0) { tableFillLow } else { tableFillHigh }, + table.header([*Zeichen*], [*Gleichung*], [*Abbildung*]), + + // Quellen: // + // Spannungs-quelle + [ + Spannungs-quelle + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + vsource( + "b1", + fill: none, + (0, 0), + (1.75, 0), + ) + })) + ], + [ + + ], + [ + + ], + + // Strom-quelle + [ + Strom-quelle + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + isource( + "b1", + fill: none, + (0, 0), + (1.75, 0), + ) + })) + ], + [ + + ], + [ + + ], + + // Wiederstand + [ + Wiederstand + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + resistor( + fill: none, + "b1", + (0, 0), + (2, 0), + ) + })) + ], + align(center+horizon,[ + $[R] = Omega = V/A \ + [G] = S = A/V$ + ]), + [ + + ], + + // Induktivität + [ + Induktivität + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + inductor( + "b1", + (0, 0), + (2, 0), + variant: "ieee", + ) + })) + ], + [ + + ], + [ + + ], + + // Kapazität + [ + Kapazität + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + capacitor( + fill: none, + "b1", + (0, 0), + (2, 0), + ) + })) + ], + [ + + ], + [ + + ], + + // Kurzschluss + [ + Kurzschluss (KS) + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + wire((1,0), (-1,0), i: (content: $i_"ll"$, invert: true, anchor: "south")) + + set-style(mark: (end: ("straight"))) + line((-0.5,0.2), (0.5, 0.2), stroke: (thickness: 0.02)) + content((0,0.555), $u_"ll" = 0$) + + })) + ], + align(center+horizon, [ + $u_"ll" = 0 unit("V")\ + i_"ll" = "bel." + $ + ]), + [ + + ], + + // Leerlauf + [ + Leerlauf (LL) + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + node("N0",(-0.5,0)) + node("N1",(0.5,0)) + wire((-1,0), "N0") + wire((1,0), "N1", i: (content: $i_"ll" = 0$, invert: true, anchor: "south")) + + set-style(mark: (end: ("straight"))) + line((-0.3,0), (0.3, 0), stroke: (thickness: 0.02)) + content((0,0.35), $u_"ll"$) + + })) + ], + align(center+horizon, [ + $u_"ll" = "bel."\ + i_"ll" = 0 unit("A") + $ + ]), + [ + + ], + + // Nullator + [ + Nullator + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + joham.nullator("N0", (-1,0), (1,0), scale: 0.5, i: (anchor: "south", content: $i_"null"$)) + + set-style(mark: (end: ("straight"))) + line((-0.3,0.3), (0.3, 0.3), stroke: (thickness: 0.02)) + content((0,0.6), $u_"null"$) + })) + ], + align(center+horizon, [ + $u_"null" = 0 unit("V")\ + i_"ll" = 0 unit("A") + $ + ]), + [ + + ], + + // Norator + [ + Norator + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + joham.norator("N0", (-1,0), (1,0), scale: 0.5, i: (anchor: "south", content: $i_"nor"$)) + + set-style(mark: (end: ("straight"))) + line((-0.3,0.3), (0.3, 0.3), stroke: (thickness: 0.02)) + content((0,0.6), $u_"nor"$) + })) + ], + align(center+horizon, [ + $u_"null" = "bel."\ + i_"ll" = "bel." + $ + ]), + [ + + ], + + // Dioden :// + // + // ideale Diode + [ + ideale Diode + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + diode("b1", (0, 0), (1., 0), stroke: black, fill: white) + })) + ], + [ + $u=0$ falls $i>0$ + $i=0$ falls $u<0$ + ], + [ + /* + #scale(x: 50%, y: 50%, + cetz.canvas({ + import cetz.draw: * + line((-1.5, 0), (1.5, 0), mark: (end: "straight")) + line((0, -1.5), (0, 1.5), mark: (end: "straight")) + + content( (1.55, 0), $u$, anchor: "west") + content( (0.15, 1.4), $i$, anchor: "west") + + line((-1.5, 0), (0, 0), stroke: red) // u = 0 + line((0, 0), (0, 1.35), stroke: red) // i = 0 + + })) + */ + #scale(x: 75%, y: 75%, cetz.canvas({ + import cetz.draw: * + import cetz-plot: * + + let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) + + plot.plot(axis-style: "school-book", ..opts, name: "plot", { + plot.add(((-1, 0), (0, 0)), style: (stroke: red)) + plot.add(((0, 0), (0, 1)), style: (stroke: red)) + }) + })) + ], + //table.hline(start: 1, end: 2), + + // reale/pn Diode + [ + reale/pn Diode + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + diode("b1", (0, 0), (1., 0), stroke: black, fill: black) + })) + ], + + [ + $u_D = u_T*ln((i_D/I_S)+1)$ + $i_D = I_S*(e^(u_D/U_T)-1)$ + ], + [ + #scale(x: 75%, y: 75%, cetz.canvas({ + import cetz.draw: * + import cetz-plot: * + + let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) + let data = plot.add(x => calc.exp(x) - 1, domain: (-2, 2), style: (stroke: red)) + + plot.plot(axis-style: "school-book", ..opts, data, name: "plot") + })) + ], + + // Photodiode + [ + Photodiode + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + photodiode("b1", (0, 0), (1., 0), stroke: black, fill: black) + })) + ], + [ + $i = I_S*(e^(u_D/U_T)-1)- i_L$ + ], + [ + #scale(x: 75%, y: 75%, cetz.canvas({ + import cetz.draw: * + import cetz-plot: * + + let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) + + plot.plot(axis-style: "school-book", ..opts, name: "plot", { + plot.add(x => calc.exp(x) - 1, domain: (-2, 2), style: (stroke: red)) + + plot.add(x => calc.exp(x) - 2, domain: (-2, 2), style: (stroke: red)) + + plot.add(x => calc.exp(x) - 3, domain: (-2, 2), style: (stroke: red)) + }) + })) + ], + + // Zenerdiode + [ + Zenerdiode + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + zener("b1", (0, 0), (1., 0), stroke: black, fill: black) + })) + ], + [ + Durchbruch bei $u=U_Z$ : + $u<=U_Z$ stark leitend + ], + [ + + ], + + // Tunneldiode + [ + Tunneldiode + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + tunnel("b1", (0, 0), (1., 0), stroke: black, fill: black) + })) + ], + [ + + ], + [ + + ], + + ); + + + ] ] #bgBlock(fill: colorZweiTore, width: 100%)[ From 2b0579adb9fa581164b1f2a734ea6b99022bd0e7 Mon Sep 17 00:00:00 2001 From: alexander Date: Sat, 7 Feb 2026 16:47:23 +0100 Subject: [PATCH 05/51] Removed alex version of Bauelemente --- src/cheatsheets/Schaltungstheorie.typ | 350 -------------------------- 1 file changed, 350 deletions(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index e66ec2e..a9321af 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -1573,356 +1573,6 @@ ) ] - - #colbreak() - - // Bauelemente - #bgBlock(fill: colorEineTore)[ - #subHeading(fill: colorEineTore)[Bauelemente] - #table( - columns: (1fr, 1fr, 1fr), - stroke: none, - align: center, - fill: (x, y) => if (calc.rem(y, 2) == 0) { tableFillLow } else { tableFillHigh }, - table.header([*Zeichen*], [*Gleichung*], [*Abbildung*]), - - // Quellen: // - // Spannungs-quelle - [ - Spannungs-quelle - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - vsource( - "b1", - fill: none, - (0, 0), - (1.75, 0), - ) - })) - ], - [ - - ], - [ - - ], - - // Strom-quelle - [ - Strom-quelle - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - isource( - "b1", - fill: none, - (0, 0), - (1.75, 0), - ) - })) - ], - [ - - ], - [ - - ], - - // Wiederstand - [ - Wiederstand - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - resistor( - fill: none, - "b1", - (0, 0), - (2, 0), - ) - })) - ], - align(center+horizon,[ - $[R] = Omega = V/A \ - [G] = S = A/V$ - ]), - [ - - ], - - // Induktivität - [ - Induktivität - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - inductor( - "b1", - (0, 0), - (2, 0), - variant: "ieee", - ) - })) - ], - [ - - ], - [ - - ], - - // Kapazität - [ - Kapazität - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - capacitor( - fill: none, - "b1", - (0, 0), - (2, 0), - ) - })) - ], - [ - - ], - [ - - ], - - // Kurzschluss - [ - Kurzschluss (KS) - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - wire((1,0), (-1,0), i: (content: $i_"ll"$, invert: true, anchor: "south")) - - set-style(mark: (end: ("straight"))) - line((-0.5,0.2), (0.5, 0.2), stroke: (thickness: 0.02)) - content((0,0.555), $u_"ll" = 0$) - - })) - ], - align(center+horizon, [ - $u_"ll" = 0 unit("V")\ - i_"ll" = "bel." - $ - ]), - [ - - ], - - // Leerlauf - [ - Leerlauf (LL) - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - node("N0",(-0.5,0)) - node("N1",(0.5,0)) - wire((-1,0), "N0") - wire((1,0), "N1", i: (content: $i_"ll" = 0$, invert: true, anchor: "south")) - - set-style(mark: (end: ("straight"))) - line((-0.3,0), (0.3, 0), stroke: (thickness: 0.02)) - content((0,0.35), $u_"ll"$) - - })) - ], - align(center+horizon, [ - $u_"ll" = "bel."\ - i_"ll" = 0 unit("A") - $ - ]), - [ - - ], - - // Nullator - [ - Nullator - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - joham.nullator("N0", (-1,0), (1,0), scale: 0.5, i: (anchor: "south", content: $i_"null"$)) - - set-style(mark: (end: ("straight"))) - line((-0.3,0.3), (0.3, 0.3), stroke: (thickness: 0.02)) - content((0,0.6), $u_"null"$) - })) - ], - align(center+horizon, [ - $u_"null" = 0 unit("V")\ - i_"ll" = 0 unit("A") - $ - ]), - [ - - ], - - // Norator - [ - Norator - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - joham.norator("N0", (-1,0), (1,0), scale: 0.5, i: (anchor: "south", content: $i_"nor"$)) - - set-style(mark: (end: ("straight"))) - line((-0.3,0.3), (0.3, 0.3), stroke: (thickness: 0.02)) - content((0,0.6), $u_"nor"$) - })) - ], - align(center+horizon, [ - $u_"null" = "bel."\ - i_"ll" = "bel." - $ - ]), - [ - - ], - - // Dioden :// - // - // ideale Diode - [ - ideale Diode - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - diode("b1", (0, 0), (1., 0), stroke: black, fill: white) - })) - ], - [ - $u=0$ falls $i>0$ - $i=0$ falls $u<0$ - ], - [ - /* - #scale(x: 50%, y: 50%, - cetz.canvas({ - import cetz.draw: * - line((-1.5, 0), (1.5, 0), mark: (end: "straight")) - line((0, -1.5), (0, 1.5), mark: (end: "straight")) - - content( (1.55, 0), $u$, anchor: "west") - content( (0.15, 1.4), $i$, anchor: "west") - - line((-1.5, 0), (0, 0), stroke: red) // u = 0 - line((0, 0), (0, 1.35), stroke: red) // i = 0 - - })) - */ - #scale(x: 75%, y: 75%, cetz.canvas({ - import cetz.draw: * - import cetz-plot: * - - let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) - - plot.plot(axis-style: "school-book", ..opts, name: "plot", { - plot.add(((-1, 0), (0, 0)), style: (stroke: red)) - plot.add(((0, 0), (0, 1)), style: (stroke: red)) - }) - })) - ], - //table.hline(start: 1, end: 2), - - // reale/pn Diode - [ - reale/pn Diode - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - diode("b1", (0, 0), (1., 0), stroke: black, fill: black) - })) - ], - - [ - $u_D = u_T*ln((i_D/I_S)+1)$ - $i_D = I_S*(e^(u_D/U_T)-1)$ - ], - [ - #scale(x: 75%, y: 75%, cetz.canvas({ - import cetz.draw: * - import cetz-plot: * - - let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) - let data = plot.add(x => calc.exp(x) - 1, domain: (-2, 2), style: (stroke: red)) - - plot.plot(axis-style: "school-book", ..opts, data, name: "plot") - })) - ], - - // Photodiode - [ - Photodiode - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - photodiode("b1", (0, 0), (1., 0), stroke: black, fill: black) - })) - ], - [ - $i = I_S*(e^(u_D/U_T)-1)- i_L$ - ], - [ - #scale(x: 75%, y: 75%, cetz.canvas({ - import cetz.draw: * - import cetz-plot: * - - let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) - - plot.plot(axis-style: "school-book", ..opts, name: "plot", { - plot.add(x => calc.exp(x) - 1, domain: (-2, 2), style: (stroke: red)) - - plot.add(x => calc.exp(x) - 2, domain: (-2, 2), style: (stroke: red)) - - plot.add(x => calc.exp(x) - 3, domain: (-2, 2), style: (stroke: red)) - }) - })) - ], - - // Zenerdiode - [ - Zenerdiode - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - zener("b1", (0, 0), (1., 0), stroke: black, fill: black) - })) - ], - [ - Durchbruch bei $u=U_Z$ : - $u<=U_Z$ stark leitend - ], - [ - - ], - - // Tunneldiode - [ - Tunneldiode - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - tunnel("b1", (0, 0), (1., 0), stroke: black, fill: black) - })) - ], - [ - - ], - [ - - ], - - ); - - - ] ] #bgBlock(fill: colorZweiTore, width: 100%)[ From f4b3e9753fe32cf536270acc8f74da72c727235f Mon Sep 17 00:00:00 2001 From: alexander Date: Sat, 7 Feb 2026 16:55:29 +0100 Subject: [PATCH 06/51] moved table --- src/cheatsheets/Schaltungstheorie.typ | 842 +++++++++++++------------- 1 file changed, 421 insertions(+), 421 deletions(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index a9321af..1fa0ca0 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -407,427 +407,6 @@ ] */ - // Bauelemente - #bgBlock(fill: colorEineTore)[ - #subHeading(fill: colorEineTore)[Bauelemente] - #table( - columns: (1fr, 1fr, 1fr), - stroke: none, - align: center, - table.header([*Zeichen*], [*Gleichungen*], [*Abbildung*]), - - // Nullator - [ - Nullator - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - joham.nullator("nullator1",(0,0), (-1.75,0)) - })) - ], - [ - $u = 0$ - - $i = 0$ - ], - [ - #scale(x: 75%, y: 75%, cetz.canvas({ - import cetz.draw: * - import cetz-plot: * - - let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) - - plot.plot(axis-style: "school-book", ..opts, name: "plot", { - - plot.add(((0,0), (0,0)), - mark-style: (stroke: red, fill: red), mark: "o", ) - }) - })) - ], - - // Norator - [ - Norator - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - joham.norator("norator1",(0,0), (-1.75,0)) - })) - ], - [ - u = beliebig - i = beliebig - ], - [ - #scale(x: 75%, y: 75%, cetz.canvas({ - import cetz.draw: * - import cetz-plot: * - - let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) - - plot.plot(axis-style: "school-book", ..opts, name: "plot", { - plot.add-contour(x-domain: (-3, 3), y-domain: (-3, 3), - style: (fill: rgb("#f7000832"), stroke: none), - fill: true, - op: "<", // Find contours where data < z - z: (0,100000), // Z values to find contours for - (x, y) => calc.sqrt(x*x + y * y)) - }) - })) - ], - - table.hline(), - - // Kurzschluss - [ - Kurzschluss - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - - node("n1", (0, 0)) - node("n2", (1, 0)) - wire((0,0), (1,0)) - wire((-0.25,0), (0,0)) - wire((1,0), (1.25,0)) - - })) - ], - [ - $u = 0$ - - i = beliebig - ], - [ - #scale(x: 75%, y: 75%, cetz.canvas({ - import cetz.draw: * - import cetz-plot: * - - let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) - - plot.plot(axis-style: "school-book", ..opts, name: "plot", { - - plot.add(((0, -1), (0, 1)), style: (stroke: red)) - }) - })) - ], - - // Leerlauf - [ - Leerlauf - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - node("n1", (0, 0)) - node("n2", (1, 0)) - - wire((-0.25,0), (0,0)) - wire((1,0), (1.25,0)) - })) - ], - [ - u = beliebig - $i = 0$ - ], - [ - #scale(x: 75%, y: 75%, cetz.canvas({ - import cetz.draw: * - import cetz-plot: * - - let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) - - plot.plot(axis-style: "school-book", ..opts, name: "plot", { - - plot.add(((-1, 0), (1, 0)), style: (stroke: red)) - }) - })) - ], - - table.hline(), - // Quellen: // - // Spannungs-quelle - [ - Spannungs-quelle - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - vsource( - "b1", - (0, 0), - (1.75, 0), - ) - })) - ], - [ - $u = U_0$ - - i = beliebig - ], - [ - #scale(x: 75%, y: 75%, cetz.canvas({ - import cetz.draw: * - import cetz-plot: * - - let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) - - plot.plot(axis-style: "school-book", ..opts, name: "plot", { - - plot.add(((1, -1), (1, 1)), style: (stroke: red)) - plot.add-anchor("pt",(1,0)) - }) - content("plot.pt", [$U_0$], anchor: "north-west", padding: .1) - })) - ], - - // Strom-quelle - [ - Strom-quelle - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - isource( - "b1", - (0, 0), - (1.75, 0), - ) - })) - ], - [ - u = beliebig - - $i = I_0$ - ], - [ - #scale(x: 75%, y: 75%, cetz.canvas({ - import cetz.draw: * - import cetz-plot: * - - let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) - - plot.plot(axis-style: "school-book", ..opts, name: "plot", { - - plot.add(((-1, 1), (1, 1)), style: (stroke: red)) - plot.add-anchor("pt",(0,1)) - }) - content("plot.pt", [$I_0$], anchor: "south-east", padding: .1) - })) - ], - - table.hline(), - -// Wiederstand - [ - Wiederstand - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - resistor( - "b1", - (0, 0), - (2, 0), - ) - })) - ], - [ - $u = r * i$ - $i = u/r$ - ], - [ - #scale(x: 75%, y: 75%, cetz.canvas({ - import cetz.draw: * - import cetz-plot: * - - let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) - - plot.plot(axis-style: "school-book", ..opts, name: "plot", { - - plot.add(((-1, -1), (1, 1)), style: (stroke: red)) - }) - })) - ], - - // Induktivität - [ - Induktivität - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - inductor( - "b1", - (0, 0), - (2, 0), - variant: "ieee", - ) - })) - ], - [ - - ], - [ - - ], - - // Kapazität - [ - Kapazität - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - capacitor( - "b1", - (0, 0), - (2, 0), - ) - })) - ], - [ - - ], - [ - - ], - - table.hline(), - - // Dioden :// - // - // ideale Diode - [ - ideale Diode - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - diode("b1", (0, 0), (1., 0), stroke: black, fill: white) - })) - ], - [ - $u=0$ falls $i>0$ - $i=0$ falls $u<0$ - ], - [ - /* - #scale(x: 50%, y: 50%, - cetz.canvas({ - import cetz.draw: * - line((-1.5, 0), (1.5, 0), mark: (end: "straight")) - line((0, -1.5), (0, 1.5), mark: (end: "straight")) - - content( (1.55, 0), $u$, anchor: "west") - content( (0.15, 1.4), $i$, anchor: "west") - - line((-1.5, 0), (0, 0), stroke: red) // u = 0 - line((0, 0), (0, 1.35), stroke: red) // i = 0 - - })) - */ - #scale(x: 75%, y: 75%, cetz.canvas({ - import cetz.draw: * - import cetz-plot: * - - let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) - - plot.plot(axis-style: "school-book", ..opts, name: "plot", { - plot.add(((-1, 0), (0, 0)), style: (stroke: red)) - plot.add(((0, 0), (0, 1)), style: (stroke: red)) - }) - })) - ], - //table.hline(start: 1, end: 2), - - // reale/pn Diode - [ - reale/pn Diode - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - diode("b1", (0, 0), (1., 0), stroke: black, fill: black) - })) - ], - - [ - $u_D = u_T*ln((i_D/I_S)+1)$ - $i_D = I_S*(e^(u_D/U_T)-1)$ - ], - [ - #scale(x: 75%, y: 75%, cetz.canvas({ - import cetz.draw: * - import cetz-plot: * - - let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) - let data = plot.add(x => calc.exp(x) - 1, domain: (-2, 2), style: (stroke: red)) - - plot.plot(axis-style: "school-book", ..opts, data, name: "plot") - })) - ], - - // Photodiode - [ - Photodiode - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - photodiode("b1", (0, 0), (1., 0), stroke: black, fill: black) - })) - ], - [ - $i = I_S*(e^(u_D/U_T)-1)- i_L$ - ], - [ - #scale(x: 75%, y: 75%, cetz.canvas({ - import cetz.draw: * - import cetz-plot: * - - let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) - - plot.plot(axis-style: "school-book", ..opts, name: "plot", { - plot.add(x => calc.exp(x) - 1, domain: (-2, 2), style: (stroke: red)) - - plot.add(x => calc.exp(x) - 2, domain: (-2, 2), style: (stroke: red)) - - plot.add(x => calc.exp(x) - 3, domain: (-2, 2), style: (stroke: red)) - }) - })) - ], - - // Zenerdiode - [ - Zenerdiode - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - zener("b1", (0, 0), (1., 0), stroke: black, fill: black) - })) - ], - [ - Durchbruch bei $u=U_Z$ : - $u<=U_Z$ stark leitend - ], - [ - - ], - - // Tunneldiode - [ - Tunneldiode - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - tunnel("b1", (0, 0), (1., 0), stroke: black, fill: black) - })) - ], - [ - - ], - [ - - ], - - - ); - - - ] - // Graphen und Matrizen #bgBlock(fill: colorAnalyseVerfahren)[ #subHeading(fill: colorAnalyseVerfahren)[Graphen und Matrizen] @@ -1573,6 +1152,427 @@ ) ] + + #colbreak() + + // Bauelemente + #bgBlock(fill: colorEineTore)[ + #subHeading(fill: colorEineTore)[Bauelemente] + #table( + columns: (1fr, 1fr, 1fr), + stroke: none, + fill: (x, y) => if (calc.rem(y, 2) == 0) { tableFillLow } else { tableFillHigh }, + align: center, + table.header([*Zeichen*], [*Gleichungen*], [*Abbildung*]), + table.hline(), + + // Nullator + [ + Nullator + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + joham.nullator("nullator1",(0,0), (-1.75,0)) + })) + ], + align(center+horizon, + $u = 0 \ i = 0$ + ), + [ + #scale(x: 75%, y: 75%, cetz.canvas({ + import cetz.draw: * + import cetz-plot: * + + let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) + + plot.plot(axis-style: "school-book", ..opts, name: "plot", { + + plot.add(((0,0), (0,0)), + mark-style: (stroke: red, fill: red), mark: "o", ) + }) + })) + ], + + // Norator + [ + Norator + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + joham.norator("norator1",(0,0), (-1.75,0)) + })) + ], + [ + $u = "bel." \ + i = "bel."$ + ], + [ + #scale(x: 75%, y: 75%, cetz.canvas({ + import cetz.draw: * + import cetz-plot: * + + let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) + + plot.plot(axis-style: "school-book", ..opts, name: "plot", { + plot.add-contour(x-domain: (-3, 3), y-domain: (-3, 3), + style: (fill: rgb("#f7000832"), stroke: none), + fill: true, + op: "<", // Find contours where data < z + z: (0,100000), // Z values to find contours for + (x, y) => calc.sqrt(x*x + y * y)) + }) + })) + ], + + table.hline(), + + // Kurzschluss + [ + Kurzschluss + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + + node("n1", (0, 0)) + node("n2", (1, 0)) + wire((0,0), (1,0)) + wire((-0.25,0), (0,0)) + wire((1,0), (1.25,0)) + + })) + ], + [ + $u = 0$ + + i = bel. + ], + [ + #scale(x: 75%, y: 75%, cetz.canvas({ + import cetz.draw: * + import cetz-plot: * + + let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) + + plot.plot(axis-style: "school-book", ..opts, name: "plot", { + + plot.add(((0, -1), (0, 1)), style: (stroke: red)) + }) + })) + ], + + // Leerlauf + [ + Leerlauf + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + node("n1", (0, 0)) + node("n2", (1, 0)) + + wire((-0.25,0), (0,0)) + wire((1,0), (1.25,0)) + })) + ], + [ + $u = "bel." \ + i = 0$ + ], + [ + #scale(x: 75%, y: 75%, cetz.canvas({ + import cetz.draw: * + import cetz-plot: * + + let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) + + plot.plot(axis-style: "school-book", ..opts, name: "plot", { + + plot.add(((-1, 0), (1, 0)), style: (stroke: red)) + }) + })) + ], + + table.hline(), + // Quellen: // + // Spannungs-quelle + [ + Spannungs-quelle + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + vsource( + "b1", + (0, 0), + (1.75, 0), + ) + })) + ], + [ + $u = U_0$ + + i = bel. + ], + [ + #scale(x: 75%, y: 75%, cetz.canvas({ + import cetz.draw: * + import cetz-plot: * + + let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) + + plot.plot(axis-style: "school-book", ..opts, name: "plot", { + + plot.add(((1, -1), (1, 1)), style: (stroke: red)) + plot.add-anchor("pt",(1,0)) + }) + content("plot.pt", [$U_0$], anchor: "north-west", padding: .1) + })) + ], + + // Strom-quelle + [ + Strom-quelle + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + isource( + "b1", + (0, 0), + (1.75, 0), + ) + })) + ], + [ + u = bel. + + $i = I_0$ + ], + [ + #scale(x: 75%, y: 75%, cetz.canvas({ + import cetz.draw: * + import cetz-plot: * + + let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) + + plot.plot(axis-style: "school-book", ..opts, name: "plot", { + + plot.add(((-1, 1), (1, 1)), style: (stroke: red)) + plot.add-anchor("pt",(0,1)) + }) + content("plot.pt", [$I_0$], anchor: "south-east", padding: .1) + })) + ], + + table.hline(), + +// Wiederstand + [ + Wiederstand + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + resistor( + "b1", + (0, 0), + (2, 0), + ) + })) + ], + align(center+horizon, + $u = r dot i \ + i = u/r$ + ), + [ + #scale(x: 75%, y: 75%, cetz.canvas({ + import cetz.draw: * + import cetz-plot: * + + let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) + + plot.plot(axis-style: "school-book", ..opts, name: "plot", { + + plot.add(((-1, -1), (1, 1)), style: (stroke: red)) + }) + })) + ], + + // Induktivität + [ + Induktivität + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + inductor( + "b1", + (0, 0), + (2, 0), + variant: "ieee", + ) + })) + ], + [ + + ], + [ + + ], + + // Kapazität + [ + Kapazität + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + capacitor( + "b1", + (0, 0), + (2, 0), + ) + })) + ], + [ + + ], + [ + + ], + + table.hline(), + + // Dioden :// + // + // ideale Diode + [ + ideale Diode + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + diode("b1", (0, 0), (1., 0), stroke: black, fill: white) + })) + ], + [ + $u=0$ falls $i>0$ + $i=0$ falls $u<0$ + ], + [ + /* + #scale(x: 50%, y: 50%, + cetz.canvas({ + import cetz.draw: * + line((-1.5, 0), (1.5, 0), mark: (end: "straight")) + line((0, -1.5), (0, 1.5), mark: (end: "straight")) + + content( (1.55, 0), $u$, anchor: "west") + content( (0.15, 1.4), $i$, anchor: "west") + + line((-1.5, 0), (0, 0), stroke: red) // u = 0 + line((0, 0), (0, 1.35), stroke: red) // i = 0 + + })) + */ + #scale(x: 75%, y: 75%, cetz.canvas({ + import cetz.draw: * + import cetz-plot: * + + let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) + + plot.plot(axis-style: "school-book", ..opts, name: "plot", { + plot.add(((-1, 0), (0, 0)), style: (stroke: red)) + plot.add(((0, 0), (0, 1)), style: (stroke: red)) + }) + })) + ], + //table.hline(start: 1, end: 2), + + // reale/pn Diode + [ + reale/pn Diode + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + diode("b1", (0, 0), (1., 0), stroke: black, fill: black) + })) + ], + + [ + $u_D = u_T dot ln((i_D/I_S)+1) \ + i_D = I_S dot (e^(u_D/U_T)-1)$ + ], + [ + #scale(x: 75%, y: 75%, cetz.canvas({ + import cetz.draw: * + import cetz-plot: * + + let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) + let data = plot.add(x => calc.exp(x) - 1, domain: (-2, 2), style: (stroke: red)) + + plot.plot(axis-style: "school-book", ..opts, data, name: "plot") + })) + ], + + // Photodiode + [ + Photodiode + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + photodiode("b1", (0, 0), (1., 0), stroke: black, fill: black) + })) + ], + align(horizon+center, + $i = I_S*(e^(u_D/U_T)-1)- i_L$ + ), + [ + #scale(x: 75%, y: 75%, cetz.canvas({ + import cetz.draw: * + import cetz-plot: * + + let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) + + plot.plot(axis-style: "school-book", ..opts, name: "plot", { + plot.add(x => calc.exp(x) - 1, domain: (-2, 2), style: (stroke: red)) + + plot.add(x => calc.exp(x) - 2, domain: (-2, 2), style: (stroke: red)) + + plot.add(x => calc.exp(x) - 3, domain: (-2, 2), style: (stroke: red)) + }) + })) + ], + + // Zenerdiode + [ + Zenerdiode + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + zener("b1", (0, 0), (1., 0), stroke: black, fill: black) + })) + ], + [ + Durchbruch bei $u=U_Z$ : + $u<=U_Z$ stark leitend + ], + [ + + ], + + // Tunneldiode + [ + Tunneldiode + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + tunnel("b1", (0, 0), (1., 0), stroke: black, fill: black) + })) + ], + [ + + ], + [ + + ], + + + ); + ] ] #bgBlock(fill: colorZweiTore, width: 100%)[ From bdb138396d99331cffdb6ef860818a400bd6ea02 Mon Sep 17 00:00:00 2001 From: alexander Date: Sat, 7 Feb 2026 17:04:46 +0100 Subject: [PATCH 07/51] alexes magic numbers --- src/cheatsheets/Schaltungstheorie.typ | 28 +++++++++++++++++---------- 1 file changed, 18 insertions(+), 10 deletions(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index 1fa0ca0..150d7d7 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -1590,7 +1590,7 @@ columns: (auto, auto, auto, 1fr, 1fr, 1fr), [*Name*], [*Schaltbild*], [*Ersatz-Schaltbild*], [*Eigenschaften*], [*Beschreibung*], [*Knotenspannungs Analyse*], - [Nullor], [], [], [], [$A = mat(0, 0; 0, 0)$], [], + [Nullor], [], [], [], [$ A = mat(0, 0; 0, 0) $], [], [OpAmp \ lin], [], [], [], [], [], @@ -1598,15 +1598,21 @@ [OpAmp \ $U_"sat-"$], [], [], [], [], [], - [VCVS], [], [], [], [$H' = mat(0, 0; mu, 0) quad A = mat(1/mu 0; 0, 0)$], [], + [VCVS], [], [], [], [$ H' = mat(0, 0; mu, 0) quad A = mat(1/mu, 0; 0, 0) $], [], - [VCCS], [], [], [], [$G = mat(0, 0; g, 0) quad A = mat(0, -1/g; 0, 0)$], [], + [VCCS], [], [], [], [$ G = mat(0, 0; g, 0) quad A = mat(0, -1/g; 0, 0) $], [], - [CCVS], [], [], [], [$R = mat(0, 0, r, 0) quad A = mat(0, 0; 1/r, 0)$], [], + [CCVS], [], [], [], [$ R = mat(0, 0; r, 0) quad A = mat(0, 0; 1/r, 0) $], [], - [CCCS], [], [], [], [$H = mat(0, 0; beta, 0) quad A = mat(0, 0; 0, -1/beta)$], [], + [CCCS], [], [], [], [$ H = mat(0, 0; beta, 0) quad A = mat(0, 0; 0, -1/beta) $], [], - [Übertrager], [], [], [], [], [], + [Übertrager], [], [], + [], + [$ H = mat(0, ü; -ü, 0) quad + H' = mat(0, -1/ü; 1/ü, 0) \ + A = mat(ü, 0; 0, 1/ü) quad A' = mat(1/ü, 0; 0, ü) + $], + [], [Gyrator], [], @@ -1615,19 +1621,21 @@ - Antireziprok, Antisymetrisch - Auch Positiv-Immitanz-Inverter ], - [$R = mat(0, -R_d; R_d, 0) quad G = mat(0, G_d; -G_d, 0) \ A = mat(0, R_d; 1/R_d, 0) quad A' = mat(0, -R_d; -1/R_d, 0)$], + [$ R = mat(0, -R_d; R_d, 0) quad G = mat(0, G_d; -G_d, 0) \ A = mat(0, R_d; 1/R_d, 0) quad A' = mat(0, -R_d; -1/R_d, 0) + quad + $], [], [NIK], [], [], - [], [ - - Akitv + - Aktiv - Antireziprok - Symetrisch für $abs(k) = 1$ ], - [$H = mat(0, -k; -k, 0) quad H' = mat(0, -1/k; -1/k, 0); A = mat(-k, 0; 0, 1/k) quad A'= mat(-1/k, 0; 0, k)$], + [$ H = mat(0, -k; -k, 0) quad H' = mat(0, -1/k; -1/k, 0) \ A = mat(-k, 0; 0, 1/k) quad A'= mat(-1/k, 0; 0, k) $], + [], [T-Glied], [], From 3ce057fbc3b2916b38812e5c394375053dbc252b Mon Sep 17 00:00:00 2001 From: levi Date: Sat, 7 Feb 2026 18:09:38 +0100 Subject: [PATCH 08/51] Leistungs Update --- src/cheatsheets/Schaltungstheorie.typ | 19 ++++++++++--------- 1 file changed, 10 insertions(+), 9 deletions(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index 150d7d7..a13864d 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -1049,22 +1049,23 @@ #bgBlock(fill: colorComplexAC)[ #subHeading(fill: colorComplexAC)[*Levi's Lustig Leistung*] - - $P = 1/2 U dot I^*$\ - + $P=P_W + j P_B$\ + #table( columns: (auto, 1fr, auto), fill: (x, y) => if calc.rem(y, 2) == 0 { tableFillLow } else { tableFillHigh }, [Scheinleitsung], [$S = abs(P)$], [$["VA"]$], - [Wirkleistung], [$P_w = "Re"{P}$], [$["W"]$], - [Blindleistung], [$P_b = "Im"{P}$], [$["var"]$], + [Wirkleistung], [$P_W = "Re"{P}$], [$["W"]$], + [Blindleistung], [$P_B = "Im"{P}$], [$["var"]$], ) - Bei Wiederstand: $R$ - - $P_w = U_m^2 / 2R = (I_m^2 R)/2$ - $P = 1/2 U I^* = 1/2 abs(U)^2 Y^* = 1/2 abs(I)^2 Z^*$ + + //Bei Wiederstand: $R$ + + //$P_w = U_m^2 / 2R = (I_m^2 R)/2$ + + $U_"eff" = U_m/sqrt(2), I_"eff" = I_m / sqrt(2)$ ] From 2c9c26de9912289f9652ee885eb9e2f98d56354c Mon Sep 17 00:00:00 2001 From: alexander Date: Sat, 7 Feb 2026 22:23:27 +0100 Subject: [PATCH 09/51] Added diagram memristiv --- src/cheatsheets/Schaltungstheorie.typ | 76 ++++++++++++++++++++++++++- 1 file changed, 74 insertions(+), 2 deletions(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index a13864d..5fb93f8 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -874,7 +874,7 @@ [], [ $[u(t)] = unit("V")$ \ - $[Phi(t)] = unit("A s") = unit("W b")$ \ + $[Phi(t)] = unit("V s") = unit("W b")$ \ ], [ @@ -885,7 +885,7 @@ ], [], [ - $")) + line((-size + margin, size), (size - margin, size), + stroke: (thickness: 0.2mm, paint: rgb("#005500")) + ) + line((-size + margin, -size), (size - margin, -size), + stroke: (thickness: 0.2mm, paint: rgb("#008b00")) + ) + + + set-style(mark: (symbol: ">")) + line((-size+margin, -size+margin), (size -margin, size -margin), + stroke: (thickness: 0.2mm, paint: rgb("#2534ff")) + ) + line((size -margin, -size+margin), (-size+margin, size -margin), + stroke: (thickness: 0.2mm, paint: rgb("#ff4625")) + ) + + scale(y: 75%, x: 75%) + content((0.0, -size - 0.8), text(rgb("#008b00"))[$"Memristiv" q = f(Phi)$], auto-scale: true) + + content((0.0, size+0.8), text(rgb("#005500"))[$"Resitiv" u = r(i)$], auto-scale: true) + + + content((0.0, 0.2), text(rgb("#ff4625"))[$"Induktiv" quad i = lambda(Phi)$], angle: -45deg, auto-scale: true) + + + content((-0.2, 0.1), text(rgb("#2534ff"))[$"Kapazitiv" quad u = chi(Phi)$], angle: 45deg, auto-scale: true) + }) + ]) + + *Allgemeine Beziehungen (gilt immer)* + #align(center+horizon, [ + #canvas({ + import cetz.draw : content, set-style, line, bezier + content((-size, size), $i$) + content((size, size), $u$) + content((-size, -size), $q$) + content((size, -size), $Phi$) + + set-style(mark: (end: ">")) + bezier((-size -margin*0.5, -size +margin), (-size -margin*0.5, size -margin), (-size - 0.5, 0), stroke: (thickness: 0.2mm, paint: rgb("#00318b"))) + bezier((size -margin*0.5, -size +margin), (size -margin*0.5, size -margin), (size - 0.5, 0), stroke: (thickness: 0.2mm, paint: rgb("#00318b"))) + + + bezier((-size +margin*0.5, size -margin), (-size +margin*0.5, -size +margin), (-size + 0.5, 0), stroke: (thickness: 0.2mm, paint: rgb("#8b2000"))) + bezier((size +margin*0.5, size -margin), (size +margin*0.5, -size +margin), (size + 0.5, 0), stroke: (thickness: 0.2mm, paint: rgb("#8b2000"))) + + content((-size + 0.2, 0), scale(75%, text(rgb("#8b2000"), $integral i(tau) d tau$)), anchor: "west") + content((-size - 0.3, 0), scale(75%, text(rgb("#00318b"), $(d q)/(d t)$)), anchor: "east") + + content((size + 0.2, 0), scale(75%, text(rgb("#8b2000"), $integral u(tau) d tau$)), anchor: "west") + content((size - 0.3, 0), scale(75%, text(rgb("#00318b"), $(d Phi)/(d t)$)), anchor: "east") + + }) + ]) + ] + // AC Components #bgBlock(fill: colorComplexAC)[ #subHeading(fill: colorComplexAC)[Komplexe Komponent] From 48fa668059b3f7b3199bdb0e9f3907aa74acbd95 Mon Sep 17 00:00:00 2001 From: alexander Date: Sat, 7 Feb 2026 23:19:03 +0100 Subject: [PATCH 10/51] Added norator/nullator to knoten potenziell --- src/cheatsheets/Schaltungstheorie.typ | 257 +++++++++++------- .../knotenpotenzial/norator.jpg | Bin 0 -> 84825 bytes .../knotenpotenzial/nullator.jpg | Bin 0 -> 84792 bytes 3 files changed, 152 insertions(+), 105 deletions(-) create mode 100644 src/images/schaltungstheorie/knotenpotenzial/norator.jpg create mode 100644 src/images/schaltungstheorie/knotenpotenzial/nullator.jpg diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index 5fb93f8..ca69903 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -54,6 +54,8 @@ [Schaltungstheorie], )) +#set text(8.5pt) + #columns(4, gutter: 2mm)[ // Allgemein #bgBlock(fill: colorAllgemein)[ @@ -73,7 +75,7 @@ [ KCL: $sum_(k=1)^n i_k =0$ (Knotenregel) ], - [ + /*[ #cetz.canvas(length: 8mm, { import cetz.draw: * @@ -88,12 +90,12 @@ line((angle: 120deg, radius: 1.2), (angle: 120deg, radius: 0.4), stroke: red) line((angle: 240deg, radius: 1.2), (angle: 240deg, radius: 0.4), stroke: red) }) - ], + ],*/ [ KVL: $sum_(k=1)^n u_k =0$ (Maschenregel) ], - [ + /*[ #zap.circuit({ import zap: wire import cetz.draw: * @@ -113,7 +115,7 @@ translate((0, -2mm)) mark((angle: 0deg, radius: 4mm), 270deg, symbol: "straight", stroke: blue, scale: 0.75) }) - ], + ],*/ ) $u dot i > 0$: Nimmt Energie auf\ @@ -121,7 +123,7 @@ $u dot i < 0$: Gibt Energie ab\ ] - // Eintrag + // Verschaltung #bgBlock(fill: colorAllgemein)[ #subHeading(fill: colorAllgemein)[Verschaltung] @@ -178,7 +180,6 @@ ) ] - // // Quell Wandlung #bgBlock(fill: colorEineTore)[ @@ -206,6 +207,7 @@ ) ] + // Lineare Quelle #bgBlock(fill: colorEineTore)[ #subHeading(fill: colorEineTore)[Lineare Quelle] @@ -407,6 +409,106 @@ ] */ + + // Linearsierung + #bgBlock(fill: colorEineTore)[ + #subHeading(fill: colorEineTore)[Linearisierung (Ein-Tore)] + + 1. Arbeitspunkt bestimmen \ $"AP" =(u_"AP", i_"AP")$ + + 2. Ableitung $g_cal(F)(u)$/$r_cal(F)(i)$ bilden \ $g'_cal(F)(u)$/$r'_cal(F)(i)$ + + #colbreak() + + #line(length: 100%) + + *Stromgesteuert* $quad r(i) = u$ + + *Groß-Signal* \ + #grid(columns: (1fr, 1fr), + column-gutter: 4mm, + $I_0 = i_"AP" - g'_cal(F)(u_"AP")u_"AP"$, + $g_0 = g'_cal(F)(u_"AP")u$ + ) + + #linebreak() + + $i_"lin" = g_"lin" (u) = g'_cal(F)(u_"AP")(u-u_"AP") + i_"AP"\ + i_"lin" = g_"lin" (u) = g_0 u + I_0$ + + #block( + height: 20mm, + scale(x: 75%, y: 75%, zap.circuit({ + import zap: * + import cetz.draw: content, line + + isource("I0", (0, 1.5), (0, -1.5), fill: none) + node("n0", (2, 1.5)) + node("n1", (2, -1.5)) + + node("n2", (3.5, 1.5), fill: false) + node("n3", (3.5, -1.5), fill: false) + + resistor("g0", "n1", "n0", fill: none, label: (content: $g_0$, anchor: "south", distance: 0.2)) + wire("I0.in", "n0", "n2") + wire("I0.out", "n1", "n3") + wire("n0", "n2", i: (content: $i_"lin"$, anchor: "south", invert: true)) + wire((0, 0.6), "I0.in", i: (content: $I_0$, anchor: "east", invert: true)) + + set-style(mark: (end: ">", fill: black)) + line((3.5, 1.2), (3.5, -1.2), stroke: 0.5pt) + content((3.9, 0), $u$) + })), + ); + + #linebreak() + + *Klein-Signal* $quad i_"lin" = g_"lin" (u) = g'(u_"AP")u$ + + #line(length: 100%) + + + *Spannungsgesteuert* $quad g(u) = i$ + + *Groß-Signal* \ + #grid(columns: (1fr, 1fr), + column-gutter: 4mm, + $U_0 = u_"AP" - r'(i_"AP") i_"AP"$, + $r_0 = r'(i_"AP")$ + ) + #linebreak() + $u_"lin" = r_"lin" (i) = r'(i_"AP")(i-i_"AP") + u_"AP"\ + u_"lin" = r_"lin" (i) = r_0 i + U_0$ + #block( + height: 25mm, + scale(x: 75%, y: 75%, zap.circuit({ + import zap: * + import cetz.draw: content, line + + vsource("U0", (0, 1.5), (0, -1.5), fill: none) + + node("n2", (3.5, 1.5), fill: false) + node("n3", (3.5, -1.5), fill: false) + + resistor("R0", "U0.in", "n2", fill: none, label: (content: $r_0$, anchor: "south", distance: 0.1)) + wire("U0.out", "n3") + + wire((2.49, 1.5), "n2", i: (content: $i$, anchor: "south", invert: true)) + + set-style(mark: (end: ">", fill: black)) + line((3.5, 1.2), (3.5, -1.2), stroke: 0.5pt) + content((3.9, 0), $u_"lin"$) + + line((0.7, 0.5), (0.7, -0.5), stroke: 0.5pt) + content((1.2, 0), $U_0$) + })), + ); + #linebreak() + *Klein-Signal* $quad u_"lin" = r_"lin" (i) = r'(i_"AP")i$ + ] + + + #colbreak() // Graphen und Matrizen #bgBlock(fill: colorAnalyseVerfahren)[ #subHeading(fill: colorAnalyseVerfahren)[Graphen und Matrizen] @@ -425,7 +527,7 @@ $bold(A) : bold(i_k) -> text("Knotenstrombilanz") = 0$ \ $bold(A^T) : bold(u_b)-> bold(u_k)$ $ - bold(A) = quad mannot.mark( + bold(A) = quad space space mannot.mark( mat( a_11, a_12, ..., a_(1m); a_21, a_22, ..., a_(2m); @@ -433,13 +535,13 @@ a_(n 1), a_(n 2), ..., a_(n m) ), tag: #<1> ) - #mannot.annot(<1>, pos: left, text(rgb("#404296"))[#rotate(-90deg)[$<-$ Knoten]], dx: 5mm) - #mannot.annot(<1>, pos: bottom, text(rgb("#404296"))[Zweige $->$], dy: -0.5mm) + #mannot.annot(<1>, pos: left, text(rgb("#404296"))[#rotate(-90deg)[$<-$ Knoten \ ($n-1$)]], dx: 2mm) + #mannot.annot(<1>, pos: bottom, text(rgb("#404296"))[Zweige ($b$) $->$], dy: -0.5mm) a in {-1, 0, 1} $ - - $-1$: In Knoten rein \ - $1$: Aus Knoten raus \ + #linebreak() + $-1 &: "In Knoten rein" \ + 1 &: "Aus Knoten raus"$ #line(length: 100%, stroke: (thickness: 0.2mm)) @@ -450,21 +552,22 @@ $bold(B^T) : bold(i_m) -> i_b$ $ - bold(B) = quad mannot.mark(mat( + bold(B) = quad space space mannot.mark(mat( b_11, b_12, ..., b_(1m); b_21, b_22, ..., b_(2m); dots.v, dots.v, dots.down, dots.v; b_(n 1), b_(n 2), ..., b_(n m) ), tag: #<1>) - #mannot.annot(<1>, pos:left, text(rgb("#404296"))[#rotate(-90deg)[$<-$ Maschen]], dx: 6mm) - #mannot.annot(<1>, pos:bottom, text(rgb("#404296"))[Zweige $->$], dy: -0.5mm) + #mannot.annot(<1>, pos:left, text(rgb("#404296"))[#rotate(-90deg)[$<-$ Maschen \ $b-(n-1)$]], dx: 4mm) + #mannot.annot(<1>, pos:bottom, text(rgb("#404296"))[Zweige ($b$) $->$], dy: -0.5mm) b in {-1, 0, 1} $ - $-1$: Gegen Maschenrichtung - $1$: In Maschenrichtung + #linebreak() + $-1 &: "Gegen Maschenrichtung" \ + 1 &: "In Maschenrichtung"$ #line(length: 100%, stroke: (thickness: 0.2mm)) @@ -476,6 +579,9 @@ KVL in Nullraum: $bold(B) bold(u_b) = bold(0)$ \ KCL in Bildraum: $bold(B^T) bold(i_m) = bold(i_b)$ \ + #line(length: 100%, stroke: (thickness: 0.2mm)) + + *Tellegen'sche Satz* \ $bold(A B^T) = bold(B^T A) = 0$ \ $bold(u_b^T i_b) = 0$ @@ -729,88 +835,6 @@ ) ], - // Linearsierung - #bgBlock(fill: colorEineTore)[ - #subHeading(fill: colorEineTore)[Linearisierung (Ein-Tore)] - - 1. Arbeitspunkt bestimmen \ $"AP" =(u_"AP", i_"AP")$ - - 2. Ableitung $g_cal(F)(u)$/$r_cal(F)(i)$ bilden \ $g'_cal(F)(u)$/$r'_cal(F)(i)$ - - *Stromgesteuert $r(i) = u$* - - Groß-Signal: - - $i_"lin" = g_"lin" (u) = g'_cal(F)(u_"AP")(u-u_"AP") + i_"AP" = \ - g'_cal(F)(u_"AP")u - g'_cal(F)(u_"AP")u_"AP" + i_"AP"$ - - $I_0 = i_"AP" - g'_cal(F)(u_"AP")u_"AP"$ - - $g_0 = g'_cal(F)(u_"AP")u$ - - #block( - height: 20mm, - scale(x: 75%, y: 75%, zap.circuit({ - import zap: * - import cetz.draw: content, line - - isource("I0", (0, 1.5), (0, -1.5), fill: none) - node("n0", (2, 1.5)) - node("n1", (2, -1.5)) - - node("n2", (3.5, 1.5), fill: false) - node("n3", (3.5, -1.5), fill: false) - - resistor("g0", "n1", "n0", fill: none, label: (content: $g_0$, anchor: "south", distance: 0.2)) - wire("I0.in", "n0", "n2") - wire("I0.out", "n1", "n3") - wire("n0", "n2", i: (content: $i_"lin"$, anchor: "south", invert: true)) - wire((0, 0.6), "I0.in", i: (content: $I_0$, anchor: "east", invert: true)) - - set-style(mark: (end: ">", fill: black)) - line((3.5, 1.2), (3.5, -1.2), stroke: 0.5pt) - content((3.9, 0), $u$) - })), - ); - - #linebreak() - - Klein-Signal:$i_"lin" = g_"lin" (u) = g'(u_"AP")u$ - - *Spannungsgesteuert $g(u) = i$* - - $u_"lin" = r_"lin" (i) = r'(i_"AP")(i-i_"AP") + u_"AP"$ - - $U_0 = u_"AP" - r'(i_"AP") i_"AP"$ - - #block( - height: 25mm, - scale(x: 75%, y: 75%, zap.circuit({ - import zap: * - import cetz.draw: content, line - - vsource("U0", (0, 1.5), (0, -1.5), fill: none) - - node("n2", (3.5, 1.5), fill: false) - node("n3", (3.5, -1.5), fill: false) - - resistor("R0", "U0.in", "n2", fill: none, label: (content: $r_0$, anchor: "south", distance: 0.1)) - wire("U0.out", "n3") - - wire((2.49, 1.5), "n2", i: (content: $i$, anchor: "south", invert: true)) - - set-style(mark: (end: ">", fill: black)) - line((3.5, 1.2), (3.5, -1.2), stroke: 0.5pt) - content((3.9, 0), $u_"lin"$) - - line((0.7, 0.5), (0.7, -0.5), stroke: 0.5pt) - content((1.2, 0), $U_0$) - })), - ); - Klein-Signal: $u_"lin" = r_"lin" (i) = r'(i_"AP")i$ - ] - #colbreak() - // Linearsierung (N-Tore) #bgBlock(fill: colorZweiTore)[ #subHeading(fill: colorZweiTore)[Linearisierung (N-Tore)] @@ -905,16 +929,32 @@ columns: (1fr, 0pt, 1fr), row-gutter: 4mm, column-gutter: 2mm, - [ - *Kapazitiv* - ], + [*Kapazitiv*], grid.vline(stroke: 0.75pt), [], + [*Induktivität*], [ - *Induktivität* + $q = c(u) \ u = chi(q)$\ ], + [], [ - $q = c(u) \ chi(q) = u$\ + $Phi = l(i) \ i = lambda(Phi)$ + ], + + [$u,q$ stetig und beschränkt], + [], + [$i,Phi$ stetig und beschränkt], + + grid.hline(stroke: 0.75pt), + [], + [], + [], + + [*Restiv*], + [], + [*Memristiv*], + [ + $i = g(u) \ u = r(i)$\ ], [], [ @@ -927,6 +967,8 @@ [], ) + #line(length: 100%, stroke: (thickness: 0.2mm)) + #align(center, [*Lineare Bauelemente*]) #grid( columns: (1fr, 0pt, 1fr), @@ -1198,7 +1240,7 @@ #subHeading(fill: colorAnalyseVerfahren)[Knotenpotenzial-Analyse Komponetent] #import mannot: * - #let ImageHeight = 3.0cm + #let ImageHeight = 2.5cm #table( columns: (1fr, 1fr), @@ -1222,6 +1264,10 @@ align(center, image("../images/schaltungstheorie/knotenpotenzial/schaltKontenPotenziell1.png", height: ImageHeight, fit: "contain")), align(center, image("../images/schaltungstheorie/knotenpotenzial/schaltKontenPotenziell2.png", height: ImageHeight, fit: "contain")), + + align(center, image("../images/schaltungstheorie/knotenpotenzial/nullator.jpg", height: ImageHeight, fit: "contain")), + + align(center, image("../images/schaltungstheorie/knotenpotenzial/norator.jpg", height: ImageHeight, fit: "contain")), ) ] @@ -1231,6 +1277,7 @@ // Bauelemente #bgBlock(fill: colorEineTore)[ #subHeading(fill: colorEineTore)[Bauelemente] + #table( columns: (1fr, 1fr, 1fr), stroke: none, diff --git a/src/images/schaltungstheorie/knotenpotenzial/norator.jpg b/src/images/schaltungstheorie/knotenpotenzial/norator.jpg new file mode 100644 index 0000000000000000000000000000000000000000..c55a638953dc8a43bda5126055bc2a709ea1e7bc GIT binary patch literal 84825 zcmeFZ2|Sc>}v=y 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00:45:34 +0100 Subject: [PATCH 11/51] added zweitor bildchen --- src/cheatsheets/Schaltungstheorie.typ | 49 +++++++++++++++++++++++++-- 1 file changed, 46 insertions(+), 3 deletions(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index 5fb93f8..e077af4 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -1663,15 +1663,58 @@ columns: (auto, auto, auto, 1fr, 1fr, 1fr), [*Name*], [*Schaltbild*], [*Ersatz-Schaltbild*], [*Eigenschaften*], [*Beschreibung*], [*Knotenspannungs Analyse*], - [Nullor], [], [], [], [$ A = mat(0, 0; 0, 0) $], [], + [Nullor], [], [#scale(x: 50%, y: 50%, zap.circuit({ + import zap: * + import cetz.draw: content, line + joham.nullor("nullor", (0,0)) + }))], [], [$ A = mat(0, 0; 0, 0) $], [], [OpAmp \ lin], [], [], [], [], [], - [OpAmp \ $U_"sat+"$], [], [], [], [], [], + [OpAmp \ $U_"sat+"$\ (4-polig)], [#scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + zap.opamp("opamp", variant: "ieee",(0,0)) + + //- + zap.wire((0,0.45),(-1.3,0.45)) + //+ + zap.wire((0,-0.45),(-1.3,-0.45)) + //out + zap.wire((0,0),(1.3,0)) + // mass + zap.wire((0,0),(0,-1.1)) + + joham.norator("null-op", + (0.2,0),(0.2,0), + scale: .4) + + }))], [], [], [], [], [OpAmp \ $U_"sat-"$], [], [], [], [], [], - [VCVS], [], [], [], [$ H' = mat(0, 0; mu, 0) quad A = mat(1/mu, 0; 0, 0) $], [], + [VCVS], [#scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + //tor1 + wire((-1,0), (-1.75,0)) + node("n2_1", (-1.75, 0)) + + wire((-1.75,2.5),(-1,2.5), i: (content: $i_1$, anchor: "south")) + node("n2_1", (-1.75, 2.5), f:$f$) + + + //tor 2 + zap.dvsource("dv1", + (0,2.5),(0,0), u:$alpha u_1$, i:$i_2$) + + + wire((0,0), (1.3,0)) + node("n2_1", (1.3, 0)) + wire((0,2.5), (1.3,2.5)) + node("n2_2", (1.3,2.5), n:"o-o") + + }))], [], [], [$ H' = mat(0, 0; mu, 0) quad A = mat(1/mu, 0; 0, 0) $], [], [VCCS], [], [], [], [$ G = mat(0, 0; g, 0) quad A = mat(0, -1/g; 0, 0) $], [], From d798587420f77647590da1c4984e8bf19f70fc85 Mon Sep 17 00:00:00 2001 From: alexander Date: Sun, 8 Feb 2026 13:25:46 +0100 Subject: [PATCH 12/51] Started compleating zweitor table --- src/cheatsheets/Schaltungstheorie.typ | 412 +++++++++++++----- .../schaltungstheorie/tumCustomSymbols.typ | 28 +- 2 files changed, 338 insertions(+), 102 deletions(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index b1c7b7d..7de7847 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -266,6 +266,7 @@ $R_i$: Innenwiderstand $R_i = U_0/I_0$ + *Quell Wandlung* #table( columns: (1fr, 1fr), fill: (x, y) => if calc.rem(x, 2) == 1 { tableFillLow } else { tableFillHigh }, @@ -319,7 +320,7 @@ )) wire((0, -1.5), (1.75, -1.5)) - cetz.draw.content((0.62, -0.75), [$R_i$]) + cetz.draw.content((0.9, -0.4), [$R_i$]) cetz.draw.set-style(mark: (end: ">", fill: black, scale: 0.6)) cetz.draw.content((1.95, -0.75), [$u$]) cetz.draw.line((1.75, -0.1), (1.75, -1.4), stroke: 0.5pt) @@ -334,9 +335,18 @@ $i = G_i u - I_0$ ], - align(center, text(size: 7mm, $-->$)), [$G_i = 1/R_i \ I_0 = U_0 G_i$], - [$R_i = 1/G_i \ U_0 = I_0 R_i$], align(center, text(size: 7mm, $<--$)), + table.cell(colspan: 2)[ + #align(center, [*$u"-gesteuert" --> i"-gestuert"$*]) + + $ R_i = 1/G_i quad quad quad U_0 = -I_0 1/G_i $ + ], + + table.cell(colspan: 2, fill: tableFillLow)[ + #align(center, [*$i"-gesteuert" --> u"-gestuert"$*]) + + $ G_i = 1/R_i quad quad quad I_0 = -U_0 1/R_i $ + ], ) ] @@ -513,6 +523,19 @@ #bgBlock(fill: colorAnalyseVerfahren)[ #subHeading(fill: colorAnalyseVerfahren)[Graphen und Matrizen] + $n:$ Knotenanzahle (mit Referenzknoten) + + $b:$ Zweiganzahle + + *Lineare Unabhänige KCL/KVLs* + + Für $2b$ unbekannte ($b$ Ströme + $b$ Spannungen) + + KCLs: $n-1$\ + KVLs: $b-(n-1)$ + + #line(length: 100%, stroke: (thickness: 0.2mm)) + $bold(i_b)$ (oder $bold(i)$): Zweigstrom-Vektor \ $bold(u_b)$ (oder $bold(u)$): Zweigspannungs-Vektor \ $bold(i_m)$ : Maschenstrom-Vektor \ @@ -590,15 +613,41 @@ // Baumkonzept #bgBlock(fill: colorAnalyseVerfahren)[ #subHeading(fill: colorAnalyseVerfahren)[Baumkonzept] - KCLs: $n-1$\ - KVLs: $b-(n-1)$ - Baum einzeichnen (Keine Schleifen!) + + 1. Baum einzeichnen (Keine Schleifen!) \ + Muss alle Knoten umfassen + + 2. $n-1$ KCLs: \ + Superknoten mit NUR einer Baumkante \ + $jMat(A) = mat(jMat(1)_(n-1), jMat(A)_e)$ \ + + + 3. $b - (n-1)$ KVLs: \ + Maschen mit NUR einer NICHT Baumkante \ + $jMat(B) = mat(jMat(B)_t, jMat(1)_(b-(n-1)))$ + + + *Nur bei Baumkonzept:* $B_t = - A_e^T$ + ] // Tablauematrix #bgBlock(fill: colorAnalyseVerfahren)[ #subHeading(fill: colorAnalyseVerfahren)[Tablauematrix] + + Alle Element Gleichungen in Nullraum + KVLs/KCLs in eine Matrix + + KCLs: $jMat(A) jVec(i) = jVec(0)$\ + KVLs: $jMat(B) jVec(u) = jVec(0)$\ + Elementgleichungen: $jMat(N) jVec(u) + jMat(M) jVec(i) = jVec(e)$ + + $ mat( + jMat(B), jMat(0); + jMat(0), jMat(A); + jMat(M), jMat(N) + ) vec(jVec(u), jVec(i)) = vec(jVec(0), jVec(0), jVec(e)) $ + ] // Machenstrom-/Knotenpotenzial-Analyse #bgBlock(fill: colorAnalyseVerfahren)[ @@ -1209,32 +1258,6 @@ #let NodeBlue = rgb("#6156ff") #let NodeYellow = rgb("#ffa856") -#let nodeSymbol(s, center, color, ..style) = { - import cetz.draw: * - ( - ctx => { - // Define a default style - let def-style = (n: 5, inner-radius: .5, radius: 1, stroke: auto, fill: auto) - - // Resolve center to a vector - let (ctx, center) = cetz.coordinate.resolve(ctx, center) - - // Resolve the current style ("star") - let style = cetz.styles.resolve(ctx.style, merge: style.named(), base: def-style, root: "star") - - let paths = ( - cetz.drawable.ellipse(center.at(0), center.at(1), 0, 0.25, 0.25, fill: color, stroke: black), - cetz.drawable.content((center.at(0),center.at(1) + 0.025), 1, 1, none, s), - ) - ( - ctx: ctx, - drawables: cetz.drawable.apply-transform(ctx.transform, paths) - ) - }, - ) -} - - #columns(2)[ #bgBlock(fill: colorAnalyseVerfahren)[ #subHeading(fill: colorAnalyseVerfahren)[Knotenpotenzial-Analyse Komponetent] @@ -1322,10 +1345,10 @@ joham.norator("norator1",(0,0), (-1.75,0)) })) ], - [ + align(horizon+center, [ $u = "bel." \ i = "bel."$ - ], + ]), [ #scale(x: 75%, y: 75%, cetz.canvas({ import cetz.draw: * @@ -1361,11 +1384,10 @@ })) ], - [ - $u = 0$ - - i = bel. - ], + align(horizon+center, [ + $u = 0 \ + i = "bel."$ + ]), [ #scale(x: 75%, y: 75%, cetz.canvas({ import cetz.draw: * @@ -1393,10 +1415,10 @@ wire((1,0), (1.25,0)) })) ], - [ + align(horizon+center, [ $u = "bel." \ i = 0$ - ], + ]), [ #scale(x: 75%, y: 75%, cetz.canvas({ import cetz.draw: * @@ -1420,17 +1442,17 @@ import zap: * import cetz.draw: content, line vsource( + fill: none, "b1", (0, 0), (1.75, 0), ) })) ], - [ - $u = U_0$ - - i = bel. - ], + align(horizon+center, [ + $u = U_0 \ + i = "bel."$ + ]), [ #scale(x: 75%, y: 75%, cetz.canvas({ import cetz.draw: * @@ -1454,17 +1476,17 @@ import zap: * import cetz.draw: content, line isource( + fill: none, "b1", (0, 0), (1.75, 0), ) })) ], - [ - u = bel. - - $i = I_0$ - ], + align(horizon+center, [ + $u = "bel." \ + i = I_0$ + ]), [ #scale(x: 75%, y: 75%, cetz.canvas({ import cetz.draw: * @@ -1565,13 +1587,13 @@ #scale(x: 100%, y: 100%, zap.circuit({ import zap: * import cetz.draw: content, line - diode("b1", (0, 0), (1., 0), stroke: black, fill: white) + diode("b1", (0, 0), (1., 0), stroke: black, fill: none) })) ], - [ - $u=0$ falls $i>0$ - $i=0$ falls $u<0$ - ], + align(horizon+center, [ + $u=0 &"falls" i>0 \ + i=0 &"falls" u<0$ + ]), [ /* #scale(x: 50%, y: 50%, @@ -1612,10 +1634,10 @@ })) ], - [ + align(horizon+center, [ $u_D = u_T dot ln((i_D/I_S)+1) \ i_D = I_S dot (e^(u_D/U_T)-1)$ - ], + ]), [ #scale(x: 75%, y: 75%, cetz.canvas({ import cetz.draw: * @@ -1638,7 +1660,7 @@ })) ], align(horizon+center, - $i = I_S*(e^(u_D/U_T)-1)- i_L$ + $i = I_S dot (e^(u_D/U_T)-1)- i_L$ ), [ #scale(x: 75%, y: 75%, cetz.canvas({ @@ -1666,10 +1688,10 @@ zener("b1", (0, 0), (1., 0), stroke: black, fill: black) })) ], - [ + align(horizon+center, [ Durchbruch bei $u=U_Z$ : $u<=U_Z$ stark leitend - ], + ]), [ ], @@ -1702,13 +1724,37 @@ ] // Zwei-Tor Tabelle -#bgBlock(fill: colorZweiTore, width: 100%)[ + +#grid(columns: (2fr, 1fr))[ + #bgBlock(fill: colorZweiTore, width: 100%)[ #subHeading(fill: colorZweiTore)[Zwei-Tor-Übersichts] + + #let opampSymbol = zap.circuit({ + import zap : wire, node + import cetz.draw : line, rect + + joham.ideal-opamp("Op", (0,0), scale: 0.7, invert: true) + + wire("Op.plus", (rel: (-0.25, 0))) + wire("Op.minus", (rel: (-0.25, 0))) + wire("Op.ground", (rel: (0, -0.3))) + wire("Op.out", (rel: (0.2,0))) + + node("a", (to: "Op.plus", rel: (-0.25, 0)), fill: false, label: (content: text($alpha$, fill: rgb("#8b2000")), anchor: "west", distance: 0.05)) + node("b", (to: "Op.minus", rel: (-0.25, 0)), fill: false, label: (content: text($beta$, fill: rgb("#8b2000")), anchor: "west", distance: 0.05)) + node("c", (to: "Op.out", rel: (0.25, 0)), fill: false, label: (content: text($gamma$, fill: rgb("#00318b")), anchor: "east", distance: 0.05)) + node("d", (to: "Op.ground", rel: (0, -0.3)), fill: false, label: (content: text($delta$, fill: rgb("#00318b")), anchor: "south", distance: 0.05)) + + joham.voltage((to: "Op.plus", rel: (-0.25, 0)), (to: "Op.minus", rel: (-0.25, 0)), $u_"in"$) + + joham.voltage((to: "Op.out", rel: (0.25, 0)), (to: "Op.out", rel: (0.25, -0.7)), $u_"out"$, anchor: "west") + }) + #table( fill: (x, y) => if calc.rem(y, 2) == 0 { tableFillHigh } else { tableFillLow }, - columns: (auto, auto, auto, 1fr, 1fr, 1fr), - [*Name*], [*Schaltbild*], [*Ersatz-Schaltbild*], [*Eigenschaften*], [*Beschreibung*], [*Knotenspannungs Analyse*], + columns: (auto, auto, auto, auto, auto), + [*Name*], [*Schaltbild*], [*Ersatz-Schaltbild*], [*Eigenschaften*], [*Beschreibung*], [Nullor], [], [#scale(x: 50%, y: 50%, zap.circuit({ import zap: * @@ -1716,7 +1762,14 @@ joham.nullor("nullor", (0,0)) }))], [], [$ A = mat(0, 0; 0, 0) $], [], - [OpAmp \ lin], [], [], [], [], [], + rect((-0.2,-0.1), (0.7,1.1), + stroke: (paint: rgb("#666666"), dash: "densely-dashed") + ) + })], + [ + - Verlustlos + - Reziprok + ], [$ A = mat(0, 0; 0, 0) $], [OpAmp \ $U_"sat+"$\ (4-polig)], [#scale(x: 100%, y: 100%, zap.circuit({ import zap: * @@ -1738,7 +1791,10 @@ }))], [], [], [], [], - [OpAmp \ $U_"sat-"$], [], [], [], [], [], + node("a", (to: (0, 1), rel: (-0.4, 0)), fill: false, label: (content: text($alpha$, fill: rgb("#8b2000")), anchor: "west", distance: 0.05)) + node("b", (to: (0, 0), rel: (-0.4, 0)), fill: false, label: (content: text($beta$, fill: rgb("#8b2000")), anchor: "west", distance: 0.05)) + node("c", (to: (0.5, 1), rel: (0.4, 0)), fill: false, label: (content: text($gamma$, fill: rgb("#00318b")), anchor: "east", distance: 0.05)) + node("d", (to: (0.6, 0), rel: (0, -0.25)), fill: false, label: (content: text($delta$, fill: rgb("#00318b")), anchor: "east", distance: 0.05)) [VCVS], [#scale(x: 100%, y: 100%, zap.circuit({ import zap: * @@ -1763,31 +1819,197 @@ }))], [], [], [$ H' = mat(0, 0; mu, 0) quad A = mat(1/mu, 0; 0, 0) $], [], - [VCCS], [], [], [], [$ G = mat(0, 0; g, 0) quad A = mat(0, -1/g; 0, 0) $], [], + [OpAmp \ $U_"sat+"$], opampSymbol, [#zap.circuit({ + import zap : wire, vsource, node + import cetz.draw : line, rect - [CCVS], [], [], [], [$ R = mat(0, 0; r, 0) quad A = mat(0, 0; 1/r, 0) $], [], + node("a", (0,1), fill: false, label: (content: text($alpha$, fill: rgb("#8b2000")), anchor: "west", distance: 0.05)) + node("b", (0,0), fill: false, label: (content: text($beta$, fill: rgb("#8b2000")), anchor: "west", distance: 0.05)) - [CCCS], [], [], [], [$ H = mat(0, 0; beta, 0) quad A = mat(0, 0; 0, -1/beta) $], [], + wire((0,1), (0.4, 1)) + wire((0,0), (0.4, 0)) - [Übertrager], [], [], - [], - [$ H = mat(0, ü; -ü, 0) quad + joham.voltage((0.4, 1), (0.4, 0), $u_d$) + joham.voltage((1.3, 1), (1.3, 0), $U_"sat"$, anchor: "west") + + vsource("v", (1,1), (1,0), scale: 0.4, fill: none) + + wire((1,1), (1.3,1)) + wire((1,0), (1.3,0)) + + node("c", (1.3,1), fill: false, label: (content: text($gamma$, fill: rgb("#00318b")), anchor: "east", distance: 0.05)) + node("d", (1.3,0), fill: false, label: (content: text($delta$, fill: rgb("#00318b")), anchor: "east", distance: 0.05)) + })], [], [], + + [OpAmp \ $U_"sat-"$], opampSymbol, [#zap.circuit({ + import zap : wire, vsource, node + import cetz.draw : line, rect + + node("a", (0,1), fill: false, label: (content: text($alpha$, fill: rgb("#8b2000")), anchor: "west", distance: 0.05)) + node("b", (0,0), fill: false, label: (content: text($beta$, fill: rgb("#8b2000")), anchor: "west", distance: 0.05)) + node("c", (1.3,1), fill: false, label: (content: text($gamma$, fill: rgb("#00318b")), anchor: "east", distance: 0.05)) + node("d", (1.3,0), fill: false, label: (content: text($delta$, fill: rgb("#00318b")), anchor: "east", distance: 0.05)) + + wire((0,1), (0.4, 1)) + wire((0,0), (0.4, 0)) + + joham.voltage((0.4, 1), (0.4, 0), $u_d$) + joham.voltage((1.3, 1), (1.3, 0), $- U_"sat"$, anchor: "west") + + vsource("v", (1,1), (1,0), scale: 0.4, fill: none) + + wire((1,1), (1.3,1)) + wire((1,0), (1.3,0)) + + + })], [], [], + + [VCVS], [#zap.circuit({ + import zap : vsource, node, disource, dvsource, wire + import cetz.draw : line, rect, mark, content + + node("A", (0,0), fill: false) + node("B", (0,1), fill: false) + node("C", (0.8,0), fill: false) + node("D", (0.8,1), fill: false) + + joham.voltage((0, 1), (0, 0), $u_"in"$, anchor: "west") + dvsource("S", (0.8,0), (0.8,1), fill: none, scale: 0.4) + + joham.voltage((1.1, 1), (1.1, 0), $u_"out" = mu u_"in"$, anchor: "west") + })], [], [ + - NICHT Verlustlos + - NICHT Reziprok + - Aktiv + - NICHT Symetrisch + ], [$ H' = mat(0, 0; mu, 0) quad A = mat(1/mu, 0; 0, 0) $], + + [VCCS], [#zap.circuit({ + import zap : vsource, node, disource, dvsource, wire + import cetz.draw : line, rect, mark, content + + node("A", (0,0), fill: false) + node("B", (0,1), fill: false) + node("C", (0.8,0), fill: false) + node("D", (0.8,1), fill: false) + + joham.voltage((0, 1), (0, 0), $u_"in"$, anchor: "west") + disource("S", (0.8,0), (0.8,1), fill: none, scale: 0.4) + + line((0.8,0.10), (0.8,0.09), mark: (end: ">", scale: 0.4, fill: black)) + content((0.9, 0.15), $i_"out" = g i_"in"$, anchor: "west") + + })], [], [ + - NICHT Verlustlos + - NICHT Reziprok + - Aktiv + - NICHT Symetrisch + ], [$ G = mat(0, 0; g, 0) quad A = mat(0, -1/g; 0, 0) $], + + [CCVS], [#zap.circuit({ + import zap : vsource, node, disource, dvsource, wire + import cetz.draw : line, rect, mark, content + + node("A", (0,0), fill: false) + node("B", (0,1), fill: false) + node("C", (0.8,0), fill: false) + node("D", (0.8,1), fill: false) + + wire((0,0), (0,1), i: (content: $i_"in"$, invert: true, anchor: "east", distance: 0.1), size: 0.2) + dvsource("S", (0.8,0), (0.8,1), fill: none, scale: 0.4) + + joham.voltage((1.1, 1), (1.1, 0), $u_"out" = r i_"in"$, anchor: "west") + })], [], [ + - NICHT Verlaustlos + - NICHT Reziprok + - Aktiv + - NICHT Symetrisch + ], [$ R = mat(0, 0; r, 0) quad A = mat(0, 0; 1/r, 0) $], + + [CCCS], [#zap.circuit({ + import zap : vsource, node, disource, dvsource, wire + import cetz.draw : line, rect, mark, content + + node("A", (0,0), fill: false) + node("B", (0,1), fill: false) + node("C", (0.8,0), fill: false) + node("D", (0.8,1), fill: false) + + wire((0,0), (0,1), i: (content: $i_"in"$, invert: true, anchor: "east", distance: 0.1), size: 0.2) + disource("S", (0.8,0), (0.8,1), fill: none, scale: 0.4) + + line((0.8,0.15), (0.8,0.1), mark: (end: ">", scale: 0.2, fill: black)) + content((0.9, 0.15), $i_"out" = beta i_"in"$, anchor: "west") + })], [], [ + - NICHT Verlustlos + - NICHT Reziprok + - Aktiv + - NICHT Symetrisch + ], [$ H = mat(0, 0; beta, 0) quad A = mat(0, 0; 0, -1/beta) $], + + [Übertrager], [#zap.circuit({ + import zap : vsource, node, disource, dvsource, wire + import cetz.draw : line, rect, mark, content + + joham.transformer("T", (0,0), scale: 0.35) + + line((-0.6,0.58), (-0.5,0.58), mark: (end: ">", scale: 0.4, fill: black)) + line((0.5,0.58), (0.6,0.58), mark: (start: ">", scale: 0.4, fill: black)) + + content((0.5, 0.8), $i_2$, anchor: "west") + content((-0.65, 0.8), $i_1$, anchor: "west") + joham.voltage((0.9, 0.7), (0.9, -0.7), $u_2$, anchor: "west") + joham.voltage((-0.9, 0.7), (-0.9, -0.7), $u_1$, anchor: "east") + }) + $ i_2 &= - ü i_1 &quad i_1 &= - 1/ü i_2 \ + u_2 &= 1/ü u_1 &quad u_1 &= ü u_2 + $ + ], [], + [ + - Verlustlos + - Reziprok + - Passiv + - Schief-Symetrisch (Symetrisch für $ü = plus.minus 1$) + + ], + [$ H = mat(0, ü; -ü, 0) &quad H' = mat(0, -1/ü; 1/ü, 0) \ - A = mat(ü, 0; 0, 1/ü) quad A' = mat(1/ü, 0; 0, ü) + A = mat(ü, 0; 0, 1/ü) &quad A' = mat(1/ü, 0; 0, ü) \ + + M = mat(1, -ü; 0, 0) &quad N = mat(0, 0; ü, 1) $], - [], + [Gyrator], - [], + [#zap.circuit({ + import zap : * + import cetz.draw : line, rect, mark, content + + joham.gyrator("G", (0, 0), scale: 0.35) + + line((-0.6,0.58), (-0.5,0.58), mark: (end: ">", scale: 0.4, fill: black)) + line((0.5,0.58), (0.6,0.58), mark: (start: ">", scale: 0.4, fill: black)) + + content((0.5, 0.8), $i_2$, anchor: "west") + content((-0.65, 0.8), $i_1$, anchor: "west") + joham.voltage((1, 0.7), (1, -0.7), $u_2$, anchor: "west") + joham.voltage((-1, 0.7), (-1, -0.7), $u_1$, anchor: "east") + + content((-0.7, -0.8), text([Output $cal(F)^d$], fill: rgb("#8b2000"))) + + content((0.8, -0.8), text([Input $cal(F)$], fill: rgb("#00318b"))) + + })], [], [ - - Antireziprok, Antisymetrisch - - Auch Positiv-Immitanz-Inverter + - Verlustlos + - NICHT Reziprok (Antireziprok) + - Nicht Symetrisch (schiefsysmetrisch) + + Der Pfeil zeigt AUF die NORMAL Eintor ], - [$ R = mat(0, -R_d; R_d, 0) quad G = mat(0, G_d; -G_d, 0) \ A = mat(0, R_d; 1/R_d, 0) quad A' = mat(0, -R_d; -1/R_d, 0) - quad + [$ R = mat(0, -R_d; R_d, 0) &quad G = mat(0, G_d; -G_d, 0) \ A = mat(0, R_d; 1/R_d, 0) &quad A' = mat(0, -R_d; -1/R_d, 0) $], - [], [NIK], [], @@ -1797,27 +2019,11 @@ - Antireziprok - Symetrisch für $abs(k) = 1$ ], - [$ H = mat(0, -k; -k, 0) quad H' = mat(0, -1/k; -1/k, 0) \ A = mat(-k, 0; 0, 1/k) quad A'= mat(-1/k, 0; 0, k) $], - [], - - [T-Glied], - [], - [], - [], - [ - - ], - [], - - [$pi$-Glied], - [], - [], - [ - - ], + [$ H = mat(0, -k; -k, 0) quad H' = mat(0, -1/k; -1/k, 0) \ A = mat(-k, 0; 0, 1/k) quad A'= mat(-1/k, 0; 0, k) $] ) ] +] // Knoten Spannungs Analyse // Tor Eigenschaften @@ -1834,8 +2040,9 @@ [*passiv*\ (nimmt Energie auf)\ $not$aktiv], [$forall (u,i) in cal(F): u dot i >= 0$], [ - $jMat(U)^T jMat(I) + jMat(I)^T jMat(U)$\ - $forall vec(jVec(u), jVec(v)) in cal(F) : jVec(u)^T jVec(i) >=0$ + $jMat(U)^T jMat(I) + jMat(I)^T jMat(U) = 0$\ + $forall vec(jVec(u), jVec(v)) in cal(F) : jVec(u)^T jVec(i) >=0 \ + jMat(G) = - jMat(G)^T quad jMat(R) = - jMat(R)^T$ ], [], @@ -1883,13 +2090,16 @@ $jMat(G) = jMat(P) jMat(G) jMat(P), space jMat(R) = jMat(P) jMat(R) jMat(P), quad jMat(P) = mat(0, 1; 1, 0) \ det(H) = 1,$ + Streng Linear $=>$ Umkehrbar + ], [], [*Reziprok*], [Immer Reziprok], [ - $cal(F)$ symetrisch $=> cal(F)$ reziprok + Symetrisch $=>$ Reziprok \ + Streng Linear $=>$ Reziprok $jMat(U)^T jMat(I) - jMat(I)^T jMat(U) = 0 \ jMat(R)^T = jMat(R), quad jMat(G)^T = jMat(G) quad h_21 = -h_12 \ det(jMat(A)) = 1 quad det(jMat(A')) = 1 quad h'_21 = -h'_12$], diff --git a/src/lib/schaltungstheorie/tumCustomSymbols.typ b/src/lib/schaltungstheorie/tumCustomSymbols.typ index 570214f..60a9190 100644 --- a/src/lib/schaltungstheorie/tumCustomSymbols.typ +++ b/src/lib/schaltungstheorie/tumCustomSymbols.typ @@ -259,7 +259,7 @@ let custom-style = ( width: 5 * scale, height: 5 * scale, - length: 0.5 * scale, + length: 0, ) let draw(ctx, position, style) = { @@ -428,3 +428,29 @@ voltage(from, to, anchor: anchor, distance: if anchor in ("east", "north") { -distance } else { distance }, label) } + +#let labeledNode(s, center, color: rgb("#00000000"), scale_t: 1, ..style) = { + + ( + ctx => { + // Define a default style + let def-style = (n: 5, inner-radius: .5, radius: 1, stroke: auto, fill: auto) + + // Resolve center to a vector + let (ctx, center) = cetz.coordinate.resolve(ctx, center) + + // Resolve the current style ("star") + let style = cetz.styles.resolve(ctx.style, merge: style.named(), base: def-style, root: "star") + + let paths = ( + cetz.drawable.ellipse(center.at(0), center.at(1), 0, scale_t*0.15, scale_t*0.15, fill: color, stroke: (paint: black, thickness: scale_t + *0.25mm)), + cetz.drawable.content((center.at(0),center.at(1)+0.03), 1, 1, none, text(size: 7pt * scale_t, s)), + ) + ( + ctx: ctx, + drawables: cetz.drawable.apply-transform(ctx.transform, paths) + ) + }, + ) +} \ No newline at end of file From 29c5d3dfeb3f7b88264fb5ca2bd67455d094a505 Mon Sep 17 00:00:00 2001 From: alexander Date: Sun, 8 Feb 2026 13:32:42 +0100 Subject: [PATCH 13/51] Got stuff working after merg --- src/cheatsheets/Schaltungstheorie.typ | 17 +++++++---------- 1 file changed, 7 insertions(+), 10 deletions(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index 7de7847..0c528f7 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -1757,15 +1757,11 @@ [*Name*], [*Schaltbild*], [*Ersatz-Schaltbild*], [*Eigenschaften*], [*Beschreibung*], [Nullor], [], [#scale(x: 50%, y: 50%, zap.circuit({ - import zap: * - import cetz.draw: content, line - joham.nullor("nullor", (0,0)) - }))], [], [$ A = mat(0, 0; 0, 0) $], [], + import zap: * + import cetz.draw: content, line, rect + joham.nullor("nullor", (0,0)) - rect((-0.2,-0.1), (0.7,1.1), - stroke: (paint: rgb("#666666"), dash: "densely-dashed") - ) - })], + }))], [ - Verlustlos - Reziprok @@ -1789,12 +1785,13 @@ (0.2,0),(0.2,0), scale: .4) - }))], [], [], [], [], + node("a", (to: (0, 1), rel: (-0.4, 0)), fill: false, label: (content: text($alpha$, fill: rgb("#8b2000")), anchor: "west", distance: 0.05)) node("b", (to: (0, 0), rel: (-0.4, 0)), fill: false, label: (content: text($beta$, fill: rgb("#8b2000")), anchor: "west", distance: 0.05)) node("c", (to: (0.5, 1), rel: (0.4, 0)), fill: false, label: (content: text($gamma$, fill: rgb("#00318b")), anchor: "east", distance: 0.05)) node("d", (to: (0.6, 0), rel: (0, -0.25)), fill: false, label: (content: text($delta$, fill: rgb("#00318b")), anchor: "east", distance: 0.05)) + }))], [], [], [], [], [VCVS], [#scale(x: 100%, y: 100%, zap.circuit({ import zap: * @@ -2022,8 +2019,8 @@ [$ H = mat(0, -k; -k, 0) quad H' = mat(0, -1/k; -1/k, 0) \ A = mat(-k, 0; 0, 1/k) quad A'= mat(-1/k, 0; 0, k) $] ) ] - ] + // Knoten Spannungs Analyse // Tor Eigenschaften From 69129c32fdae643378f03c883aeb4a9587532a22 Mon Sep 17 00:00:00 2001 From: alexander Date: Sun, 8 Feb 2026 13:38:42 +0100 Subject: [PATCH 14/51] Cleand Up zweitor Tabel Added All controlled voltage sources --- src/cheatsheets/Schaltungstheorie.typ | 57 ++------------------------- 1 file changed, 4 insertions(+), 53 deletions(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index 0c528f7..e26a114 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -1767,54 +1767,7 @@ - Reziprok ], [$ A = mat(0, 0; 0, 0) $], - [OpAmp \ $U_"sat+"$\ (4-polig)], [#scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - zap.opamp("opamp", variant: "ieee",(0,0)) - - //- - zap.wire((0,0.45),(-1.3,0.45)) - //+ - zap.wire((0,-0.45),(-1.3,-0.45)) - //out - zap.wire((0,0),(1.3,0)) - // mass - zap.wire((0,0),(0,-1.1)) - - joham.norator("null-op", - (0.2,0),(0.2,0), - scale: .4) - - - - node("a", (to: (0, 1), rel: (-0.4, 0)), fill: false, label: (content: text($alpha$, fill: rgb("#8b2000")), anchor: "west", distance: 0.05)) - node("b", (to: (0, 0), rel: (-0.4, 0)), fill: false, label: (content: text($beta$, fill: rgb("#8b2000")), anchor: "west", distance: 0.05)) - node("c", (to: (0.5, 1), rel: (0.4, 0)), fill: false, label: (content: text($gamma$, fill: rgb("#00318b")), anchor: "east", distance: 0.05)) - node("d", (to: (0.6, 0), rel: (0, -0.25)), fill: false, label: (content: text($delta$, fill: rgb("#00318b")), anchor: "east", distance: 0.05)) - }))], [], [], [], [], - - [VCVS], [#scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - //tor1 - wire((-1,0), (-1.75,0)) - node("n2_1", (-1.75, 0)) - - wire((-1.75,2.5),(-1,2.5), i: (content: $i_1$, anchor: "south")) - node("n2_1", (-1.75, 2.5), f:$f$) - - - //tor 2 - zap.dvsource("dv1", - (0,2.5),(0,0), u:$alpha u_1$, i:$i_2$) - - - wire((0,0), (1.3,0)) - node("n2_1", (1.3, 0)) - wire((0,2.5), (1.3,2.5)) - node("n2_2", (1.3,2.5), n:"o-o") - - }))], [], [], [$ H' = mat(0, 0; mu, 0) quad A = mat(1/mu, 0; 0, 0) $], [], + [OpAmp \ $U_"sat+"$\ (4-polig)], opampSymbol, [], [], [], [OpAmp \ $U_"sat+"$], opampSymbol, [#zap.circuit({ import zap : wire, vsource, node @@ -1857,8 +1810,6 @@ wire((1,1), (1.3,1)) wire((1,0), (1.3,0)) - - })], [], [], [VCVS], [#zap.circuit({ @@ -1879,7 +1830,7 @@ - NICHT Reziprok - Aktiv - NICHT Symetrisch - ], [$ H' = mat(0, 0; mu, 0) quad A = mat(1/mu, 0; 0, 0) $], + ], [$ H' = mat(0, 0; mu, 0) quad A = mat(1/mu, 0; 0, 0) $], [VCCS], [#zap.circuit({ import zap : vsource, node, disource, dvsource, wire @@ -1901,7 +1852,7 @@ - NICHT Reziprok - Aktiv - NICHT Symetrisch - ], [$ G = mat(0, 0; g, 0) quad A = mat(0, -1/g; 0, 0) $], + ], [$ G = mat(0, 0; g, 0) quad A = mat(0, -1/g; 0, 0) $], [CCVS], [#zap.circuit({ import zap : vsource, node, disource, dvsource, wire @@ -1921,7 +1872,7 @@ - NICHT Reziprok - Aktiv - NICHT Symetrisch - ], [$ R = mat(0, 0; r, 0) quad A = mat(0, 0; 1/r, 0) $], + ], [$ R = mat(0, 0; r, 0) quad A = mat(0, 0; 1/r, 0) $], [CCCS], [#zap.circuit({ import zap : vsource, node, disource, dvsource, wire From 5f0bd74756d5ba89a758a584105ff658f12191eb Mon Sep 17 00:00:00 2001 From: alexander Date: Sun, 8 Feb 2026 13:41:48 +0100 Subject: [PATCH 15/51] Added NIk Symbol --- src/cheatsheets/Schaltungstheorie.typ | 10 +++++++--- 1 file changed, 7 insertions(+), 3 deletions(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index e26a114..04fa904 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -1765,6 +1765,8 @@ [ - Verlustlos - Reziprok + - Passiv + - Symetrisch ], [$ A = mat(0, 0; 0, 0) $], [OpAmp \ $U_"sat+"$\ (4-polig)], opampSymbol, [], [], [], @@ -1960,7 +1962,9 @@ $], [NIK], - [], + [#zap.circuit({ + joham.zweitor("NIK", (0,0), label: "NIK") + })], [], [ - Aktiv @@ -2038,7 +2042,7 @@ $jMat(G) = jMat(P) jMat(G) jMat(P), space jMat(R) = jMat(P) jMat(R) jMat(P), quad jMat(P) = mat(0, 1; 1, 0) \ det(H) = 1,$ - Streng Linear $=>$ Umkehrbar + Für Eintore: Streng Linear $=>$ Umkehrbar ], [], @@ -2047,7 +2051,7 @@ [Immer Reziprok], [ Symetrisch $=>$ Reziprok \ - Streng Linear $=>$ Reziprok + Für Eintore: Streng Linear $=>$ Reziprok $jMat(U)^T jMat(I) - jMat(I)^T jMat(U) = 0 \ jMat(R)^T = jMat(R), quad jMat(G)^T = jMat(G) quad h_21 = -h_12 \ det(jMat(A)) = 1 quad det(jMat(A')) = 1 quad h'_21 = -h'_12$], From 4bca75043f9f30d1c059b5b3c87414b81d7a458c Mon Sep 17 00:00:00 2001 From: levi Date: Sun, 8 Feb 2026 14:42:52 +0100 Subject: [PATCH 16/51] =?UTF-8?q?kleine=20=C3=A4nderungen?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- src/cheatsheets/Schaltungstheorie.typ | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index b1c7b7d..4308d8e 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -1569,8 +1569,9 @@ })) ], [ - $u=0$ falls $i>0$ - $i=0$ falls $u<0$ + + $i=0$ falls $u<0$\ + $i>=0$. falls $u=0$ ], [ /* From 5b497eb4ac30b84c722d97963b4fdff72d4bde41 Mon Sep 17 00:00:00 2001 From: alexander Date: Sun, 8 Feb 2026 18:03:30 +0100 Subject: [PATCH 17/51] misc changes --- src/cheatsheets/Schaltungstheorie.typ | 334 +++++++++++++++++++++++--- src/lib/common_rewrite.typ | 6 +- 2 files changed, 299 insertions(+), 41 deletions(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index 04fa904..0f14550 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -419,6 +419,54 @@ ] */ + // Dual Wandlung + #bgBlock(fill: colorAllgemein)[ + #subHeading(fill: colorAllgemein)[Dual Wandlung] + Stumpfe Ersetzung mit: + + #table( + columns: (1fr, 1fr), + fill: (x, y) => if calc.rem(y, 2) == 0 { tableFillHigh } else { tableFillLow }, + + $ u --> R_d i^d $, + $ i --> u^d / R_d $, + $ Phi --> R_d q^d $, + $ q --> Phi / R_d $, + + $ R --> G^d = R / R_d^2 $, + $ G --> R^d = R_d^2 G $, + + $C --> L^d = R_d^2 C$, + $L --> C^d = L / R_d^2$, + + $"KS" --> "LL"$, $"LL" -> "KS"$, + + $"Parallel" --> "Seriell"$, + $"Seriell" --> "Parallel"$, + + table.cell(colspan: 2)[ + *Dualwandlung: Steurende & Ausgangs Größe* + $ + "VCVS": u_"out" = mu dot u_"in" &--> i_"out" R_d = mu dot i_"in" R_d \ + "VCCS": u_"out" = g dot i_"in" &--> \ + "CCVS": u_"out" = r dot i_"in" &--> \ + "CCCS": i_"out" = beta dot i_"in" &--> \ + $ + ], + + table.cell(colspan: 2)[ + *Dualwandlung: Nur Ausgangs Größe* + $ + "VCVS": u_"out" = mu dot u_"in" &--> \ + "VCCS": u_"out" = g dot i_"in" &--> \ + "CCVS": u_"out" = r dot i_"in" &--> \ + "CCCS": i_"out" = beta dot i_"in" &--> \ + $ + ], + + table.cell(colspan: 2)[$ (u, i) in cal(F) --> (u_d, i_d) in cal(F) = (R_d i, 1/R_d u) $] + ) + ] // Linearsierung #bgBlock(fill: colorEineTore)[ @@ -517,8 +565,6 @@ *Klein-Signal* $quad u_"lin" = r_"lin" (i) = r'(i_"AP")i$ ] - - #colbreak() // Graphen und Matrizen #bgBlock(fill: colorAnalyseVerfahren)[ #subHeading(fill: colorAnalyseVerfahren)[Graphen und Matrizen] @@ -594,6 +640,7 @@ #line(length: 100%, stroke: (thickness: 0.2mm)) + #colbreak() *KCL und KVL* \ KCL in Nullraum: $bold(A) bold(i_b) = bold(0)$ \ @@ -634,29 +681,82 @@ // Tablauematrix #bgBlock(fill: colorAnalyseVerfahren)[ - #subHeading(fill: colorAnalyseVerfahren)[Tablauematrix] + #subHeading(fill: colorAnalyseVerfahren)[Allgemeine Analyse Verfahren] + + *Tableaugleichung* Alle Element Gleichungen in Nullraum + KVLs/KCLs in eine Matrix - KCLs: $jMat(A) jVec(i) = jVec(0)$\ - KVLs: $jMat(B) jVec(u) = jVec(0)$\ - Elementgleichungen: $jMat(N) jVec(u) + jMat(M) jVec(i) = jVec(e)$ + KCLs in Nullraum: $jMat(A) jVec(i)_b = jVec(0)$\ + KVLs in Nullraum: $jMat(B) jVec(u)_b = jVec(0)$\ + Elementgleichungen: $jMat(N) jVec(u)_b + jMat(M) jVec(i)_b = jVec(e)$ - $ mat( + $ mannot.mark(mat( jMat(B), jMat(0); jMat(0), jMat(A); jMat(M), jMat(N) - ) vec(jVec(u), jVec(i)) = vec(jVec(0), jVec(0), jVec(e)) $ + ), tag: #<1>) vec(jVec(u)_b, jVec(i)_b) = vec(jVec(0), jVec(0), jVec(e)) - ] - // Machenstrom-/Knotenpotenzial-Analyse - #bgBlock(fill: colorAnalyseVerfahren)[ - #subHeading(fill: colorAnalyseVerfahren)[Machenstrom-/Knotenpotenzial-Analyse] + #mannot.annot(<1>, text($b - (n-1) space$, rgb("#00318b")), pos: left, dy: -2.8mm, dx: 1mm) + #mannot.annot(<1>, text($n-1 space$, rgb("#00318b")), pos: left, dy: 0mm, dx: 1mm) + #mannot.annot(<1>, text($b space$, rgb("#00318b")), pos: left, dy: 2.8mm, dx: 1mm) + #mannot.annot(<1>, text($2b$, rgb("#00318b")), pos: bottom, dy: -0.5mm) + $ + + #line(stroke: (thickness: 0.2mm), length: 100%) + + *Knotenspannungs-Analyse* + + KVL in Bildraum: $jVec(u)_b = jMat(A)^T jVec(u)_k$\ + KCLs in Nullraum: $jMat(A) jVec(i)_b = jVec(0)$\ + Elementgleichungen: $jMat(N) jVec(u)_b + jMat(M) jVec(i)_b = jVec(e)$ + + $ + mannot.mark(mat( + -jMat(A)^T, jMat(1), jMat(0); + jMat(0), jMat(0), jMat(A); + jMat(0), jMat(M), jMat(N) + ), tag: #<1>) vec(jVec(u)_k, jVec(u)_b, jVec(i)_b) = vec(jVec(0), jVec(0), jVec(e)) + + #mannot.annot(<1>, text($b space$, rgb("#00318b")), pos: left, dy: -2.8mm, dx: 1mm) + #mannot.annot(<1>, text($n-1 space$, rgb("#00318b")), pos: left, dy: 0mm, dx: 1mm) + #mannot.annot(<1>, text($b space$, rgb("#00318b")), pos: left, dy: 2.8mm, dx: 1mm) + #mannot.annot(<1>, text($2b + (n-1)$, rgb("#00318b")), pos: bottom, dy: -0.5mm) + $ + + #line(stroke: (thickness: 0.2mm), length: 100%) + + *Maschenstrom-Analyse* + + Nur für Planare Schaltungen + + KCL in Bildraum: $jVec(i)_b = jMat(B)^T jVec(i)_m$\ + KCLs in Nullraum: $jMat(B) jVec(u)_b = jVec(0)$\ + Elementgleichungen: $jMat(N) jVec(u)_b + jMat(M) jVec(i)_b = jVec(e)$ + + $ + mannot.mark(mat( + jMat(B), jMat(0), jMat(0); + jMat(0), jMat(1), -jMat(B)^T; + jMat(M), jMat(N), jMat(0) + ), tag: #<1>) vec(jVec(u)_b, jVec(i)_b, jVec(i)_m) = vec(jVec(0), jVec(0), jVec(e)) + + #mannot.annot(<1>, text($b - (n-1) space$, rgb("#00318b")), pos: left, dy: -2.8mm, dx: 1mm) + #mannot.annot(<1>, text($b space$, rgb("#00318b")), pos: left, dy: 0mm, dx: 1mm) + #mannot.annot(<1>, text($b space$, rgb("#00318b")), pos: left, dy: 2.8mm, dx: 1mm) + #mannot.annot(<1>, text($3b - (n-1)$, rgb("#00318b")), pos: bottom, dy: -0.5mm) + $ + + #line(stroke: (thickness: 0.2mm), length: 100%) + + Nicht Lineare Gleichungen: $underline(f)'(jVec(u), jVec(i)) = 0$ ] - // Reduziert Knotenpotenzial + // Netwon Rephson #bgBlock(fill: colorAnalyseVerfahren)[ - #subHeading(fill: colorAnalyseVerfahren)[Reduzierte Knotenpotenzial-Analyse] + #subHeading(fill: colorAnalyseVerfahren)[Netwen-Raphson] + + ] // ZweiTor Beschreibungen @@ -885,15 +985,11 @@ ], // Linearsierung (N-Tore) - #bgBlock(fill: colorZweiTore)[ - #subHeading(fill: colorZweiTore)[Linearisierung (N-Tore)] + #bgBlock(fill: colorAnalyseVerfahren)[ + #subHeading(fill: colorAnalyseVerfahren)[Linearisierung (N-Tore)] - 1. Arbeitspunk bestimmen $vec(jVec(u)_"AP", jVec(i)_"AP") hat(=) vec(jVec(x)_"AP", jVec(y)_"AP")$ - - $f_1(x_1, x_2, ... x_n) &= y_1\ - f_2(x_1, x_2, ... x_n) &= y_2\ - &dots.v \ - f_n (x_1, x_2, ... x_n) &= y_n$ + 1. Arbeitspunk bestimmen/schätzen/ist gegeben \ + $vec(jVec(u)_"AP", jVec(i)_"AP") hat(=) vec(jVec(x)_"AP", jVec(y)_"AP")$ $bold(f)(jVec(x))=jVec(y)$ @@ -922,10 +1018,29 @@ // Netwen-Raphson N-Tore #bgBlock(fill: colorZweiTore)[ #subHeading(fill: colorZweiTore)[Newton-Raphson (N-Tore)] - Nicht lineare Beschreibung in Nullraum/Impliziter Darstellung: - $f(jVec(x)) = jVec(0)$\ + Nicht lineare Beschreibung in Nullraum/Implizit Darstellung: + $jVec(f)'(jVec(x)) = jVec(0)$\ - $jVec(x)_(n+1) = jVec(x)_n - (jMat(J)|_(jVec(x)_"AP"))^(-1) f(jVec(x))$ + + 0. Jakobi Matrix $jMat(J)(x^((k)))$ aufstellen (ableiten) + + Schrit $n+1$ Berechnen: + + 1. Jacobi Matrix $jMat(J)(x^((n)))$ ausrechnen + + 2. Linearisiertes Gleichungs System aufstellen: \ + $M_"lin"^((n)) jVec(u)^((n)) + N_"lin"^((n)) jVec(i)^((n))$ aus $jMat(J)(x^((n)))$ rauslesen + + $jVec(e)_"lin" = jMat(J)(x^((n))) dot x^((n)) - jVec(f)(x^((n)))$ + + $n$te-Linearisierte Elementgleichungen: \ + $M_"lin"^((n)) jVec(u)^((n)) + N_"lin"^((n)) jVec(i)^((n)) = jVec(e)^((n))_"lin"$ + + Tablaue: $jMat(T)^((n)) jVec(x)^((n + 1)) = jVec(e)^((n))$ \ + + 3. Gleichungsystem lösen: $jVec(x)^((n+1))$ + + 4. Fehler $epsilon$ berechnen ] // Reaktive Elemeten @@ -940,12 +1055,16 @@ row-gutter: 10mm, column-gutter: 2mm, [ + *Kapazitiv* + $[i(t)] = unit("A")$\ $[q(t)] = unit("A s") = unit("C")$\ ], grid.vline(stroke: 0.75pt), [], [ + *Induktiv* + $[u(t)] = unit("V")$ \ $[Phi(t)] = unit("V s") = unit("W b")$ \ ], @@ -965,7 +1084,11 @@ ], ) - $W(t_1, t_2) = integral_(t_1)^(t_2) P(tau) d tau = integral_(t_1)^(t_2) u(tau) i(tau) d tau$ + #linebreak() + + $P(t) = u(t) i(t)$ + + $W(t_1, t_2) = integral_(t_1)^(t_2) P(tau) d tau$ $W(t_1, t_2) > 0$: Nimmt Energie auf\ $W(t_1, t_2) = 0$: Verlustlos\ @@ -981,13 +1104,17 @@ [*Kapazitiv*], grid.vline(stroke: 0.75pt), [], - [*Induktivität*], + [*Induktiv*], [ $q = c(u) \ u = chi(q)$\ + + $W(t_1, t_2), integral_(q_1 = q(t_1))^(q_2 = q(t_2)) chi(q) d q$ ], [], [ - $Phi = l(i) \ i = lambda(Phi)$ + $Phi = l(i) \ i = lambda(Phi)$ \ + + $W(t_1, t_2), integral_(Phi_1 = Phi(t_1))^(Phi_2 = Phi(t_2)) lambda(Phi) d Phi$ ], [$u,q$ stetig und beschränkt], @@ -1080,7 +1207,7 @@ #subHeading(fill: colorComplexAC)[Komplex Wechselstrom Rechnnung] Im Eingeschwungenem Zustand - $u(t) =U_m "Re"{e^(j omega t + phi)}$ + $u(t) = "Re"{U_m e^(j omega t + phi)}$ $u(t) = U_m cos(omega t + alpha)$ \ $i(t) = I_m cos(omega t + beta)$ @@ -1239,7 +1366,16 @@ #ComplexNumbersSection(i: $j$) + *Trigonometire* + #grid( + columns: (auto, auto), + column-gutter: 2mm, + row-gutter: 3mm, + $cos(x) = cos(-x)$, $sin(-x) = -sin(x)$, $cos(x)^2 + sin(x)^2 = 1$, $cos(x) = sin(x + pi/2)$, $sin(x) = cos(x - pi/2)$, $$, + grid.cell(colspan: 2, $cos(x + y) = cos(x)cos(y) - sin(x)sin(y)$), + grid.cell(colspan: 2, $sin(x + y) = sin(x)cos(y) + cos(x)sin(y)$) + ) ] // SinTable @@ -1260,11 +1396,40 @@ #columns(2)[ #bgBlock(fill: colorAnalyseVerfahren)[ - #subHeading(fill: colorAnalyseVerfahren)[Knotenpotenzial-Analyse Komponetent] + #subHeading(fill: colorAnalyseVerfahren)[Reduzierte Knotenpotenzial-Analyse Komponetent] #import mannot: * #let ImageHeight = 2.5cm + Reduzierte Knotenpotenzial-Analyse: $jMat(G_k) = jVec(u)_k = jVec(i)_q$ + + *Cramersche Regel:* $u_(k i) = (det jMat(G)_(k i))/(det jMat(G)_k)$ ($jMat(G)_(k i)$ entshet aus $G_k$ durch ersetzen der $i$-ten Splate mit $jVec(i)_q$) + + #table( + grid( + columns: 3, + zap.circuit({ + import zap : * + + vsource("V", (0,0), (0,1.5), scale: 0.4, fill: none) + joham.voltage((-0.3,1), (-0.3,0), $U_0$) + resistor("G", (0,1.5), (1,1.5), scale: 0.4, fill: none) + wire("V.in", (1,0)) + }), + align(center+horizon, $==>$), + zap.circuit({ + import zap : * + + isource("V", (0,0), (0,1.5), scale: 0.4, fill: none, i: (content: $G U_0 space $, invert: false, distance: 0.2, anchor: "east")) + + resistor("G", (0,1.5), (1,1.5), scale: 0.4, fill: none) + wire("V.in", (1,0)) + }) + ), + + + ) + #table( columns: (1fr, 1fr), fill: (x, y) => if calc.rem(y, 2) == 0 { tableFillHigh } else { tableFillLow }, @@ -1725,7 +1890,7 @@ // Zwei-Tor Tabelle -#grid(columns: (2fr, 1fr))[ +#grid(columns: (1fr))[ #bgBlock(fill: colorZweiTore, width: 100%)[ #subHeading(fill: colorZweiTore)[Zwei-Tor-Übersichts] @@ -1748,7 +1913,7 @@ joham.voltage((to: "Op.plus", rel: (-0.25, 0)), (to: "Op.minus", rel: (-0.25, 0)), $u_"in"$) - joham.voltage((to: "Op.out", rel: (0.25, 0)), (to: "Op.out", rel: (0.25, -0.7)), $u_"out"$, anchor: "west") + joham.voltage((to: "Op.out", rel: (0.25, 0)), (to: "Op.out", rel: (0.25, -0.7)), $u_"out"$, anchor: "west") }) #table( @@ -1914,7 +2079,25 @@ $ i_2 &= - ü i_1 &quad i_1 &= - 1/ü i_2 \ u_2 &= 1/ü u_1 &quad u_1 &= ü u_2 $ - ], [], + ], [ + #align(horizon+center, zap.circuit({ + import zap : * + import cetz.draw : line, rect, mark, content + + joham.gyrator("G1", (0,0), scale: 0.4, constant: $G_d$) + joham.gyrator("G2", (1.6,0), scale: 0.4, constant: $ü G_d$) + joham.ground("G", (0.8, -0.67)) + + node("N1", "G1.12", fill: false, label: (content: $beta$, distance: 0.1)) + node("N1", "G1.11", fill: false, label: (content: $alpha$, distance: 0.1)) + node("N1", "G2.22", fill: false, label: (content: $delta$, distance: 0.1)) + node("N1", "G2.21", fill: false, label: (content: $gamma$, distance: 0.1)) + + node("N1", (0.8, 0.67), label: (content: $epsilon$, distance: 0.1)) + node("N1", (0.8, -0.67)) + + })) + ], [ - Verlustlos - Reziprok @@ -1948,8 +2131,11 @@ content((-0.7, -0.8), text([Output $cal(F)^d$], fill: rgb("#8b2000"))) content((0.8, -0.8), text([Input $cal(F)$], fill: rgb("#00318b"))) - - })], + }) + $ u_1 = - R_d i_2 &quad i_1 = 1/R_d u_2 \ + u_2 = R_d i_1 &quad u_2 = - 1/R_d u_1 + $ + ], [], [ - Verlustlos @@ -1958,14 +2144,77 @@ Der Pfeil zeigt AUF die NORMAL Eintor ], - [$ R = mat(0, -R_d; R_d, 0) &quad G = mat(0, G_d; -G_d, 0) \ A = mat(0, R_d; 1/R_d, 0) &quad A' = mat(0, -R_d; -1/R_d, 0) + [$ R = mat(0, -R_d; R_d, 0) &quad G = mat(0, G_d; -G_d, 0) \ + A = mat(0, R_d; 1/R_d, 0) &quad A' = mat(0, -R_d; -1/R_d, 0) \ + R_d = 1/G_d + $], [NIK], [#zap.circuit({ joham.zweitor("NIK", (0,0), label: "NIK") })], - [], + [#grid( + columns: (auto, auto), + column-gutter: -3mm, + align(center+horizon, scale(75%, zap.circuit({ + import zap : * + import cetz.draw : line, rect, mark, content + + node("A", (-2, 0), fill: false) + node("B", (2, 0), fill: false) + node("C", (-2, 1.5), fill: false) + node("D", (2, 1.5), fill: false) + + wire("A", "B") + + joham.norator("Q1", (-1.5, 2), (1.5, 2), scale: 0.5) + node("N1", (-1.5,1.5)) + node("N2", (0,1.5)) + node("N3", (1.5,1.5)) + resistor("R1", "N1", "N2", scale: 0.5, fill: none, label: (content: $R$, anchor: "south", distance: 1mm)) + resistor("R2", "N2", "N3", scale: 0.5, fill: none, label: (content: $R$, anchor: "south", distance: 1mm)) + wire("N1", "Q1.in") + wire("N3", "Q1.out") + wire("N1", "C", i: (content: $i_1$, invert: true)) + wire("N3", "D", i: (content: $i_2$, invert: true)) + joham.nullator("Q0", "N2", n:"*-*", (0,0), scale: 0.5) + + joham.voltage("C", "A", $u_1$) + joham.voltage("D", "B", $u_2$) + + content((0,-0.4), $k = +1$, anchor: "south") + }))), + align(center+horizon, scale(75%, zap.circuit({ + import zap : * + import cetz.draw : line, rect, mark, content + + node("A", (-2, 0), fill: false) + node("B", (2, 0), fill: false) + node("C", (-2, 1.5), fill: false) + node("D", (2, 1.5), fill: false) + + wire("A", "B") + + joham.nullator("Q1", (-1.5, 2), (1.5, 2), scale: 0.5) + node("N1", (-1.5,1.5)) + node("N2", (0,1.5)) + node("N3", (1.5,1.5)) + resistor("R1", "N1", "N2", scale: 0.5, fill: none, label: (content: $R$, anchor: "south", distance: 1mm)) + resistor("R2", "N2", "N3", scale: 0.5, fill: none, label: (content: $R$, anchor: "south", distance: 1mm)) + wire("N1", "Q1.in") + wire("N3", "Q1.out") + wire("N1", "C", i: (content: $i_1$, invert: true)) + wire("N3", "D", i: (content: $i_2$, invert: true)) + joham.norator("Q0", "N2", n:"*-*", (0,0), scale: 0.5) + + joham.voltage("C", "A", $u_1$) + joham.voltage("D", "B", $u_2$) + + content((0,-0.4), $k = -1$, anchor: "south") + })))) + + ], [ - Aktiv - Antireziprok @@ -1973,7 +2222,7 @@ ], [$ H = mat(0, -k; -k, 0) quad H' = mat(0, -1/k; -1/k, 0) \ A = mat(-k, 0; 0, 1/k) quad A'= mat(-1/k, 0; 0, k) $] ) -] + ] ] // Knoten Spannungs Analyse @@ -2005,12 +2254,17 @@ Kennline nur $u\/i$-Achsen ], [$forall vec(jVec(u), jVec(v)) in cal(F) : jVec(u)^T jVec(i) = 0$], + grid(columns: (auto, auto), + column-gutter: 5mm, [ $u\/q$-Plot: Wenn keine Schleifen \ - $i\/Phi$-Plot: Wenn keine Schleifen \ + $i\/Phi$-Plot: Wenn keine Schleifen + ], [ $u\/i$-Plot: Wenn Auf Achse \ $Phi\/q$-Plot: Wenn auf Achse \ - ], + ], [ + + ]), [*linear*], [Kennline ist Gerade], diff --git a/src/lib/common_rewrite.typ b/src/lib/common_rewrite.typ index a7b73d7..81ab6d3 100644 --- a/src/lib/common_rewrite.typ +++ b/src/lib/common_rewrite.typ @@ -69,7 +69,11 @@ $z^* = a - #i b = r e^(-#i phi)$ Konjungiert Erweitern:\ - $(a + b #i)/(c + d #i) = ((a + b #i)(c - d #i))/(c^2 + d² )$ + #grid(columns: (1fr, 1fr), + $(a + b #i)/(c + d #i) = ((a + b #i)(c - d #i))/(c^2 + d² )$, + $1/(a + j b) = (a - j b)/(a^2 + b^2)$ + ) + $r = abs(z) quad phi = cases( + arccos(a/r) space : space a >= 0, From 1b8153a20c88a4077a992f5601055fabf81fceb1 Mon Sep 17 00:00:00 2001 From: levi Date: Sun, 8 Feb 2026 18:10:48 +0100 Subject: [PATCH 18/51] changes diode --- src/cheatsheets/Schaltungstheorie.typ | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index 04fa904..4aa5ed1 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -1591,8 +1591,8 @@ })) ], align(horizon+center, [ - $u=0 &"falls" i>0 \ - i=0 &"falls" u<0$ + $i=0$ falls $u<0$\ + $i>=0$. falls $u=0$ ]), [ /* From ea4c9aaa64e56a9ba63f9fe4787f82478726a72b Mon Sep 17 00:00:00 2001 From: alexander Date: Sun, 8 Feb 2026 19:28:09 +0100 Subject: [PATCH 19/51] =?UTF-8?q?Added=20gestuerte=20Quellen=20f=C3=BCr=20?= =?UTF-8?q?Knotenpotenzial=20Analyse?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- src/cheatsheets/Schaltungstheorie.typ | 208 +++++++++++++++++++++++++- 1 file changed, 203 insertions(+), 5 deletions(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index e480e35..9a23648 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -1406,29 +1406,227 @@ *Cramersche Regel:* $u_(k i) = (det jMat(G)_(k i))/(det jMat(G)_k)$ ($jMat(G)_(k i)$ entshet aus $G_k$ durch ersetzen der $i$-ten Splate mit $jVec(i)_q$) #table( + columns: (1fr, 1fr), + fill: (x, y) => if calc.rem(y, 2) == 0 { tableFillHigh } else { tableFillLow }, + grid( columns: 3, + column-gutter: 5mm, + row-gutter: 3mm, zap.circuit({ import zap : * vsource("V", (0,0), (0,1.5), scale: 0.4, fill: none) joham.voltage((-0.3,1), (-0.3,0), $U_0$) - resistor("G", (0,1.5), (1,1.5), scale: 0.4, fill: none) + resistor("G", (0,1.5), (1,1.5), scale: 0.4, fill: none, label: (content: $G$, distance: 0.6mm, anchor: "south")) wire("V.in", (1,0)) }), align(center+horizon, $==>$), zap.circuit({ import zap : * - isource("V", (0,0), (0,1.5), scale: 0.4, fill: none, i: (content: $G U_0 space $, invert: false, distance: 0.2, anchor: "east")) + isource("V", (0,0), (0,1.5), scale: 0.4, fill: none, i: (content: $G U_0 space$, invert: false, distance: 0.2, anchor: "east")) - resistor("G", (0,1.5), (1,1.5), scale: 0.4, fill: none) - wire("V.in", (1,0)) - }) + resistor("G", (1,0), (1,1.5), n: "*-*", scale: 0.4, fill: none, label: (content: $G$, distance: 0.6mm)) + wire("V.in", (1.5,0)) + wire("V.out", (1.5,1.5)) + }), ), + grid( + columns: 3, + column-gutter: 5mm, + row-gutter: 3mm, + zap.circuit({ + import zap : * + + vsource("V", (0,0), (0,1.5), scale: 0.4, fill: none) + joham.voltage((-0.3,1), (-0.3,0), $U_0$) + + wire("V.in", (1,0)) + wire("V.out", (1,1.5)) + }), + align(center+horizon, $==>$), + zap.circuit({ + import zap : * + isource("V", (0,0), (0,1.5), scale: 0.4, fill: none, i: (content: $G U_0 space$, invert: false, distance: 0.2, anchor: "east")) + + resistor("G", (1,0), (1,1.5), n: "*-*", scale: 0.4, fill: none, label: (content: $G$, distance: 0.6mm)) + resistor("-G", (2.3,1.5), (1,1.5), scale: 0.4, fill: none, label: (content: $-G$, distance: 0.6mm)) + wire("V.in", (2.3,0)) + wire("V.out", "G.out") + }), + ), + + grid( + columns: 3, + column-gutter: 5mm, + row-gutter: 3mm, + zap.circuit({ + import zap : * + + vsource("V", (0,0), (0,1.5), scale: 0.4, fill: none) + joham.voltage((-0.3,1), (-0.3,0), $U_0$) + + wire("V.in", (1,0)) + wire("V.out", (1,1.5)) + }), + align(center+horizon, $==>$), + zap.circuit({ + import zap : * + joham.gyrator("G", (0,0), scale: 0.4, constant: $G_d$, invert: true) + joham.ground("GND", "G.12") + node("A", "G.12") + node("B", (-0.75,0.67), label: (content: $alpha$, distance: 0.1)) + isource("V", "G.12", "G.11", scale: 0.4, fill: none, i: (content: $G_d U_0 space$, invert: true, distance: 0.3, anchor: "east")) + }), + ), + + [*Übertrager/NIK* siehe Zweitor-Tabelle], + + scale(90%, grid( + columns: (auto, 0mm, 1fr), + column-gutter: 5mm, + row-gutter: 3mm, + + [ + *VCVS + 1 Knoten* \ + #zap.circuit({ + import zap : vsource, node, disource, dvsource, wire + import cetz.draw : line, rect, mark, content + + node("A", (0,0), fill: false) + node("B", (0,1), fill: false) + node("C", (0.8,0), fill: false) + node("D", (0.8,1), fill: false) + + joham.voltage((0, 1), (0, 0), $u_"in"$, anchor: "west") + dvsource("S", (0.8,0), (0.8,1), fill: none, scale: 0.4) + + joham.voltage((1.1, 1), (1.1, 0), $u_"out"$, anchor: "west") + }) + + $u_"out" = mu u_"in"$ + ], + align(center+horizon, $==>$), + [ + #zap.circuit({ + import zap : vsource, node, disource, dvsource, wire + import cetz.draw : line, rect, mark, content + + joham.gyrator("G0", (3,0), scale: 0.4, invert: true, constant: $G_d$) + + disource("S", "G0.11", "G0.12", scale: 0.4, fill: none, i: (content: $i_"out"$, distance: 0.3, anchor: "west", invert: true)) + node("N4", "G0.11", label: (content: $beta$, distance: 0.1),) + node("N3", "G0.12",) + joham.ground("GND1", "N3") + + node("A", (1, 0.67), fill: false) + node("B", (1, -0.67), fill: false) + joham.voltage((1, 0.7), (1, -0.7), $u_"in"$, anchor: "west") + + }) + $i_"out" = mu G_d u_"in"$ + ], + )), + + scale(90%, grid( + columns: (auto, 0mm, 1fr), + column-gutter: 5mm, + row-gutter: 3mm, + + [ + *CCCS + 1 Knoten* \ + #zap.circuit({ + import zap : vsource, node, disource, dvsource, wire + import cetz.draw : line, rect, mark, content + + node("A", (0,0), fill: false) + node("B", (0,1), fill: false) + node("C", (0.8,0), fill: false) + node("D", (0.8,1), fill: false) + + wire((0,0), (0,1), i: (content: $i_"in"$, invert: true, anchor: "east", distance: 0.1), size: 0.2) + disource("S", (0.8,0), (0.8,1), fill: none, scale: 0.4) + + line((0.8,0.15), (0.8,0.1), mark: (end: ">", scale: 0.2, fill: black)) + content((0.9, 0.15), $i_"out"$, anchor: "west") + }) + $i_"out" = beta i_"in"$ + ], + align(center+horizon, $==>$), + [ + #zap.circuit({ + import zap : vsource, node, disource, dvsource, wire + import cetz.draw : line, rect, mark, content + + joham.gyrator("G1", (0,0), scale: 0.4, constant: $G_d$) + + node("A", (1.8,-0.67)) + node("B", (1.8,0.67)) + + disource("S", "A", "B", scale: 0.4, fill: none, i: (content: $i_"out"$, distance: 0.2, label-distance: -0.4, anchor: "east", invert: true)) + node("N1", "G1.21", label: (content: $alpha$, distance: 0.1),) + node("N2", "G1.22",) + joham.ground("GND1", "N2") + + joham.voltage("G1.21", "G1.22", $u_"in"$) + }) + $i_"out" = beta G_d u_in$ + ], + )), + + table.cell( + align(center+horizon, grid( + columns: (auto, 0mm, auto), + column-gutter: 5mm, + row-gutter: 3mm, + [ + *CCVS + 2 Knoten* \ + #zap.circuit({ + import zap : vsource, node, disource, dvsource, wire + import cetz.draw : line, rect, mark, content + + node("A", (0,0), fill: false) + node("B", (0,1), fill: false) + node("C", (0.8,0), fill: false) + node("D", (0.8,1), fill: false) + + wire((0,0), (0,1), i: (content: $i_"in"$, invert: true, anchor: "east", distance: 0.1), size: 0.2) + dvsource("S", (0.8,0), (0.8,1), fill: none, scale: 0.4) + + joham.voltage((1.1, 1), (1.1, 0), $u_"out"$, anchor: "west") + }) + + $u_"out" = r i_"in"$ + ], + align(center+horizon, $==>$), + [ + #zap.circuit({ + import zap : vsource, node, disource, dvsource, wire + import cetz.draw : line, rect, mark, content + + joham.gyrator("G1", (0,0), scale: 0.4, constant: $G_d$) + joham.gyrator("G0", (3,0), scale: 0.4, invert: true, constant: $G_d$) + + disource("S", "G0.11", "G0.12", scale: 0.4, fill: none, i: (content: $i_"out"$, distance: 0.3, anchor: "west", invert: true)) + node("N1", "G1.21", label: (content: $alpha$, distance: 0.1),) + node("N4", "G0.11", label: (content: $beta$, distance: 0.1),) + node("N2", "G1.22",) + node("N3", "G0.12",) + joham.ground("GND1", "N3") + joham.ground("GND1", "N2") + + joham.voltage("G1.21", "G1.22", $u_"in"$) + }) + $i_"out" = r G_d^2 u_"in"$ + ], + )), + colspan: 2 + ) ) + #table( columns: (1fr, 1fr), From a11e22b7ed03a6190f211cc2caf6dc186772c569 Mon Sep 17 00:00:00 2001 From: alexander Date: Sun, 8 Feb 2026 19:36:15 +0100 Subject: [PATCH 20/51] asd --- src/cheatsheets/Schaltungstheorie.typ | 6 ++---- 1 file changed, 2 insertions(+), 4 deletions(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index 9a23648..49ecd51 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -476,8 +476,6 @@ 2. Ableitung $g_cal(F)(u)$/$r_cal(F)(i)$ bilden \ $g'_cal(F)(u)$/$r'_cal(F)(i)$ - #colbreak() - #line(length: 100%) *Stromgesteuert* $quad r(i) = u$ @@ -521,7 +519,7 @@ #linebreak() - *Klein-Signal* $quad i_"lin" = g_"lin" (u) = g'(u_"AP")u$ + *Klein-Signal* $quad Delta i_"lin" = g_"lin" (Delta u) = g'(u_"AP") Delta u$ #line(length: 100%) @@ -562,7 +560,7 @@ })), ); #linebreak() - *Klein-Signal* $quad u_"lin" = r_"lin" (i) = r'(i_"AP")i$ + *Klein-Signal* $quad Delta u_"lin" = r_"lin" (Delta i) = r'(i_"AP") Delta i$ ] // Graphen und Matrizen From 612b991aed12ae4c350c1b2111402799ec0b23af Mon Sep 17 00:00:00 2001 From: alexander Date: Sun, 8 Feb 2026 21:35:18 +0100 Subject: [PATCH 21/51] did stuff --- src/cheatsheets/Schaltungstheorie.typ | 111 ++++++++++++++++++++++---- 1 file changed, 94 insertions(+), 17 deletions(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index 49ecd51..9f42b7e 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -205,8 +205,62 @@ $i_(cal(F),2) = i_(cal(F),1)$ ], ) + + *Kennline Addition* \ + + #grid( + columns: (1fr, auto, 1fr), + row-gutter: 2mm, + column-gutter: 3mm, + [Parallel-Schaltung], $-->$, [$i$-Richtung], + [Reihe-Schaltung], $-->$, [$u$-Richtung], + + ) ] + #bgBlock(fill: colorAllgemein)[ + #subHeading(fill: colorAllgemein)[Spannungs Teiler/Strom Teiler] + + #table( + columns: (1fr, 1fr), + fill: (x, y) => if calc.rem(x, 2) == 1 { tableFillLow } else { tableFillHigh }, + [*Spannungsteiler*], + [*Stromteiler*], + zap.circuit({ + import zap : * + + node("N1", (0,1.5)) + node("N2", (0,0)) + node("N3", (0,-1.5)) + + resistor("R1", "N1", "N2", label: (content: $R_2$, distance: 0.1), scale: 0.7, fill: none) + resistor("R2", "N2", "N3", label: (content: $R_1$, distance: 0.1), scale: 0.7, fill: none) + + joham.voltage((-0.4, 0), (-0.4, -1.5), $u_"out"$) + joham.voltage((0.8, 1.5), (0.8, -1.5), $u_"ges"$, anchor: "west") + + wire((-0.6, 1.5),(0.8, 1.5)) + wire((-0.6, -1.5),(0.8, -1.5)) + wire((-0.6, 0),(0,0)) + }), + zap.circuit({ + import zap : * + + node("N1", (0,0)) + node("N2", (0,2)) + + resistor("R1", "N1", "N2", label: (content: $R_1$, distance: 0.1), scale: 0.7, fill: none, i: (content: $i_"out"$, anchor: "south", distance: 0.25, invert: true)) + resistor("R2", (1,0), (1,2), label: (content: $R_2$, distance: 0.1), scale: 0.7, fill: none) + + wire((-1, 0), "R2.in") + wire((-1, 2), "R2.out") + wire((-1, 2), "N2", i: (content: $i_"ges"$, distance: 0.1)) + + }), + $ u_"out" = R_1/(R_1 + R_2) $, $ i_"out" = R_2/(R_1 + R_2) i_"ges" $, + $ u_"out" = G_2/(G_1 + G_2) $, $ i_"out" = G_1/(G_1 + G_2) i_"ges" $ + ) + ] // Lineare Quelle #bgBlock(fill: colorEineTore)[ @@ -440,6 +494,7 @@ $L --> C^d = L / R_d^2$, $"KS" --> "LL"$, $"LL" -> "KS"$, + $"Nullator" --> "Nullator"$, $"Norator" -> "Norator"$, $"Parallel" --> "Seriell"$, $"Seriell" --> "Parallel"$, @@ -447,20 +502,10 @@ table.cell(colspan: 2)[ *Dualwandlung: Steurende & Ausgangs Größe* $ - "VCVS": u_"out" = mu dot u_"in" &--> i_"out" R_d = mu dot i_"in" R_d \ - "VCCS": u_"out" = g dot i_"in" &--> \ - "CCVS": u_"out" = r dot i_"in" &--> \ - "CCCS": i_"out" = beta dot i_"in" &--> \ - $ - ], - - table.cell(colspan: 2)[ - *Dualwandlung: Nur Ausgangs Größe* - $ - "VCVS": u_"out" = mu dot u_"in" &--> \ - "VCCS": u_"out" = g dot i_"in" &--> \ - "CCVS": u_"out" = r dot i_"in" &--> \ - "CCCS": i_"out" = beta dot i_"in" &--> \ + "VCVS" &: u_"out" &= mu dot u_"in" &--> i_"out"^d = mu i_"in"^d\ + "VCCS" &: i_"out" &= g dot u_"in" &--> u_"out"^d = g R_d^2 dot i_"in"^d \ + "CCVS" &: u_"out" &= r dot i_"in" &--> i_"out"^d = r/R_d^2 dot u_"in"\ + "CCCS" &: i_"out" &= beta dot i_"in" &--> u_"out"^d = beta u_"in"^d\ $ ], @@ -982,6 +1027,26 @@ ) ], + // KS/LL + #bgBlock(fill: colorZweiTore)[ + #subHeading(fill: colorZweiTore)[Kurzschluss/Leerlauf Methode für Zweitore] + + 1. Was sind die Input-Größen/Output-Größen? \ + $u"-gesteuert:" u = 0 &--> "Kurzschluss (KS)" \ + i"-gesteuert:" i = 0 &--> "Leerlauf (LL)"$ \ + + 2. Steuernde Größe 1 beschalten KS/LL \ + $-->$ BEIDE gesteuerten Größe errechen \ + (2. Spalte der Matrix) + 3. Steuernde Größe 2 beschalten KS/LL \ + $-->$ BEIDE gesteuerten Größe errechen \ + (1. Spalte der Matrix) + + 4. Matrix/Gleichung aufstellen \ + Addition der Beschreibung pro gesteuerter Größe \ + (Superpositions Prinzip) + ] + // Linearsierung (N-Tore) #bgBlock(fill: colorAnalyseVerfahren)[ #subHeading(fill: colorAnalyseVerfahren)[Linearisierung (N-Tore)] @@ -1625,7 +1690,6 @@ ) ) - #table( columns: (1fr, 1fr), fill: (x, y) => if calc.rem(y, 2) == 0 { tableFillHigh } else { tableFillLow }, @@ -2208,7 +2272,7 @@ disource("S", (0.8,0), (0.8,1), fill: none, scale: 0.4) line((0.8,0.10), (0.8,0.09), mark: (end: ">", scale: 0.4, fill: black)) - content((0.9, 0.15), $i_"out" = g i_"in"$, anchor: "west") + content((0.9, 0.15), $i_"out" = g u_"in"$, anchor: "west") })], [], [ - NICHT Verlustlos @@ -2597,7 +2661,6 @@ inset: (bottom: 4mm, top: 4mm), gutter: 0.1mm, fill: (x, y) => if x != 0 and calc.rem(x, 2) == 0 { rgb("#c5c5c5") } else { white }, - [], $bold(R) jVec(i) = jVec(u)$, $bold(G) jVec(u) = jVec(i)$, @@ -2605,5 +2668,19 @@ $bold(H') vec(u_1, i_2) = vec(i_1, u_2)$, $bold(A) vec(u_2, -i_2) = vec(i_1, u_1)$, $bold(A') vec(u_1, -i_1) = vec(i_2, u_2)$, + [], + [Stromge-steuert], + [Spannung-gesteuert], + [Hybrid-beschreibung], + [Inverse-Hybrid], + [Ketten-Beschreibung], + [Inverse-Ketten], + [], + $jVec(r)vec(i_1, i_2) = vec(u_1, u_2)$, + $jVec(g)vec(u_1, u_2) = vec(i_1, i_2)$, + $jVec(h) vec(i_1, u_2) = vec(u_1, i_2)$, + $jVec(h') vec(u_1, i_2) = vec(i_1, u_2)$, + $jVec(a) vec(u_2, -i_2) = vec(i_1, u_1)$, + $jVec(a') vec(u_1, -i_1) = vec(i_2, u_2)$, ) ] From cbd6fa82b7b24170f2ad434ddf3b22c0ceb484a3 Mon Sep 17 00:00:00 2001 From: levi Date: Sun, 8 Feb 2026 23:31:14 +0100 Subject: [PATCH 22/51] more eintoooore --- src/cheatsheets/Schaltungstheorie.typ | 125 ++++++++++++++++++++++---- 1 file changed, 107 insertions(+), 18 deletions(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index e480e35..75d5c42 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -1467,13 +1467,15 @@ #subHeading(fill: colorEineTore)[Bauelemente] #table( - columns: (1fr, 1fr, 1fr), + columns: (1fr, 1fr, 1fr, 1fr), stroke: none, fill: (x, y) => if (calc.rem(y, 2) == 0) { tableFillLow } else { tableFillHigh }, align: center, - table.header([*Zeichen*], [*Gleichungen*], [*Abbildung*]), + table.header( + [*Zeichen*], [*Gleichungen*], [*Abbildung*], [*Eigenschaften*]), table.hline(), + // Nullator [ Nullator @@ -1500,6 +1502,14 @@ }) })) ], + align(left+top)[ + - Verlustlos + - Streng linear + - Linear + - Quellenfrei + - Ungepolt + - Resitiv, Induktiv, Kapazitiv, Memristiv + ], // Norator [ @@ -1531,7 +1541,14 @@ }) })) ], - + align(left+top)[ + - #text("NICHT", red) Verlustlos + - Streng linear + - Linear + - Quellenfrei + - Ungepolt + - Resitiv, Induktiv, Kapazitiv, Memristiv + ], table.hline(), // Kurzschluss @@ -1541,8 +1558,9 @@ import zap: * import cetz.draw: content, line - node("n1", (0, 0)) - node("n2", (1, 0)) + node("n1", (0, 0), fill: false) + node("n2", (1, 0), fill: false) + wire((0,0), (1,0)) wire((-0.25,0), (0,0)) wire((1,0), (1.25,0)) @@ -1566,6 +1584,15 @@ }) })) ], + align(left+top)[ + - Verlustlos + - Streng linear + - Linear + - Quellenfrei + - Ungepolt + - #text("NICHT", red) u-gest. + - i-gest. + ], // Leerlauf [ @@ -1573,8 +1600,8 @@ #scale(x: 100%, y: 100%, zap.circuit({ import zap: * import cetz.draw: content, line - node("n1", (0, 0)) - node("n2", (1, 0)) + node("n1", (0, 0), fill: false) + node("n2", (1, 0), fill: false) wire((-0.25,0), (0,0)) wire((1,0), (1.25,0)) @@ -1597,6 +1624,15 @@ }) })) ], + align(left+top)[ + - Verlustlos + - Streng linear + - Linear + - Quellenfrei + - Ungepolt + - u-gest. + - #text("NICHT", red) i-gest. + ], table.hline(), // Quellen: // @@ -1633,6 +1669,12 @@ content("plot.pt", [$U_0$], anchor: "north-west", padding: .1) })) ], + align(left+top)[ + - Aktiv + - Linear + - Gepolt + - i-gest. + ], // Strom-quelle [ @@ -1667,12 +1709,18 @@ content("plot.pt", [$I_0$], anchor: "south-east", padding: .1) })) ], + align(left+top)[ + - Aktiv + - Linear + - Gepolt + - u-gest. + ], table.hline(), -// Wiederstand +// Ohmscher Wiederstand [ - Wiederstand + Ohm'sche Wiederstand #scale(x: 100%, y: 100%, zap.circuit({ import zap: * import cetz.draw: content, line @@ -1700,6 +1748,15 @@ }) })) ], + align(left+top)[ + - #text("NICHT", red) Verlustlos + - Streng linear + - Linear + - Quellenfrei + - Ungepolt + - u-gest. + - i-gest. + ], // Induktivität [ @@ -1715,12 +1772,26 @@ ) })) ], - [ - + align(center+horizon)[ + $Phi(t) = L i(t)$\ + $u(t) = L (d i(t))/(d t)$ + $E_L (Phi_1) = Phi_1^2/(2L)$\ + $E_L (i_1) = L/2 i_1^2$ ], [ + #scale(x: 75%, y: 75%, cetz.canvas({ + import cetz.draw: * + import cetz-plot: * + let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [$Phi$], y-label: [$i$]) + + plot.plot(axis-style: "school-book", ..opts, name: "plot", { + + plot.add(((-1, -1), (1, 1)), style: (stroke: red)) + }) + })) ], + [], // Kapazität [ @@ -1735,13 +1806,27 @@ ) })) ], - [ - + align(center+horizon)[ + $q(t) = C u(t)$\ + $i(t) = C (d u(t))/(d t)$\ + $E_C (q_1) = q_1^2/(2C)$\ + $E_C (u_1) = C/2 u_1^2$ ], [ + #scale(x: 75%, y: 75%, cetz.canvas({ + import cetz.draw: * + import cetz-plot: * + let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [q]) + + plot.plot(axis-style: "school-book", ..opts, name: "plot", { + + plot.add(((-1, -1), (1, 1)), style: (stroke: red)) + }) + })) ], - + [], + table.hline(), // Dioden :// @@ -1752,7 +1837,8 @@ #scale(x: 100%, y: 100%, zap.circuit({ import zap: * import cetz.draw: content, line - diode("b1", (0, 0), (1., 0), stroke: black, fill: none) + //diode("b1", (0, 0), (1., 0), stroke: black, fill: false) + joham.diode("id_di", (0,0), (1,0)) })) ], align(horizon+center, [ @@ -1787,7 +1873,7 @@ }) })) ], - //table.hline(start: 1, end: 2), + [], // reale/pn Diode [ @@ -1814,6 +1900,7 @@ plot.plot(axis-style: "school-book", ..opts, data, name: "plot") })) ], + [], // Photodiode [ @@ -1843,6 +1930,7 @@ }) })) ], + [], // Zenerdiode [ @@ -1860,6 +1948,7 @@ [ ], + [], // Tunneldiode [ @@ -1876,7 +1965,7 @@ [ ], - + [], ); ] @@ -2279,7 +2368,7 @@ [$(qty("0", "A"), qty("0", "V")) in cal(F)$], [$(qty("0", "A"), qty("0", "V")) in cal(F)$], - [*streng linear*], [linear UND quellenfrei], [linear UND quellenfrei\ Darstellbar: Nur Matrix], [], + [*streng linear*], [linear UND quellenfrei UND ungepolt], [linear UND quellenfrei\ Darstellbar: Nur Matrix], [], [*ungepolt* \ (Punkt sym.)], [$(u,i) in cal(F) <=> (-u, -i) in cal(F)\ From b0cdfdce51b416bb5b7a79603c14dc00376f4e32 Mon Sep 17 00:00:00 2001 From: alexander Date: Mon, 9 Feb 2026 08:59:03 +0100 Subject: [PATCH 23/51] Added helmolz & fixed missing gyrators and beschreibungs umrechnung --- src/cheatsheets/Schaltungstheorie.typ | 77 ++++++++++++++---- .../schaltKnotenPotenziell12.png | Bin 0 -> 82900 bytes .../schaltKontenPotenziell11.png | Bin 0 -> 92278 bytes src/lib/common_rewrite.typ | 3 +- 4 files changed, 61 insertions(+), 19 deletions(-) create mode 100644 src/images/schaltungstheorie/knotenpotenzial/schaltKnotenPotenziell12.png create mode 100644 src/images/schaltungstheorie/knotenpotenzial/schaltKontenPotenziell11.png diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index d785d9d..1d329b8 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -214,8 +214,10 @@ column-gutter: 3mm, [Parallel-Schaltung], $-->$, [$i$-Richtung], [Reihe-Schaltung], $-->$, [$u$-Richtung], - ) + + Bei Idealer Diode: Ruhe Bewahren. \ + Sich vorstellen als hätte die Diode eine endlich Steigung! ] #bgBlock(fill: colorAllgemein)[ @@ -325,7 +327,13 @@ columns: (1fr, 1fr), fill: (x, y) => if calc.rem(x, 2) == 1 { tableFillLow } else { tableFillHigh }, inset: 3mm, - align(center, [*$u$-gesteuert*]), align(center, [*$i$-gesteuert*]), + align(center, [ + *$u$-gesteuert* \ + Helmholz / Thévenin + ]), align(center, [ + *$i$-gesteuert* \ + Mayer / Norton + ]), align( horizon + center, @@ -523,7 +531,7 @@ #line(length: 100%) - *Stromgesteuert* $quad r(i) = u$ + *Stromgesteuert* *Groß-Signal* \ #grid(columns: (1fr, 1fr), @@ -569,7 +577,7 @@ #line(length: 100%) - *Spannungsgesteuert* $quad g(u) = i$ + *Spannungsgesteuert* *Groß-Signal* \ #grid(columns: (1fr, 1fr), @@ -813,32 +821,61 @@ *Linear:* $vec(jVec(u), jVec(i)) = mat(jMat(U); jMat(I))jVec(c) + vec(jVec(u), jVec(i))$ + #line(length: 100%, stroke: (thickness: 0.2mm)) *Implizite/Kern/Nullraum* - $mat(jMat(M), jMat(N)) vec(jVec(u), jVec(i)) = 0$ + $forall (jVec(i), jVec(u))$ wo gilt $jMat(M) jVec(i) + jMat(N) jVec(u) = 0$ + + #line(length: 100%, stroke: (thickness: 0.2mm)) + *Explizit* + $r(u) = i \/ g(u) = i$ - siehe Tabelle + (siehe Tabelle) + + #line(length: 100%, stroke: (thickness: 0.2mm)) *Umrechnung* - #grid( - columns: (auto, 1fr), - column-gutter: 2mm, - row-gutter: 2mm, - $"Nullraum" "Explizit"$, + #table( + columns: (1fr), + fill: (x, y) => if calc.rem(y, 2) == 0 { tableFillHigh } else { tableFillLow }, + [ - $G = I U^(-1)\ R = U I^(-1)$\ + *$"Explizit" -> "Implizit(Nullraum)"$*\ + Umstellen nach Null: \ + $jMat(1) jVec(u) - jMat(R) jVec(i) = jVec(0) quad jMat(1) jVec(i) - jMat(G) jVec(u) = jVec(0)$ \ + $==> jMat(N)jVec(u) + jMat(M)jVec(i) = jMat(0)$ ], - $"Explizit" -> "Nullraum"$, [ - Zwei Messungen einsetzen + *Implizit $->$ Explizit* \ + $jMat(R) = -jMat(M)^(-1) jMat(N) quad jMat(G) = -jMat(N)^(-1) jMat(M)$ \ ], + [ + *Parametrisch $->$ Explizit* \ + $jMat(R) = jMat(U) jMat(I)^(-1) quad jMat(G) = jMat(I) jMat(U)^(-1)$ \ + ], + [ + *Explizit $->$ Parametrisch* \ + Zwei ausgesuchte Punkte $jVec(u) \/ jVec(i)$ einsetzen\ + $-> vec(jVec(u)_1, jVec(i)_1),vec(jVec(u)_2, jVec(i)_2)$ \ - $"Kernraum" -> "Nullraum"$, + In Matrix Eintrag: $mat(jMat(U); jMat(I)) = mat(jVec(u)_1, jVec(u)_2; jVec(i)_1, jVec(i)_2)$ + ], + [ + *Implizit $->$ Parametrisch* \ + + $vec(jMat(U), jMat(I)) = vec(-jMat(M)^(-1) jMat(N), jMat(1)) = vec(jMat(1), -jMat(N)^(-1) jMat(M))$ + ], + [ + *Parametrisch* $->$ *Implizit*\ + Paramterisch $->$ Explizit $->$ Implizit + + $-jMat(I) jMat(U)^(-1) jVec(u) + jMat(1) jVec(i) = 0 quad jMat(1)jVec(u) - jMat(U)jMat(I)^(-1) jVec(i) = 0$ + ] ) ] @@ -1697,9 +1734,9 @@ align(center, image("../images/schaltungstheorie/knotenpotenzial/schaltKontenPotenziell4.png", height: ImageHeight, fit: "contain")), - align(center, image("../images/schaltungstheorie/knotenpotenzial/schaltKontenPotenziell5.png", height: ImageHeight, fit: "contain")), + align(center, image("../images/schaltungstheorie/knotenpotenzial/schaltKnotenPotenziell12.png", height: ImageHeight, fit: "contain")), - align(center, image("../images/schaltungstheorie/knotenpotenzial/schaltKontenPotenziell6.png", height: ImageHeight, fit: "contain")), + align(center, image("../images/schaltungstheorie/knotenpotenzial/schaltKontenPotenziell11.png", height: ImageHeight, fit: "contain")), align(center, image("../images/schaltungstheorie/knotenpotenzial/schaltKontenPotenziell7.png", height: ImageHeight, fit: "contain")), @@ -2231,6 +2268,7 @@ ] ] +#pagebreak() #bgBlock(fill: colorZweiTore, width: 100%)[ #subHeading(fill: colorZweiTore)[OpAmp Schaltungen] @@ -2575,7 +2613,7 @@ ] // Knoten Spannungs Analyse - +#pagebreak() // Tor Eigenschaften #bgBlock(fill: colorEigenschaften, width: 100%)[ #subHeading(fill: colorEigenschaften)[Tor Eigenschaften] @@ -2666,6 +2704,7 @@ ) ] +#pagebreak() #bgBlock(fill: colorZweiTore)[ #set text(size: 10pt) @@ -2773,3 +2812,5 @@ $jVec(a') vec(u_1, -i_1) = vec(i_2, u_2)$, ) ] + +#place(bottom+center, float: true)[#text(rgb("#992893"), size: 60pt, font: "DejaVu Sans")[*DON'T PANIC!*]] \ No newline at end of file diff --git a/src/images/schaltungstheorie/knotenpotenzial/schaltKnotenPotenziell12.png b/src/images/schaltungstheorie/knotenpotenzial/schaltKnotenPotenziell12.png new file mode 100644 index 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zxlbNhMF|`taBdu+r}jHl+32H!!TV)3JCTv4?9E%egxF~1rh8mq_<2wsX>PA6VFf}m zfrd+-3hXV5zqEH4I5{OA#xVS?c=zsR?N0pg+U$$SE&!RJVWrUL;*>nrCHeWkHmSV! zZk2rhYR=K1MnRLhrSvDz?xRJXt4s9FzV`Rc2W3uD&!Srr5Q!_#A7;RTrI88^Gp~37^KsJzJu$7w@lgH8 z`o3|w!m1V2r>CnS5%T^hYICdhD3Q~qmv@*11sg=Jgt6ND~2x|h{a_>Ck*q=tmV*@rTI4Su(cp&{n+#eB!S z-BeldI%8GEnlQq5ph%Z@*F%gc5}po;K9FZH>v)fzNkgJVAKIedXk*AX1z-~fNz2z8$JF8h$8uXu$MO^#a!+Dk={2qP1y zhO>QDIIO!lmF*Z5nADZtU=|a=g0$$$7_}@oCT8a8^4fCIO1ylWN z75;f~>&-u=`k$Yv{Qr0F@KPNAzvu{l{{J8H&+~!5{{Q3p?@9c>w7V9rP~3%&CO2E< RkU23zT0&mDNYudp{{Y>>re^>E literal 0 HcmV?d00001 diff --git a/src/lib/common_rewrite.typ b/src/lib/common_rewrite.typ index 81ab6d3..aed8ba7 100644 --- a/src/lib/common_rewrite.typ +++ b/src/lib/common_rewrite.typ @@ -74,8 +74,9 @@ $1/(a + j b) = (a - j b)/(a^2 + b^2)$ ) + - $r = abs(z) quad phi = cases( + $r = abs(z) = sqrt(a + #i b) = sqrt(z z^*) quad phi = cases( + arccos(a/r) space : space a >= 0, - arccos(a/r) space : space a < 0, )$ From 554c9f7dd8831e6d38caba72e8c662238357e797 Mon Sep 17 00:00:00 2001 From: alexander Date: Mon, 9 Feb 2026 09:03:41 +0100 Subject: [PATCH 24/51] Fixed Nullor --- src/cheatsheets/Schaltungstheorie.typ | 18 +++++++++++++++--- 1 file changed, 15 insertions(+), 3 deletions(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index 1d329b8..d7320ba 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -2308,12 +2308,24 @@ columns: (auto, auto, auto, auto, auto), [*Name*], [*Schaltbild*], [*Ersatz-Schaltbild*], [*Eigenschaften*], [*Beschreibung*], - [Nullor], [], [#scale(x: 50%, y: 50%, zap.circuit({ + [Nullor], [], [#zap.circuit({ import zap: * import cetz.draw: content, line, rect - joham.nullor("nullor", (0,0)) - }))], + joham.nullator("a", (0,0), (0,1.5), scale: 0.5) + joham.norator("b", (0.5,0), (0.5,1.5), scale: 0.5) + + wire("a.in", (rel: (-0.5, 0))) + wire("a.out", (rel: (-0.5, 0))) + wire("b.in", (rel: (0.5, 0))) + wire("b.out", (rel: (0.5, 0))) + + node("N1", (rel: (-0.5, 0), to: "a.in"), fill: false) + node("N2", (rel: (-0.5, 0), to: "a.out"), fill: false) + node("N3", (rel: (0.5, 0), to: "b.in"), fill: false) + node("N4", (rel: (0.5, 0), to: "b.out"), fill: false) + + })], [ - Verlustlos - Reziprok From ba2c96eb5995ade514ef9ae7fc1755b44a7ac019 Mon Sep 17 00:00:00 2001 From: alexander Date: Mon, 9 Feb 2026 09:13:40 +0100 Subject: [PATCH 25/51] Added Dualwandlungs note --- src/cheatsheets/Schaltungstheorie.typ | 74 ++------------------------- 1 file changed, 5 insertions(+), 69 deletions(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index d7320ba..de5630b 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -330,6 +330,8 @@ align(center, [ *$u$-gesteuert* \ Helmholz / Thévenin + + (Strom $-I_0$ wird als $I_0$ geschrieben) ]), align(center, [ *$i$-gesteuert* \ Mayer / Norton @@ -410,77 +412,11 @@ $ G_i = 1/R_i quad quad quad I_0 = -U_0 1/R_i $ ], ) + + Bei Dualwandlung, einfach Ersetzung durchführen ] - /*// Quell Wandlung - #bgBlock(fill: colorEineTore)[ - #subHeading(fill: colorEineTore)[Quelle Wandlung] - - #grid( - columns: (1fr, 1fr), - align: center, - scale(x: 65%, y: 65%, - zap.circuit({ - import zap : * - import cetz.draw : line, content - - vsource("U0", (0, 1.5), (0, -1.5), fill: none) - - node("n2", (3.5,1.5), fill: false) - node("n3", (3.5,-1.5), fill: false) - - resistor("R0", "U0.in", "n2", fill: none, label: (content: $R_i$, anchor: "south", distance: 0.1)) - wire("U0.out", "n3") - - wire((2.49,1.5), "n2", i: (content: $i$, anchor: "south", invert: true)) - - set-style(mark: (end: ">", fill: black)) - line((3.5, 1.2), (3.5, -1.2), stroke: 0.5pt) - content((3.9, 0), $u$) - - line((0.7, 0.5), (0.7, -0.5), stroke: 0.5pt) - content((1.7, 0), $U_0 = I_0 / G_i$) - })), - scale(x: 65%, y: 65%, - zap.circuit({ - import zap : * - import cetz.draw : line, content - - isource("I0", (0, 1.5), (0, -1.5), fill: none) - node("n0", (2,1.5)) - node("n1", (2,-1.5)) - - node("n2", (3.5,1.5), fill: false) - node("n3", (3.5,-1.5), fill: false) - - resistor("g0", "n1", "n0", fill: none, label: (content: $G_i$, anchor: "south", distance: 0.2)) - wire("I0.in", "n0", "n2") - wire("I0.out", "n1", "n3") - wire("n0", "n2", i: (content: $i$, anchor: "south", invert: true)) - wire((0,0.6), "I0.in", i: (content: $I_0 = U_0 / R_i$, anchor: "east", invert: false, distance: 0.2)) - - set-style(mark: (end: ">", fill: black)) - line((3.5, 1.2), (3.5, -1.2), stroke: 0.5pt) - content((3.9, 0), $u$) - })), - [ - $U_0 = I_0 R_i$ - - $R_i=1/G_i$ - - $u = r(i) = R_i i + U_0$ - ], - [ - $I_0 = U_0 G_i$ - - $G_i=1/R_i$ - - $i = g(u) = G_i u + I_0$ - ] - ); - ] - */ - + // Dual Wandlung #bgBlock(fill: colorAllgemein)[ #subHeading(fill: colorAllgemein)[Dual Wandlung] From a050a3b49c9378ebe2d87134cd2cff2be249d9af Mon Sep 17 00:00:00 2001 From: alexander Date: Mon, 9 Feb 2026 09:17:48 +0100 Subject: [PATCH 26/51] Moved note --- src/cheatsheets/Schaltungstheorie.typ | 58 ++++++++++++++------------- 1 file changed, 31 insertions(+), 27 deletions(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index de5630b..5144900 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -330,40 +330,40 @@ align(center, [ *$u$-gesteuert* \ Helmholz / Thévenin - - (Strom $-I_0$ wird als $I_0$ geschrieben) ]), align(center, [ *$i$-gesteuert* \ Mayer / Norton ]), - align( - horizon + center, - zap.circuit({ - import zap: * - import cetz.draw + [ + #align( + horizon + center, + zap.circuit({ + import zap: * + import cetz.draw - zap.resistor("R1", (1, 0), (1, -1.5), fill: none, width: 0.8, height: 0.3) - zap.isource("I0", (0, 0), (0, -1.5), fill: none, scale: 0.6, i: ( - content: $-I_0$, - distance: 6pt, - label-distance: -11pt, - anchor: "west", - invert: true, - )) - node("N0", "R1.in") - node("N0", "R1.out") + zap.resistor("R1", (1, 0), (1, -1.5), fill: none, width: 0.8, height: 0.3) + zap.isource("I0", (0, 0), (0, -1.5), fill: none, scale: 0.6, i: ( + content: $-I_0$, + distance: 6pt, + label-distance: -11pt, + anchor: "west", + invert: true, + )) + node("N0", "R1.in") + node("N0", "R1.out") - wire("I0.out", "R1.out", (rel: (0.5, 0))) - wire("I0.in", "R1.in") - wire("R1.in", (rel: (0.5, 0)), i: (content: $i$, invert: true)) + wire("I0.out", "R1.out", (rel: (0.5, 0))) + wire("I0.in", "R1.in") + wire("R1.in", (rel: (0.5, 0)), i: (content: $i$, invert: true)) - cetz.draw.content((0.62, -0.75), [$G_i$]) - cetz.draw.set-style(mark: (end: ">", fill: black, scale: 0.6)) - cetz.draw.content((1.7, -0.75), [$u$]) - cetz.draw.line((1.5, -0.1), (1.5, -1.4), stroke: 0.5pt) - }), - ), + cetz.draw.content((0.62, -0.75), [$G_i$]) + cetz.draw.set-style(mark: (end: ">", fill: black, scale: 0.6)) + cetz.draw.content((1.7, -0.75), [$u$]) + cetz.draw.line((1.5, -0.1), (1.5, -1.4), stroke: 0.5pt) + }), + ) + ], align( horizon + center, zap.circuit({ @@ -413,7 +413,11 @@ ], ) - Bei Dualwandlung, einfach Ersetzung durchführen + - Bei Dualwandlung, einfach Ersetzung durchführen + + - Bei explizit: *Mayer-Norten*: $-I_0$ als $I_0$ schreiben und $-$ in die Variable reinziehen. + + *NICHT* die Pfeilrichtung ändern! ] From 81cf98f14efedda5ef7b5049215118487f6db2e1 Mon Sep 17 00:00:00 2001 From: alexander Date: Mon, 9 Feb 2026 10:58:36 +0100 Subject: [PATCH 27/51] Added superposition --- src/cheatsheets/Schaltungstheorie.typ | 32 ++++++++++++++++++++++++--- 1 file changed, 29 insertions(+), 3 deletions(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index 5144900..985b10e 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -243,7 +243,7 @@ wire((-0.6, 1.5),(0.8, 1.5)) wire((-0.6, -1.5),(0.8, -1.5)) - wire((-0.6, 0),(0,0)) + wire((-0.6, 0),(0,0), i: (content: $i =0 unit("A")$, distance: 0.1, anchor: "north-west")) }), zap.circuit({ import zap : * @@ -645,6 +645,8 @@ *Tellegen'sche Satz* \ $bold(A B^T) = bold(B^T A) = 0$ \ + + Prüfen oben ein AP stimmt: $bold(u_b^T i_b) = 0$ ] @@ -1084,7 +1086,6 @@ ] // Reaktive Elemeten - #colbreak() #bgBlock(fill: colorComplexAC)[ #subHeading(fill: colorComplexAC)[Reaktive Element] @@ -1135,6 +1136,31 @@ $W(t_1, t_2) < 0$: Gibt Energie ab\ ] + #bgBlock(fill: colorComplexAC)[ + #subHeading(fill: colorComplexAC)[Superpositions Prinzip] + + Sei eine lineare eindeutig lösbare Schaltung mit mehreren Erregungen ge- + geben, so setzt sich die Gesamtlösung aus den einzelnen Teillösungen zu- + sammen. + + 1. Setze alle bis auf eine unabhängige Quelle $U_k$ bzw. $I_k$ zu Null + 2. Berechne die gesuchten Größen $u_(z_k)$ bzw. $i_(y_k)$ + 3. Wiederhole Schritte 1 und 2 für alle unabhängige Quellen + 4. Gesamtlösung ergibt sich zu \ $u_z = sum u_(z_k)$ und $i_y = sum u_(y_k)$ + + #line(length: 100%, stroke: (thickness: 0.2mm)) + + *Für Komplex AC* + + Für Eingeschwungenen und lineare Schaltungnen + + Erregung kann in \ + $u_"ges"(t) = u_0(t) + u_1(t) + ... + U_"const"$ \ + wobei $u_0(t), u_1(t), ...$ verschieden $omega$ haben dürfen. + + Das gilt *NUR* zweit Abhänige Darstellung, *NICHT* für Frequenz Abhänige Darstellung + ] + #bgBlock(fill: colorComplexAC)[ #subHeading(fill: colorComplexAC)[Reaktive Bauelemente] #grid( @@ -1245,7 +1271,7 @@ // Complex AC #bgBlock(fill: colorComplexAC)[ #subHeading(fill: colorComplexAC)[Komplex Wechselstrom Rechnnung] - Im Eingeschwungenem Zustand + *Nur für Lineare und Eingeschwungenene Schaltungen* $u(t) = "Re"{U_m e^(j omega t + phi)}$ From 009b18f749c79d445b3e2080b0b9fe3357c37641 Mon Sep 17 00:00:00 2001 From: alexander Date: Mon, 9 Feb 2026 11:08:26 +0100 Subject: [PATCH 28/51] Umsorttierung --- src/cheatsheets/Schaltungstheorie.typ | 572 +++++++++++++------------- 1 file changed, 280 insertions(+), 292 deletions(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index 985b10e..36384e2 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -57,6 +57,8 @@ #set text(8.5pt) #columns(4, gutter: 2mm)[ + + // =============== Allgemein =============== // Allgemein #bgBlock(fill: colorAllgemein)[ #subHeading(fill: colorAllgemein)[Allgemeine] @@ -180,11 +182,10 @@ ) ] - - // Quell Wandlung + // Kennline Addition #bgBlock(fill: colorEineTore)[ - #subHeading(fill: colorEineTore)[Ein-Tor] - + #subHeading(fill: colorEineTore)[Kennline Addition] + /* #grid( columns: (auto, auto), column-gutter: 3mm, @@ -205,8 +206,7 @@ $i_(cal(F),2) = i_(cal(F),1)$ ], ) - - *Kennline Addition* \ + */ #grid( columns: (1fr, auto, 1fr), @@ -264,6 +264,47 @@ ) ] + // Dual Wandlung + #bgBlock(fill: colorAllgemein)[ + #subHeading(fill: colorAllgemein)[Dual Wandlung] + Stumpfe Ersetzung mit: + + #table( + columns: (1fr, 1fr), + fill: (x, y) => if calc.rem(y, 2) == 0 { tableFillHigh } else { tableFillLow }, + + $ u --> R_d i^d $, + $ i --> u^d / R_d $, + $ Phi --> R_d q^d $, + $ q --> Phi / R_d $, + + $ R --> G^d = R / R_d^2 $, + $ G --> R^d = R_d^2 G $, + + $C --> L^d = R_d^2 C$, + $L --> C^d = L / R_d^2$, + + $"KS" --> "LL"$, $"LL" -> "KS"$, + $"Nullator" --> "Nullator"$, $"Norator" -> "Norator"$, + + $"Parallel" --> "Seriell"$, + $"Seriell" --> "Parallel"$, + + table.cell(colspan: 2)[ + *Dualwandlung: Steurende & Ausgangs Größe* + $ + "VCVS" &: u_"out" &= mu dot u_"in" &--> i_"out"^d = mu i_"in"^d\ + "VCCS" &: i_"out" &= g dot u_"in" &--> u_"out"^d = g R_d^2 dot i_"in"^d \ + "CCVS" &: u_"out" &= r dot i_"in" &--> i_"out"^d = r/R_d^2 dot u_"in"\ + "CCCS" &: i_"out" &= beta dot i_"in" &--> u_"out"^d = beta u_"in"^d\ + $ + ], + + table.cell(colspan: 2)[$ (u, i) in cal(F) --> (u_d, i_d) in cal(F) = (R_d i, 1/R_d u) $] + ) + ] + + #colbreak() // Lineare Quelle #bgBlock(fill: colorEineTore)[ #subHeading(fill: colorEineTore)[Lineare Quelle] @@ -409,7 +450,7 @@ table.cell(colspan: 2, fill: tableFillLow)[ #align(center, [*$i"-gesteuert" --> u"-gestuert"$*]) - $ G_i = 1/R_i quad quad quad I_0 = -U_0 1/R_i $ + #align(center, $G_i = 1/R_i quad quad quad I_0 = -U_0 1/R_i$) ], ) @@ -420,47 +461,7 @@ *NICHT* die Pfeilrichtung ändern! ] - - // Dual Wandlung - #bgBlock(fill: colorAllgemein)[ - #subHeading(fill: colorAllgemein)[Dual Wandlung] - Stumpfe Ersetzung mit: - - #table( - columns: (1fr, 1fr), - fill: (x, y) => if calc.rem(y, 2) == 0 { tableFillHigh } else { tableFillLow }, - - $ u --> R_d i^d $, - $ i --> u^d / R_d $, - $ Phi --> R_d q^d $, - $ q --> Phi / R_d $, - - $ R --> G^d = R / R_d^2 $, - $ G --> R^d = R_d^2 G $, - - $C --> L^d = R_d^2 C$, - $L --> C^d = L / R_d^2$, - - $"KS" --> "LL"$, $"LL" -> "KS"$, - $"Nullator" --> "Nullator"$, $"Norator" -> "Norator"$, - - $"Parallel" --> "Seriell"$, - $"Seriell" --> "Parallel"$, - - table.cell(colspan: 2)[ - *Dualwandlung: Steurende & Ausgangs Größe* - $ - "VCVS" &: u_"out" &= mu dot u_"in" &--> i_"out"^d = mu i_"in"^d\ - "VCCS" &: i_"out" &= g dot u_"in" &--> u_"out"^d = g R_d^2 dot i_"in"^d \ - "CCVS" &: u_"out" &= r dot i_"in" &--> i_"out"^d = r/R_d^2 dot u_"in"\ - "CCCS" &: i_"out" &= beta dot i_"in" &--> u_"out"^d = beta u_"in"^d\ - $ - ], - - table.cell(colspan: 2)[$ (u, i) in cal(F) --> (u_d, i_d) in cal(F) = (R_d i, 1/R_d u) $] - ) - ] - + #colbreak() // Linearsierung #bgBlock(fill: colorEineTore)[ #subHeading(fill: colorEineTore)[Linearisierung (Ein-Tore)] @@ -469,7 +470,7 @@ 2. Ableitung $g_cal(F)(u)$/$r_cal(F)(i)$ bilden \ $g'_cal(F)(u)$/$r'_cal(F)(i)$ - #line(length: 100%) + #line(length: 100%, stroke: (thickness: 0.2mm)) *Stromgesteuert* @@ -514,7 +515,7 @@ *Klein-Signal* $quad Delta i_"lin" = g_"lin" (Delta u) = g'(u_"AP") Delta u$ - #line(length: 100%) + #line(length: 100%, stroke: (thickness: 0.2mm)) *Spannungsgesteuert* @@ -554,204 +555,14 @@ ); #linebreak() *Klein-Signal* $quad Delta u_"lin" = r_"lin" (Delta i) = r'(i_"AP") Delta i$ - ] - - // Graphen und Matrizen - #bgBlock(fill: colorAnalyseVerfahren)[ - #subHeading(fill: colorAnalyseVerfahren)[Graphen und Matrizen] - - $n:$ Knotenanzahle (mit Referenzknoten) - - $b:$ Zweiganzahle - - *Lineare Unabhänige KCL/KVLs* - - Für $2b$ unbekannte ($b$ Ströme + $b$ Spannungen) - - KCLs: $n-1$\ - KVLs: $b-(n-1)$ #line(length: 100%, stroke: (thickness: 0.2mm)) - $bold(i_b)$ (oder $bold(i)$): Zweigstrom-Vektor \ - $bold(u_b)$ (oder $bold(u)$): Zweigspannungs-Vektor \ - $bold(i_m)$ : Maschenstrom-Vektor \ - #text(rgb(20%, 20%, 20%))[(Strom in einer viruellen Masche)] \ - $bold(u_k)$ : Kontenspannungs-Vektor \ - #text(rgb(20%, 20%, 20%))[(Spannung zwischen Referenzknoten und Knoten k)] \ - - #line(length: 100%, stroke: (thickness: 0.2mm)) - - Knotenzidenzmatrix $bold(A)$ - - $bold(A) : bold(i_k) -> text("Knotenstrombilanz") = 0$ \ - $bold(A^T) : bold(u_b)-> bold(u_k)$ - $ - bold(A) = quad space space mannot.mark( - mat( - a_11, a_12, ..., a_(1m); - a_21, a_22, ..., a_(2m); - dots.v, dots.v, dots.down, dots.v; - a_(n 1), a_(n 2), ..., a_(n m) - ), tag: #<1> - ) - #mannot.annot(<1>, pos: left, text(rgb("#404296"))[#rotate(-90deg)[$<-$ Knoten \ ($n-1$)]], dx: 2mm) - #mannot.annot(<1>, pos: bottom, text(rgb("#404296"))[Zweige ($b$) $->$], dy: -0.5mm) - a in {-1, 0, 1} - $ - #linebreak() - $-1 &: "In Knoten rein" \ - 1 &: "Aus Knoten raus"$ - - #line(length: 100%, stroke: (thickness: 0.2mm)) - - Mascheninsidenz Matrix $bold(B)$\ - - - $bold(B) : bold(u_b) -> text("Zweigspannungsbilanz") = 0$ \ - $bold(B^T) : bold(i_m) -> i_b$ - - $ - bold(B) = quad space space mannot.mark(mat( - b_11, b_12, ..., b_(1m); - b_21, b_22, ..., b_(2m); - dots.v, dots.v, dots.down, dots.v; - b_(n 1), b_(n 2), ..., b_(n m) - ), tag: #<1>) - - #mannot.annot(<1>, pos:left, text(rgb("#404296"))[#rotate(-90deg)[$<-$ Maschen \ $b-(n-1)$]], dx: 4mm) - #mannot.annot(<1>, pos:bottom, text(rgb("#404296"))[Zweige ($b$) $->$], dy: -0.5mm) - - b in {-1, 0, 1} - $ - - #linebreak() - $-1 &: "Gegen Maschenrichtung" \ - 1 &: "In Maschenrichtung"$ - - #line(length: 100%, stroke: (thickness: 0.2mm)) - - #colbreak() - *KCL und KVL* \ - - KCL in Nullraum: $bold(A) bold(i_b) = bold(0)$ \ - KVL in Bildraum: $bold(A^T) bold(u_k) = bold(u_b)$ - - KVL in Nullraum: $bold(B) bold(u_b) = bold(0)$ \ - KCL in Bildraum: $bold(B^T) bold(i_m) = bold(i_b)$ \ - - #line(length: 100%, stroke: (thickness: 0.2mm)) - - - *Tellegen'sche Satz* \ - $bold(A B^T) = bold(B^T A) = 0$ \ - - Prüfen oben ein AP stimmt: - $bold(u_b^T i_b) = 0$ - ] - - // Baumkonzept - #bgBlock(fill: colorAnalyseVerfahren)[ - #subHeading(fill: colorAnalyseVerfahren)[Baumkonzept] - - - 1. Baum einzeichnen (Keine Schleifen!) \ - Muss alle Knoten umfassen - - 2. $n-1$ KCLs: \ - Superknoten mit NUR einer Baumkante \ - $jMat(A) = mat(jMat(1)_(n-1), jMat(A)_e)$ \ - - - 3. $b - (n-1)$ KVLs: \ - Maschen mit NUR einer NICHT Baumkante \ - $jMat(B) = mat(jMat(B)_t, jMat(1)_(b-(n-1)))$ - - - *Nur bei Baumkonzept:* $B_t = - A_e^T$ - - ] - - // Tablauematrix - #bgBlock(fill: colorAnalyseVerfahren)[ - #subHeading(fill: colorAnalyseVerfahren)[Allgemeine Analyse Verfahren] - - *Tableaugleichung* - - Alle Element Gleichungen in Nullraum + KVLs/KCLs in eine Matrix - - KCLs in Nullraum: $jMat(A) jVec(i)_b = jVec(0)$\ - KVLs in Nullraum: $jMat(B) jVec(u)_b = jVec(0)$\ - Elementgleichungen: $jMat(N) jVec(u)_b + jMat(M) jVec(i)_b = jVec(e)$ - - $ mannot.mark(mat( - jMat(B), jMat(0); - jMat(0), jMat(A); - jMat(M), jMat(N) - ), tag: #<1>) vec(jVec(u)_b, jVec(i)_b) = vec(jVec(0), jVec(0), jVec(e)) - - #mannot.annot(<1>, text($b - (n-1) space$, rgb("#00318b")), pos: left, dy: -2.8mm, dx: 1mm) - #mannot.annot(<1>, text($n-1 space$, rgb("#00318b")), pos: left, dy: 0mm, dx: 1mm) - #mannot.annot(<1>, text($b space$, rgb("#00318b")), pos: left, dy: 2.8mm, dx: 1mm) - #mannot.annot(<1>, text($2b$, rgb("#00318b")), pos: bottom, dy: -0.5mm) - $ - - #line(stroke: (thickness: 0.2mm), length: 100%) - - *Knotenspannungs-Analyse* - - KVL in Bildraum: $jVec(u)_b = jMat(A)^T jVec(u)_k$\ - KCLs in Nullraum: $jMat(A) jVec(i)_b = jVec(0)$\ - Elementgleichungen: $jMat(N) jVec(u)_b + jMat(M) jVec(i)_b = jVec(e)$ - - $ - mannot.mark(mat( - -jMat(A)^T, jMat(1), jMat(0); - jMat(0), jMat(0), jMat(A); - jMat(0), jMat(M), jMat(N) - ), tag: #<1>) vec(jVec(u)_k, jVec(u)_b, jVec(i)_b) = vec(jVec(0), jVec(0), jVec(e)) - - #mannot.annot(<1>, text($b space$, rgb("#00318b")), pos: left, dy: -2.8mm, dx: 1mm) - #mannot.annot(<1>, text($n-1 space$, rgb("#00318b")), pos: left, dy: 0mm, dx: 1mm) - #mannot.annot(<1>, text($b space$, rgb("#00318b")), pos: left, dy: 2.8mm, dx: 1mm) - #mannot.annot(<1>, text($2b + (n-1)$, rgb("#00318b")), pos: bottom, dy: -0.5mm) - $ - - #line(stroke: (thickness: 0.2mm), length: 100%) - - *Maschenstrom-Analyse* - - Nur für Planare Schaltungen - - KCL in Bildraum: $jVec(i)_b = jMat(B)^T jVec(i)_m$\ - KCLs in Nullraum: $jMat(B) jVec(u)_b = jVec(0)$\ - Elementgleichungen: $jMat(N) jVec(u)_b + jMat(M) jVec(i)_b = jVec(e)$ - - $ - mannot.mark(mat( - jMat(B), jMat(0), jMat(0); - jMat(0), jMat(1), -jMat(B)^T; - jMat(M), jMat(N), jMat(0) - ), tag: #<1>) vec(jVec(u)_b, jVec(i)_b, jVec(i)_m) = vec(jVec(0), jVec(0), jVec(e)) - - #mannot.annot(<1>, text($b - (n-1) space$, rgb("#00318b")), pos: left, dy: -2.8mm, dx: 1mm) - #mannot.annot(<1>, text($b space$, rgb("#00318b")), pos: left, dy: 0mm, dx: 1mm) - #mannot.annot(<1>, text($b space$, rgb("#00318b")), pos: left, dy: 2.8mm, dx: 1mm) - #mannot.annot(<1>, text($3b - (n-1)$, rgb("#00318b")), pos: bottom, dy: -0.5mm) - $ - - #line(stroke: (thickness: 0.2mm), length: 100%) - - Nicht Lineare Gleichungen: $underline(f)'(jVec(u), jVec(i)) = 0$ - ] - - // Netwon Rephson - #bgBlock(fill: colorAnalyseVerfahren)[ - #subHeading(fill: colorAnalyseVerfahren)[Netwen-Raphson] - - + *Newton-Raphson* + $x_(n+1) = x_n - f(x_n)/(f'(x_n))$ ] + // =============== Zwei Tore =============== // ZweiTor Beschreibungen #bgBlock(fill: colorZweiTore)[ #subHeading(fill: colorZweiTore)[Zwei-Tor Beschreibungen] @@ -1026,6 +837,196 @@ (Superpositions Prinzip) ] + #colbreak() + // Graphen und Matrizen + #bgBlock(fill: colorAnalyseVerfahren)[ + #subHeading(fill: colorAnalyseVerfahren)[Graphen und Matrizen] + + $n:$ Knotenanzahle (mit Referenzknoten) + + $b:$ Zweiganzahle + + *Lineare Unabhänige KCL/KVLs* + + Für $2b$ unbekannte ($b$ Ströme + $b$ Spannungen) + + KCLs: $n-1$\ + KVLs: $b-(n-1)$ + + #line(length: 100%, stroke: (thickness: 0.2mm)) + + $bold(i_b)$ (oder $bold(i)$): Zweigstrom-Vektor \ + $bold(u_b)$ (oder $bold(u)$): Zweigspannungs-Vektor \ + $bold(i_m)$ : Maschenstrom-Vektor \ + #text(rgb(20%, 20%, 20%))[(Strom in einer viruellen Masche)] \ + $bold(u_k)$ : Kontenspannungs-Vektor \ + #text(rgb(20%, 20%, 20%))[(Spannung zwischen Referenzknoten und Knoten k)] \ + + #line(length: 100%, stroke: (thickness: 0.2mm)) + + Knotenzidenzmatrix $bold(A)$ + + $bold(A) : bold(i_k) -> text("Knotenstrombilanz") = 0$ \ + $bold(A^T) : bold(u_b)-> bold(u_k)$ + $ + bold(A) = quad space space mannot.mark( + mat( + a_11, a_12, ..., a_(1m); + a_21, a_22, ..., a_(2m); + dots.v, dots.v, dots.down, dots.v; + a_(n 1), a_(n 2), ..., a_(n m) + ), tag: #<1> + ) + #mannot.annot(<1>, pos: left, text(rgb("#404296"))[#rotate(-90deg)[$<-$ Knoten \ ($n-1$)]], dx: 2mm) + #mannot.annot(<1>, pos: bottom, text(rgb("#404296"))[Zweige ($b$) $->$], dy: -0.5mm) + a in {-1, 0, 1} + $ + #linebreak() + $-1 &: "In Knoten rein" \ + 1 &: "Aus Knoten raus"$ + + #line(length: 100%, stroke: (thickness: 0.2mm)) + + Mascheninsidenz Matrix $bold(B)$\ + + + $bold(B) : bold(u_b) -> text("Zweigspannungsbilanz") = 0$ \ + $bold(B^T) : bold(i_m) -> i_b$ + + $ + bold(B) = quad space space mannot.mark(mat( + b_11, b_12, ..., b_(1m); + b_21, b_22, ..., b_(2m); + dots.v, dots.v, dots.down, dots.v; + b_(n 1), b_(n 2), ..., b_(n m) + ), tag: #<1>) + + #mannot.annot(<1>, pos:left, text(rgb("#404296"))[#rotate(-90deg)[$<-$ Maschen \ $b-(n-1)$]], dx: 4mm) + #mannot.annot(<1>, pos:bottom, text(rgb("#404296"))[Zweige ($b$) $->$], dy: -0.5mm) + + b in {-1, 0, 1} + $ + + #linebreak() + $-1 &: "Gegen Maschenrichtung" \ + 1 &: "In Maschenrichtung"$ + + #line(length: 100%, stroke: (thickness: 0.2mm)) + + #colbreak() + *KCL und KVL* \ + + KCL in Nullraum: $bold(A) bold(i_b) = bold(0)$ \ + KVL in Bildraum: $bold(A^T) bold(u_k) = bold(u_b)$ + + KVL in Nullraum: $bold(B) bold(u_b) = bold(0)$ \ + KCL in Bildraum: $bold(B^T) bold(i_m) = bold(i_b)$ \ + + #line(length: 100%, stroke: (thickness: 0.2mm)) + + + *Tellegen'sche Satz* \ + $bold(A B^T) = bold(B^T A) = 0$ \ + + Prüfen oben ein AP stimmt: + $bold(u_b^T i_b) = 0$ + ] + + // Baumkonzept + #bgBlock(fill: colorAnalyseVerfahren)[ + #subHeading(fill: colorAnalyseVerfahren)[Baumkonzept] + + + 1. Baum einzeichnen (Keine Schleifen!) \ + Muss alle Knoten umfassen + + 2. $n-1$ KCLs: \ + Superknoten mit NUR einer Baumkante \ + $jMat(A) = mat(jMat(1)_(n-1), jMat(A)_e)$ \ + + + 3. $b - (n-1)$ KVLs: \ + Maschen mit NUR einer NICHT Baumkante \ + $jMat(B) = mat(jMat(B)_t, jMat(1)_(b-(n-1)))$ + + + *Nur bei Baumkonzept:* $B_t = - A_e^T$ + + ] + + // Tablauematrix + #bgBlock(fill: colorAnalyseVerfahren)[ + #subHeading(fill: colorAnalyseVerfahren)[Allgemeine Analyse Verfahren] + + *Tableaugleichung* + + Alle Element Gleichungen in Nullraum + KVLs/KCLs in eine Matrix + + KCLs in Nullraum: $jMat(A) jVec(i)_b = jVec(0)$\ + KVLs in Nullraum: $jMat(B) jVec(u)_b = jVec(0)$\ + Elementgleichungen: $jMat(N) jVec(u)_b + jMat(M) jVec(i)_b = jVec(e)$ + + $ mannot.mark(mat( + jMat(B), jMat(0); + jMat(0), jMat(A); + jMat(M), jMat(N) + ), tag: #<1>) vec(jVec(u)_b, jVec(i)_b) = vec(jVec(0), jVec(0), jVec(e)) + + #mannot.annot(<1>, text($b - (n-1) space$, rgb("#00318b")), pos: left, dy: -2.8mm, dx: 1mm) + #mannot.annot(<1>, text($n-1 space$, rgb("#00318b")), pos: left, dy: 0mm, dx: 1mm) + #mannot.annot(<1>, text($b space$, rgb("#00318b")), pos: left, dy: 2.8mm, dx: 1mm) + #mannot.annot(<1>, text($2b$, rgb("#00318b")), pos: bottom, dy: -0.5mm) + $ + + #line(stroke: (thickness: 0.2mm), length: 100%) + + *Knotenspannungs-Analyse* + + KVL in Bildraum: $jVec(u)_b = jMat(A)^T jVec(u)_k$\ + KCLs in Nullraum: $jMat(A) jVec(i)_b = jVec(0)$\ + Elementgleichungen: $jMat(N) jVec(u)_b + jMat(M) jVec(i)_b = jVec(e)$ + + $ + mannot.mark(mat( + -jMat(A)^T, jMat(1), jMat(0); + jMat(0), jMat(0), jMat(A); + jMat(0), jMat(M), jMat(N) + ), tag: #<1>) vec(jVec(u)_k, jVec(u)_b, jVec(i)_b) = vec(jVec(0), jVec(0), jVec(e)) + + #mannot.annot(<1>, text($b space$, rgb("#00318b")), pos: left, dy: -2.8mm, dx: 1mm) + #mannot.annot(<1>, text($n-1 space$, rgb("#00318b")), pos: left, dy: 0mm, dx: 1mm) + #mannot.annot(<1>, text($b space$, rgb("#00318b")), pos: left, dy: 2.8mm, dx: 1mm) + #mannot.annot(<1>, text($2b + (n-1)$, rgb("#00318b")), pos: bottom, dy: -0.5mm) + $ + + #line(stroke: (thickness: 0.2mm), length: 100%) + + *Maschenstrom-Analyse* + + Nur für Planare Schaltungen + + KCL in Bildraum: $jVec(i)_b = jMat(B)^T jVec(i)_m$\ + KCLs in Nullraum: $jMat(B) jVec(u)_b = jVec(0)$\ + Elementgleichungen: $jMat(N) jVec(u)_b + jMat(M) jVec(i)_b = jVec(e)$ + + $ + mannot.mark(mat( + jMat(B), jMat(0), jMat(0); + jMat(0), jMat(1), -jMat(B)^T; + jMat(M), jMat(N), jMat(0) + ), tag: #<1>) vec(jVec(u)_b, jVec(i)_b, jVec(i)_m) = vec(jVec(0), jVec(0), jVec(e)) + + #mannot.annot(<1>, text($b - (n-1) space$, rgb("#00318b")), pos: left, dy: -2.8mm, dx: 1mm) + #mannot.annot(<1>, text($b space$, rgb("#00318b")), pos: left, dy: 0mm, dx: 1mm) + #mannot.annot(<1>, text($b space$, rgb("#00318b")), pos: left, dy: 2.8mm, dx: 1mm) + #mannot.annot(<1>, text($3b - (n-1)$, rgb("#00318b")), pos: bottom, dy: -0.5mm) + $ + + #line(stroke: (thickness: 0.2mm), length: 100%) + + Nicht Lineare Gleichungen: $underline(f)'(jVec(u), jVec(i)) = 0$ + ] + // Linearsierung (N-Tore) #bgBlock(fill: colorAnalyseVerfahren)[ #subHeading(fill: colorAnalyseVerfahren)[Linearisierung (N-Tore)] @@ -1051,15 +1052,9 @@ $jVec(y)_"lin" = jMat(J)|_(jVec(x)_"AP") jVec(x)_"lin"$ ] - // Newton-Raphson - #bgBlock(fill: colorEineTore)[ - #subHeading(fill: colorEineTore)[Newton-Raphson (Eine-Tor)] - $x_(n+1) = x_n - f(x_n)/(f'(x_n))$ - ] - // Netwen-Raphson N-Tore - #bgBlock(fill: colorZweiTore)[ - #subHeading(fill: colorZweiTore)[Newton-Raphson (N-Tore)] + #bgBlock(fill: colorAnalyseVerfahren)[ + #subHeading(fill: colorAnalyseVerfahren)[Newton-Raphson (N-Tore)] Nicht lineare Beschreibung in Nullraum/Implizit Darstellung: $jVec(f)'(jVec(x)) = jVec(0)$\ @@ -1084,8 +1079,9 @@ 4. Fehler $epsilon$ berechnen ] - + // Reaktive Elemeten + #colbreak() #bgBlock(fill: colorComplexAC)[ #subHeading(fill: colorComplexAC)[Reaktive Element] @@ -1161,6 +1157,7 @@ Das gilt *NUR* zweit Abhänige Darstellung, *NICHT* für Frequenz Abhänige Darstellung ] + #colbreak() #bgBlock(fill: colorComplexAC)[ #subHeading(fill: colorComplexAC)[Reaktive Bauelemente] #grid( @@ -1256,46 +1253,7 @@ ] - // Reaktive Dual Wandlung - #bgBlock(fill: colorComplexAC)[ - #subHeading(fill: colorComplexAC)[Reaktive Dualwandlung] - - #grid( - columns: (1fr, 1fr), - row-gutter: 4mm, - $u --> R_d i^d$, $i --> u^d/R_d$, - $q --> Phi^d / R_d$, $Phi --> q^d R_d$, - ) - ] - - // Complex AC - #bgBlock(fill: colorComplexAC)[ - #subHeading(fill: colorComplexAC)[Komplex Wechselstrom Rechnnung] - *Nur für Lineare und Eingeschwungenene Schaltungen* - - $u(t) = "Re"{U_m e^(j omega t + phi)}$ - - $u(t) = U_m cos(omega t + alpha)$ \ - $i(t) = I_m cos(omega t + beta)$ - - $(d u)/(d t) = A_m$ - - Kreisfrequenz: $omega = 2 pi f$ \ - Amplitude: $A_m$ \ - Phaseverschieben: $alpha$ - - *Ohm:* $u(t) = R I_m cos(omega t + beta) = omega A_m cos(omega)$) - - *Serienschaltung*\ - $u_1(t) = U_1 cos(omega t)$\ - $u_2(t) = U_2 cos(omega t + phi)$ - - $u(t)_"ges" = u_1(t) + u_2(t) = \ - U_"ges"^2 = U_1^2 + 2 U_1 U_2 + U_2^2 \ - tan(phi) = (U_2 sin(phi))/(U_1 + U_2 cos(phi))$ - ] - - + // Komplexe Beziehung #bgBlock(fill: colorComplexAC)[ #subHeading(fill: colorComplexAC)[Komplex Beziehungen] #let size = 1.4 @@ -1367,6 +1325,33 @@ ]) ] + // Complex AC + #bgBlock(fill: colorComplexAC)[ + #subHeading(fill: colorComplexAC)[Komplex Wechselstrom Rechnnung] + *Nur für Lineare und Eingeschwungenene Schaltungen* + + $u(t) = "Re"{U_m e^(j omega t + phi)}$ + + $u(t) = U_m cos(omega t + alpha)$ \ + $i(t) = I_m cos(omega t + beta)$ + + $(d u)/(d t) = A_m$ + + Kreisfrequenz: $omega = 2 pi f$ \ + Amplitude: $A_m$ \ + Phaseverschieben: $alpha$ + + *Ohm:* $u(t) = R I_m cos(omega t + beta) = omega A_m cos(omega)$) + + *Serienschaltung*\ + $u_1(t) = U_1 cos(omega t)$\ + $u_2(t) = U_2 cos(omega t + phi)$ + + $u(t)_"ges" = u_1(t) + u_2(t) = \ + U_"ges"^2 = U_1^2 + 2 U_1 U_2 + U_2^2 \ + tan(phi) = (U_2 sin(phi))/(U_1 + U_2 cos(phi))$ + ] + // AC Components #bgBlock(fill: colorComplexAC)[ #subHeading(fill: colorComplexAC)[Komplexe Komponent] @@ -1403,6 +1388,7 @@ ) ] + #colbreak() #bgBlock(fill: colorComplexAC)[ #subHeading(fill: colorComplexAC)[*Levi's Lustig Leistung*] $P=P_W + j P_B$\ @@ -1426,6 +1412,7 @@ $U_"eff" = U_m/sqrt(2), I_"eff" = I_m / sqrt(2)$ ] + #colbreak() // Komplexe Zahlen #bgBlock(fill: colorAllgemein)[ #subHeading(fill: colorAllgemein)[Komplexe Zahlen] @@ -1444,6 +1431,7 @@ ) ] + #colbreak() // SinTable #bgBlock(fill: colorAllgemein, [ #subHeading(fill: colorAllgemein, [Sin-Table]) From a20566c55c5ff8445ca431ec9bfedb24e037179c Mon Sep 17 00:00:00 2001 From: alexander Date: Mon, 9 Feb 2026 12:21:34 +0100 Subject: [PATCH 29/51] corrections matrix --- src/cheatsheets/Schaltungstheorie.typ | 69 ++++++++++++++++++++------- 1 file changed, 53 insertions(+), 16 deletions(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index 36384e2..4a72815 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -1760,6 +1760,7 @@ - Quellenfrei - Ungepolt - Resitiv, Induktiv, Kapazitiv, Memristiv + - Passiv ], // Norator @@ -1799,6 +1800,7 @@ - Quellenfrei - Ungepolt - Resitiv, Induktiv, Kapazitiv, Memristiv + - Aktiv ], table.hline(), @@ -1837,6 +1839,7 @@ ], align(left+top)[ - Verlustlos + - Passiv - Streng linear - Linear - Quellenfrei @@ -1877,6 +1880,7 @@ ], align(left+top)[ - Verlustlos + - Passiv - Streng linear - Linear - Quellenfrei @@ -2281,13 +2285,38 @@ })], [ - - Verlustlos - Reziprok - - Passiv + - Aktiv - Symetrisch ], [$ A = mat(0, 0; 0, 0) $], - [OpAmp \ $U_"sat+"$\ (4-polig)], opampSymbol, [], [], [], + [OpAmp \ linear Bereich \ (4-polig)], opampSymbol, [#zap.circuit({ + import zap: * + import cetz.draw: content, line, rect + + joham.nullator("a", (0,0), (0,1.5), scale: 0.5) + joham.norator("b", (0.5,0), (0.5,1.5), scale: 0.5) + + wire("a.in", (rel: (-0.5, 0))) + wire("a.out", (rel: (-0.5, 0))) + wire("b.in", (rel: (0.5, 0))) + wire("b.out", (rel: (0.5, 0))) + + node("N1", (rel: (-0.5, 0), to: "a.in"), fill: false, label: (content: text($beta$, fill: rgb("#8b2000")), anchor: "west", distance: 0.05)) + node("N2", (rel: (-0.5, 0), to: "a.out"), fill: false, label: (content: text($alpha$, fill: rgb("#8b2000")), anchor: "west", distance: 0.05)) + node("N3", (rel: (0.5, 0), to: "b.in"), fill: false, label: (content: text($delta$, fill: rgb("#00318b")), anchor: "east", distance: 0.05)) + node("N4", (rel: (0.5, 0), to: "b.out"), fill: false, label: (content: text($gamma$, fill: rgb("#00318b")), anchor: "east", distance: 0.05)) + + joham.voltage("N2", "N1", $u_d$) + joham.voltage("N4", "N3", $U_"out" = "bel."$, anchor: "west") + + })], [ + - Reziprok + - Aktiv + - Symetrisch + ], [ + Für $u_d = 0 <=> abs(u_"out") < U_"sat"$ \ + ], [OpAmp \ $U_"sat+"$], opampSymbol, [#zap.circuit({ import zap : wire, vsource, node @@ -2309,7 +2338,7 @@ node("c", (1.3,1), fill: false, label: (content: text($gamma$, fill: rgb("#00318b")), anchor: "east", distance: 0.05)) node("d", (1.3,0), fill: false, label: (content: text($delta$, fill: rgb("#00318b")), anchor: "east", distance: 0.05)) - })], [], [], + })], [], [Für $u_d > 0$], [OpAmp \ $U_"sat-"$], opampSymbol, [#zap.circuit({ import zap : wire, vsource, node @@ -2330,7 +2359,7 @@ wire((1,1), (1.3,1)) wire((1,0), (1.3,0)) - })], [], [], + })], [], [Für $u_d < 0$], [VCVS], [#zap.circuit({ import zap : vsource, node, disource, dvsource, wire @@ -2591,12 +2620,17 @@ fill: (x, y) => if calc.rem(y, 2) == 1 { rgb("#c5c5c5") } else { white }, table.header([], [*Ein-Tor*], [*Zwei-Tor*], [*Reaktive Elemente*]), - [*passiv*\ (nimmt Energie auf)\ $not$aktiv], - [$forall (u,i) in cal(F): u dot i >= 0$], + [*passiv*\ (nimmt Energie auf)\ $<=> not$aktiv], + [$forall (u,i) in cal(F): u dot i >= 0$ + + Verlustlos $=>$ Passiv + ], [ - $jMat(U)^T jMat(I) + jMat(I)^T jMat(U) = 0$\ + $jMat(U)^T jMat(I) + jMat(I)^T jMat(U) >= 0$\ $forall vec(jVec(u), jVec(v)) in cal(F) : jVec(u)^T jVec(i) >=0 \ - jMat(G) = - jMat(G)^T quad jMat(R) = - jMat(R)^T$ + jMat(G) = - jMat(G)^T quad jMat(R) = - jMat(R)^T$ \ + Verlustlos $=>$ Passiv + ], [], @@ -2606,7 +2640,10 @@ Kennline nur $u\/i$-Achsen ], - [$forall vec(jVec(u), jVec(v)) in cal(F) : jVec(u)^T jVec(i) = 0$], + [$ + jMat(U)^T jMat(I) + jMat(I)^T jMat(U) = 0 \ + forall vec(jVec(u), jVec(v)) in cal(F) : jVec(u)^T jVec(i) = 0 \ + $], grid(columns: (auto, auto), column-gutter: 5mm, [ @@ -2697,8 +2734,8 @@ $bold(G) quad mat(S, S; S, S)$, $bold(H) quad mat(Omega, 1; 1, S)$, $bold(H') quad mat(S, 1; 1, Omega)$, - $bold(A) quad mat(S, 1; 1, Omega)$, - $bold(A') quad mat(S, 1; 1, Omega)$, + $bold(A) quad mat(1, Omega; S, 1)$, + $bold(A') quad mat(1, Omega; S, 1)$, $bold(R)$, $mat(r_11, r_12; r_21, r_22)$, @@ -2760,8 +2797,8 @@ $bold(G) jVec(u) = jVec(i)$, $bold(H) vec(i_1, u_2) = vec(u_1, i_2)$, $bold(H') vec(u_1, i_2) = vec(i_1, u_2)$, - $bold(A) vec(u_2, -i_2) = vec(i_1, u_1)$, - $bold(A') vec(u_1, -i_1) = vec(i_2, u_2)$, + $bold(A) vec(u_2, -i_2) = vec(u_1, i_1)$, + $bold(A') vec(u_1, -i_1) = vec(u_2, i_2)$, [], [Stromge-steuert], [Spannung-gesteuert], @@ -2774,8 +2811,8 @@ $jVec(g)vec(u_1, u_2) = vec(i_1, i_2)$, $jVec(h) vec(i_1, u_2) = vec(u_1, i_2)$, $jVec(h') vec(u_1, i_2) = vec(i_1, u_2)$, - $jVec(a) vec(u_2, -i_2) = vec(i_1, u_1)$, - $jVec(a') vec(u_1, -i_1) = vec(i_2, u_2)$, + $jVec(a) vec(u_2, -i_2) = vec(u_1, i_1)$, + $jVec(a') vec(u_1, -i_1) = vec(u_2, i_2)$, ) ] From 39c47d81e63a4f085247d7e5795867bcd7c09c3d Mon Sep 17 00:00:00 2001 From: alexander Date: Mon, 9 Feb 2026 12:29:19 +0100 Subject: [PATCH 30/51] Spannguns/Stromteiler Hinweis --- src/cheatsheets/Schaltungstheorie.typ | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index 4a72815..499235f 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -260,7 +260,8 @@ }), $ u_"out" = R_1/(R_1 + R_2) $, $ i_"out" = R_2/(R_1 + R_2) i_"ges" $, - $ u_"out" = G_2/(G_1 + G_2) $, $ i_"out" = G_1/(G_1 + G_2) i_"ges" $ + $ u_"out" = G_2/(G_1 + G_2) $, $ i_"out" = G_1/(G_1 + G_2) i_"ges" $, + [Muss unbelasted sein], [Nur wenn $u_R_1 = u_R_2$] ) ] From 3001ae1af61c50c8eab02e6c56aed43a19348fe4 Mon Sep 17 00:00:00 2001 From: alexander Date: Mon, 9 Feb 2026 14:23:06 +0100 Subject: [PATCH 31/51] Added strom quelle knoten potenzial + Ohm/Semines einheiten --- src/cheatsheets/Schaltungstheorie.typ | 12 +++++++++--- .../schaltKnotenPotenziell13.png | Bin 0 -> 118438 bytes 2 files changed, 9 insertions(+), 3 deletions(-) create mode 100644 src/images/schaltungstheorie/knotenpotenzial/schaltKnotenPotenziell13.png diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index 499235f..01aa5c1 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -123,6 +123,8 @@ $u dot i > 0$: Nimmt Energie auf\ $u dot i = 0$: Verlustlos\ $u dot i < 0$: Gibt Energie ab\ + + #grid(columns: (1fr, 1fr), $[R] = Omega = "V"/"A"$, $[G] = S = "A"/"V"$) ] // Verschaltung @@ -1538,7 +1540,9 @@ }), ), - [*Übertrager/NIK* siehe Zweitor-Tabelle], + [*Übertrager/NIK* siehe Zweitor-Tabelle + + ], scale(90%, grid( columns: (auto, 0mm, 1fr), @@ -1708,7 +1712,7 @@ align(center, image("../images/schaltungstheorie/knotenpotenzial/nullator.jpg", height: ImageHeight, fit: "contain")), align(center, image("../images/schaltungstheorie/knotenpotenzial/norator.jpg", height: ImageHeight, fit: "contain")), - + align(center, image("../images/schaltungstheorie/knotenpotenzial/schaltKnotenPotenziell13.png", height: ImageHeight, fit: "contain")) ) ] @@ -1989,7 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2001 From: alexander Date: Mon, 9 Feb 2026 14:30:15 +0100 Subject: [PATCH 32/51] fixed formating --- src/cheatsheets/Schaltungstheorie.typ | 4 +--- 1 file changed, 1 insertion(+), 3 deletions(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index 01aa5c1..eeb92ea 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -65,9 +65,7 @@ *Konzentriertheitshypotese*\ $lambda >> d quad quad lambda = c/f quad quad c approx 3.10dot 10^8 m/s$ - d: größe Bauteil Dimension - - f: Maximal Frequenze + #grid(columns: (1fr, 1fr), $d: "Schaltungs Dimension"$, $f: "Maximal Frequenze"$) *Kirchhoff* From 9ab0958351492e92a7f30808b45ae405d3184e49 Mon Sep 17 00:00:00 2001 From: alexander Date: Mon, 9 Feb 2026 14:51:01 +0100 Subject: [PATCH 33/51] added energie from Wirkleistung --- src/cheatsheets/Schaltungstheorie.typ | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index eeb92ea..a196e02 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -1078,7 +1078,7 @@ 3. Gleichungsystem lösen: $jVec(x)^((n+1))$ - 4. Fehler $epsilon$ berechnen + 4. Fehler $epsilon$ berechnen: $epsilon_(n+1) = jVec(f)(jVec(x)^((n+1)))$ ] // Reaktive Elemeten @@ -1410,7 +1410,9 @@ - $U_"eff" = U_m/sqrt(2), I_"eff" = I_m / sqrt(2)$ + $U_"eff" = U_m/sqrt(2), I_"eff" = I_m / sqrt(2)$ \ + + $W = t dot P_w$ ] #colbreak() From af26032d6ee6219094e6ae3ea121698abf0b0368 Mon Sep 17 00:00:00 2001 From: alexander Date: Mon, 9 Feb 2026 17:20:28 +0100 Subject: [PATCH 34/51] Added Ableitungs Tabelle and NII and Gyrator ESD --- src/cheatsheets/Analysis1.typ | 43 +------------- src/cheatsheets/Schaltungstheorie.typ | 53 +++++++++++++++++- .../knotenpotenzial/gyraptorESD.png | Bin 0 -> 68549 bytes src/lib/ableitungs_tabelle.typ | 42 ++++++++++++++ 4 files changed, 95 insertions(+), 43 deletions(-) create mode 100644 src/images/schaltungstheorie/knotenpotenzial/gyraptorESD.png create mode 100644 src/lib/ableitungs_tabelle.typ diff --git a/src/cheatsheets/Analysis1.typ b/src/cheatsheets/Analysis1.typ index fc35741..fd474f3 100644 --- a/src/cheatsheets/Analysis1.typ +++ b/src/cheatsheets/Analysis1.typ @@ -1,5 +1,6 @@ #import "@preview/mannot:0.3.1" +#import "../lib/ableitungs_tabelle.typ" : * #import "../lib/common_rewrite.typ" : * #import "../lib/mathExpressions.typ" : * @@ -519,47 +520,7 @@ // Ableitungstabelle #block([ #set text(size: 7pt) - #table( - align: horizon, - columns: (auto, auto, auto), - table.header([*$F(x)$*], [*$f(x)$*], [*$f'(x)$*]), - row-gutter: 1mm, - inset: 1.4mm, - fill: (x, y) => if calc.rem(x, 3) == 0 { color.hsl(180deg, 89.47%, 88.82%) } - else if calc.rem(x, 3) == 1 { color.hsl(180deg, 100%, 93.14%) } else - { color.hsl(180deg, 81.82%, 95.69%) }, - [$1/(q + x) x^(q+1)$], [$x^q$], [$q x^(q-1)$], - [$ln abs(x)$], [$1/x$], [$-1/x^2$], - [$x ln(a x) - x$], [$ln(a x)$], [$a / x$], - [$2/3 sqrt(a x^3)$], [$sqrt(a x)$], [$a/(2 sqrt(a x))$], - [$e^x$], [$e^x$], [$e^x$], - [$a^x/ln(a)$], [$a^x$], [$a^x ln(a)$], - $-cos(x)$, $sin(x)$, $cos(x)$, - $sin(x)$, $cos(x)$, $-sin(x)$, - $-ln abs(cos(x))$, $tan(x)$, $1/(cos(x)^2)$, - $ln abs(sin(x))$, $cot(x)$, $-1/(sin(x)^2)$, - - [$x arcsin(x) + sqrt(1 - x^2)$], - [$arcsin(x)$], [$1/sqrt(1 - x^2)$], - - [$x arccos(x) - sqrt(1 - x^2)$], - [$arccos(x)$], [$-1/sqrt(1 - x^2)$], - - [$x arctan(x) - 1/2 ln abs(1 + x^2)$], - [$arctan(x)$], [$1/(1 + x^2)$], - - [$x op("arccot")(x) + 1/2 ln abs(1 + x^2)$], - [$op("arccot")(x)$], [$-1/(1 + x^2)$], - - [$x op("arsinH")(x) + sqrt(1 + x^2)$], - [$op("arsinH")(x)$], [$1/sqrt(1 + x^2)$], - - [$x op("arcosH")(x) + sqrt(1 + x^2)$], - [$op("arcosH")(x)$], [$1/sqrt(x^2-1)$], - - [$x op("artanH")(x) + 1/2 ln(1 - x^2)$], - [$op("artanH")(x)$], [$1/(1 - x^2)$], - ) + #ableitungsTabelle ]) // Extremstellen, Krümmung, Monotonie diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index a196e02..bf543fb 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -9,6 +9,7 @@ #import "../lib/schaltungstheorie/opampTable.typ": * #import "../lib/schaltungstheorie/tumCustomSymbols.typ" as tumSymbols +#import "../lib/ableitungs_tabelle.typ" : * #import "../lib/circuit.typ": * #import "../lib/common_rewrite.typ": * #import "../lib/circuit.typ": * @@ -1442,6 +1443,10 @@ #SineCircle() ]) + + #colbreak() + + #ableitungsTabelle ] #pagebreak() @@ -2525,7 +2530,7 @@ u_2 = R_d i_1 &quad u_2 = - 1/R_d u_1 $ ], - [], + [#align(center+horizon, image("../images/schaltungstheorie/knotenpotenzial/gyraptorESD.png", height: 3cm))], [ - Verlustlos - NICHT Reziprok (Antireziprok) @@ -2609,7 +2614,51 @@ - Antireziprok - Symetrisch für $abs(k) = 1$ ], - [$ H = mat(0, -k; -k, 0) quad H' = mat(0, -1/k; -1/k, 0) \ A = mat(-k, 0; 0, 1/k) quad A'= mat(-1/k, 0; 0, k) $] + [$ H = mat(0, -k; -k, 0) quad H' = mat(0, -1/k; -1/k, 0) \ A = mat(-k, 0; 0, 1/k) quad A'= mat(-1/k, 0; 0, k) $], + + [NII], + [#zap.circuit({ + joham.zweitor("NII", (0,0), label: "NII") + }) \ Negativ Imitanz Inverter ], + [#align(center+horizon, scale(100%, zap.circuit({ + import zap : * + import cetz.draw : line, rect, mark, content + + node("A", (-2, 0), fill: false) + node("B", (2, 0), fill: false) + node("C", (-2, 1.5), fill: false) + node("D", (2, 1.5), fill: false) + + node("A1", (-1.2, 0)) + node("B1", ( 1.2, 0)) + node("C1", (-1.2, 1.5)) + node("D1", ( 1.2, 1.5)) + + resistor("R1", "A1", "B1", scale: 0.5, label: (content: $R$, distance: 0.1)) + resistor("R1", "C1", "D1", scale: 0.5, label: (content: $R$, distance: 0.1)) + + joham.norator("N", (0,1.5/2), "D1", scale: 0.5) + wire("A1", (0,1.5/2)) + joham.nullator("N1", "C1", (0,1.5/2), scale: 0.5) + wire("B1", (0,1.5/2)) + wire("A", "A1") + wire("B", "B1") + wire("C", "C1", i: (content: $i_1$, distance: 0.1)) + wire("D", "D1", i: (content: $i_2$, distance: 0.1)) + + joham.voltage("C", "A", $u_1$) + joham.voltage("D", "B", $u_2$) + + + })))], + [ + + + ], + [ + $A_"NII" = mat(0, R; -1/R, 0)$ + ], + ) ] ] diff --git a/src/images/schaltungstheorie/knotenpotenzial/gyraptorESD.png 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sqrt(a x^3)$], [$sqrt(a x)$], [$a/(2 sqrt(a x))$], + [$e^x$], [$e^x$], [$e^x$], + [$a^x/ln(a)$], [$a^x$], [$a^x ln(a)$], + $-cos(x)$, $sin(x)$, $cos(x)$, + $sin(x)$, $cos(x)$, $-sin(x)$, + $-ln abs(cos(x))$, $tan(x)$, $1/(cos(x)^2)$, + $ln abs(sin(x))$, $cot(x)$, $-1/(sin(x)^2)$, + + [$x arcsin(x) + sqrt(1 - x^2)$], + [$arcsin(x)$], [$1/sqrt(1 - x^2)$], + + [$x arccos(x) - sqrt(1 - x^2)$], + [$arccos(x)$], [$-1/sqrt(1 - x^2)$], + + [$x arctan(x) - 1/2 ln abs(1 + x^2)$], + [$arctan(x)$], [$1/(1 + x^2)$], + + [$x op("arccot")(x) + 1/2 ln abs(1 + x^2)$], + [$op("arccot")(x)$], [$-1/(1 + x^2)$], + + [$x op("arsinH")(x) + sqrt(1 + x^2)$], + [$op("arsinH")(x)$], [$1/sqrt(1 + x^2)$], + + [$x op("arcosH")(x) + sqrt(1 + x^2)$], + [$op("arcosH")(x)$], [$1/sqrt(x^2-1)$], + + [$x op("artanH")(x) + 1/2 ln(1 - x^2)$], + [$op("artanH")(x)$], [$1/(1 - x^2)$], +) \ No newline at end of file From baae5924eb2add0ed15732fce1d67376e3cec022 Mon Sep 17 00:00:00 2001 From: levi Date: Mon, 9 Feb 2026 19:06:29 +0100 Subject: [PATCH 35/51] W expanded --- src/cheatsheets/Schaltungstheorie.typ | 10 ++++++++-- 1 file changed, 8 insertions(+), 2 deletions(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index bf543fb..02fae34 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -1125,9 +1125,15 @@ #linebreak() - $P(t) = u(t) i(t)$ + $p(t) = u(t) i(t)$ - $W(t_1, t_2) = integral_(t_1)^(t_2) P(tau) d tau$ + $ + W(t_1, t_2) = integral_(t_1)^(t_2) p(tau) d tau = + integral_(Phi (t_1))^(Phi (t_2)) lambda (Phi') d Phi' = + integral_(q (t_1))^(q (t_2)) chi (q') d q' + $ + + mit $i = lambda (Phi')$, $u = chi (q')$ $W(t_1, t_2) > 0$: Nimmt Energie auf\ $W(t_1, t_2) = 0$: Verlustlos\ From 0f899feee2eacf86f33231e0d4f16b177c29a2cb Mon Sep 17 00:00:00 2001 From: alexander Date: Mon, 9 Feb 2026 20:11:06 +0100 Subject: [PATCH 36/51] Fixed mistakes and adde Zirkulator --- src/cheatsheets/Schaltungstheorie.typ | 61 +++++++++++------- .../knotenpotenzial/circulator.png | Bin 0 -> 70205 bytes .../knotenpotenzial/zirkulatorBild.png | Bin 0 -> 79688 bytes src/images/schaltungstheorie/kw1.png | Bin 0 -> 43714 bytes src/images/schaltungstheorie/kw2.png | Bin 0 -> 52305 bytes src/lib/schaltungstheorie/opampTable.typ | 8 ++- 6 files changed, 43 insertions(+), 26 deletions(-) create mode 100644 src/images/schaltungstheorie/knotenpotenzial/circulator.png create mode 100644 src/images/schaltungstheorie/knotenpotenzial/zirkulatorBild.png create mode 100644 src/images/schaltungstheorie/kw1.png create mode 100644 src/images/schaltungstheorie/kw2.png diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index 02fae34..8d92040 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -1728,7 +1728,6 @@ ] #colbreak() - // Bauelemente #bgBlock(fill: colorEineTore)[ #subHeading(fill: colorEineTore)[Bauelemente] @@ -2013,12 +2012,26 @@ import cetz.draw: * import cetz-plot: * - let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) + let opts = (x-tick-step: none, y-tick-step: none, size: (3, 2), x-label: [u], y-label: [i]) + plot.plot(axis-style: "school-book", ..opts, name: "plot", { - - plot.add(((-1, -1), (1, 1)), style: (stroke: red)) + plot.add(((-1, -1), (2, 2)), style: (stroke: red)) }) + + line((1.7, 0.666 + 0.48), (1.7, 0.666), stroke: (paint: rgb("#009e22"))) + line((1, 0.666), (1.7, 0.666), stroke: (paint: rgb("#009e22"))) + + let offset_x = 0.7 + let offset_y = 0.6 + line((1.7 -offset_x, 0.666 + 0.58-offset_y), (1.7-offset_x, 0.666-offset_y), stroke: (paint: rgb("#009e22"))) + line((0.8-offset_x, 0.666-offset_y), (1.7-offset_x, 0.666-offset_y), stroke: (paint: rgb("#009e22"))) + + content((1.15,0.35), $1$) + content((1.40,0.48), $1$) + content((0.56,-0.1), $Omega$) + content((1.9,0.9), $S$) + })) ], align(left+top)[ @@ -2220,26 +2233,13 @@ ]), [ - ], - [], - - // Tunneldiode - [ - Tunneldiode - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - tunnel("b1", (0, 0), (1., 0), stroke: black, fill: black) - })) - ], - [ - - ], - [ - - ], - [], + ], [], + + // Konkaver Wiederstand + + table.cell(colspan: 4, image("../images/schaltungstheorie/kw1.png", height: 1cm)), + table.cell(colspan: 4, image("../images/schaltungstheorie/kw2.png", height: 1cm)), ); ] ] @@ -2533,7 +2533,7 @@ content((0.8, -0.8), text([Input $cal(F)$], fill: rgb("#00318b"))) }) $ u_1 = - R_d i_2 &quad i_1 = 1/R_d u_2 \ - u_2 = R_d i_1 &quad u_2 = - 1/R_d u_1 + u_2 = R_d i_1 &quad i_2 = - 1/R_d u_1 $ ], [#align(center+horizon, image("../images/schaltungstheorie/knotenpotenzial/gyraptorESD.png", height: 3cm))], @@ -2665,12 +2665,23 @@ $A_"NII" = mat(0, R; -1/R, 0)$ ], + [Idealer Zirkulator \ (Drei-Tor)], + [#image("../images/schaltungstheorie/knotenpotenzial/zirkulatorBild.png", height: 3cm)], + 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6270f092ef68ecd6be1285284cd478a0c0ea720e Mon Sep 17 00:00:00 2001 From: levi Date: Mon, 9 Feb 2026 20:23:40 +0100 Subject: [PATCH 37/51] stuff --- src/cheatsheets/Schaltungstheorie.typ | 59 +++++++++++---------------- 1 file changed, 24 insertions(+), 35 deletions(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index 8d92040..02fae34 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -1728,6 +1728,7 @@ ] #colbreak() + // Bauelemente #bgBlock(fill: colorEineTore)[ #subHeading(fill: colorEineTore)[Bauelemente] @@ -2012,26 +2013,12 @@ import cetz.draw: * import cetz-plot: * - let opts = (x-tick-step: none, y-tick-step: none, size: (3, 2), x-label: [u], y-label: [i]) - + let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) plot.plot(axis-style: "school-book", ..opts, name: "plot", { - plot.add(((-1, -1), (2, 2)), style: (stroke: red)) + + plot.add(((-1, -1), (1, 1)), style: (stroke: red)) }) - - line((1.7, 0.666 + 0.48), (1.7, 0.666), stroke: (paint: rgb("#009e22"))) - line((1, 0.666), (1.7, 0.666), stroke: (paint: rgb("#009e22"))) - - let offset_x = 0.7 - let offset_y = 0.6 - line((1.7 -offset_x, 0.666 + 0.58-offset_y), (1.7-offset_x, 0.666-offset_y), stroke: (paint: rgb("#009e22"))) - line((0.8-offset_x, 0.666-offset_y), (1.7-offset_x, 0.666-offset_y), stroke: (paint: rgb("#009e22"))) - - content((1.15,0.35), $1$) - content((1.40,0.48), $1$) - content((0.56,-0.1), $Omega$) - content((1.9,0.9), $S$) - })) ], align(left+top)[ @@ -2233,13 +2220,26 @@ ]), [ - ], [], - + ], + [], - // Konkaver Wiederstand + // Tunneldiode + [ + Tunneldiode + #scale(x: 100%, y: 100%, zap.circuit({ + import zap: * + import cetz.draw: content, line + tunnel("b1", (0, 0), (1., 0), stroke: black, fill: black) + })) + ], + [ + + ], + [ + + ], + [], - table.cell(colspan: 4, image("../images/schaltungstheorie/kw1.png", height: 1cm)), - table.cell(colspan: 4, image("../images/schaltungstheorie/kw2.png", height: 1cm)), ); ] ] @@ -2533,7 +2533,7 @@ content((0.8, -0.8), text([Input $cal(F)$], fill: rgb("#00318b"))) }) $ u_1 = - R_d i_2 &quad i_1 = 1/R_d u_2 \ - u_2 = R_d i_1 &quad i_2 = - 1/R_d u_1 + u_2 = R_d i_1 &quad u_2 = - 1/R_d u_1 $ ], [#align(center+horizon, image("../images/schaltungstheorie/knotenpotenzial/gyraptorESD.png", height: 3cm))], @@ -2665,23 +2665,12 @@ $A_"NII" = mat(0, R; -1/R, 0)$ ], - [Idealer Zirkulator \ (Drei-Tor)], - [#image("../images/schaltungstheorie/knotenpotenzial/zirkulatorBild.png", height: 3cm)], - [#image("../images/schaltungstheorie/knotenpotenzial/circulator.png", height: 3cm)], - [ - - NICHT Reziprok - - Verlustlos - ], - [$ G = mat(0, R, -R; -R, 0, R; R, -R, 0) quad quad quad G = mat(0, G, -G; -G, 0, G; G, -G, 0) \ - u_1 = (i_2 - i_3) R \ - u_2 = (i_3 - i_1) R \ - u_3 = -(u_1 + u_2) $] - ) ] ] // Knoten Spannungs Analyse +#pagebreak() // Tor Eigenschaften #bgBlock(fill: colorEigenschaften, width: 100%)[ #subHeading(fill: colorEigenschaften)[Tor Eigenschaften] From fd2172a751563986c6e83fd95fdcd4e2c86fb244 Mon Sep 17 00:00:00 2001 From: alexander Date: Mon, 9 Feb 2026 20:35:23 +0100 Subject: [PATCH 38/51] Revert "Fixed mistakes and adde Zirkulator" This reverts commit 0f899feee2eacf86f33231e0d4f16b177c29a2cb. --- .../knotenpotenzial/circulator.png | Bin 70205 -> 0 bytes .../knotenpotenzial/zirkulatorBild.png | Bin 79688 -> 0 bytes src/images/schaltungstheorie/kw1.png | Bin 43714 -> 0 bytes src/images/schaltungstheorie/kw2.png | Bin 52305 -> 0 bytes src/lib/schaltungstheorie/opampTable.typ | 8 +------- 5 files changed, 1 insertion(+), 7 deletions(-) delete mode 100644 src/images/schaltungstheorie/knotenpotenzial/circulator.png delete mode 100644 src/images/schaltungstheorie/knotenpotenzial/zirkulatorBild.png delete mode 100644 src/images/schaltungstheorie/kw1.png delete mode 100644 src/images/schaltungstheorie/kw2.png diff --git 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Mon Sep 17 00:00:00 2001 From: alexander Date: Mon, 9 Feb 2026 20:39:19 +0100 Subject: [PATCH 39/51] Reapply "Fixed mistakes and adde Zirkulator" This reverts commit fd2172a751563986c6e83fd95fdcd4e2c86fb244. --- .../knotenpotenzial/circulator.png | Bin 0 -> 70205 bytes .../knotenpotenzial/zirkulatorBild.png | Bin 0 -> 79688 bytes src/images/schaltungstheorie/kw1.png | Bin 0 -> 43714 bytes src/images/schaltungstheorie/kw2.png | Bin 0 -> 52305 bytes src/lib/schaltungstheorie/opampTable.typ | 8 +++++++- 5 files changed, 7 insertions(+), 1 deletion(-) create mode 100644 src/images/schaltungstheorie/knotenpotenzial/circulator.png create mode 100644 src/images/schaltungstheorie/knotenpotenzial/zirkulatorBild.png create mode 100644 src/images/schaltungstheorie/kw1.png create mode 100644 src/images/schaltungstheorie/kw2.png diff --git a/src/images/schaltungstheorie/knotenpotenzial/circulator.png b/src/images/schaltungstheorie/knotenpotenzial/circulator.png new file mode 100644 index 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zw}i~sboyu7>fds6gd^#;l@0f#k|^GRw`-L{ktB}qC_2epeBHu(6(q8`Nk)(StnsI`E+x8y{Da`$$pX9nmE#+0pLr_I`J7FNWm$K6@?wHIxnQzyJ55Q%=>j z{@cTBU~_Zx7T)sM7)nw#yXna~kQ%7eu)kN9P70P16N$KIZh;QH%ThTU4mOGSyLa!t zC##}gT0r^O{~H^VXZH(N(TM2T>Acsk2=E=e_ z9A_DU4$sSQlUQ6_{LtfhHY$2^lwwUuLnB>F-KZ3(OTzvR%ICj9;B?YEbVjh5jjsNf zYc{Xdayu3d5X`jiPUW^0{9LR?)44LDdAU#=^2tZq^vSQ2%?hqRTkz{7{%CMo*6TuH zV`FRYi0)1rB$Z9xJw;qUcT>{VE~TlizWL?%x_b2!9JBk71=!aaJS-?$$v|*pEE4|t z3KKJnu}?78@6cZK#jVS0YiFd&#!<+l@dFf8#y_!ug8Kh5UeCPqN1wi%p{Xi^3|U-QMyNzk$M^pMDN;2* literal 0 HcmV?d00001 diff --git a/src/lib/schaltungstheorie/opampTable.typ b/src/lib/schaltungstheorie/opampTable.typ index ebb512e..4612a0e 100644 --- a/src/lib/schaltungstheorie/opampTable.typ +++ b/src/lib/schaltungstheorie/opampTable.typ @@ -267,5 +267,11 @@ $u_"out" = - R_0/R_1 u_"in"$, $u_"out" = (1 + R_0 / R_1) u_"in"$, $$, - $u_"in" = -R_L i_"in"$ + $u_"in" = -R_L i_"in"$, + [], + [VCVS], + [VCVS], + [VCVS], + [], + [CCVS] ) \ No newline at end of file From e0eb088a6ac9443785868760470f6955ad3ce55f Mon Sep 17 00:00:00 2001 From: alexander Date: Mon, 9 Feb 2026 20:39:22 +0100 Subject: [PATCH 40/51] Revert "stuff" This reverts commit 6270f092ef68ecd6be1285284cd478a0c0ea720e. --- src/cheatsheets/Schaltungstheorie.typ | 61 ++++++++++++++++----------- 1 file changed, 36 insertions(+), 25 deletions(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index 02fae34..8d92040 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -1728,7 +1728,6 @@ ] #colbreak() - // Bauelemente #bgBlock(fill: colorEineTore)[ #subHeading(fill: colorEineTore)[Bauelemente] @@ -2013,12 +2012,26 @@ import cetz.draw: * import cetz-plot: * - let opts = (x-tick-step: none, y-tick-step: none, size: (2, 1), x-label: [u], y-label: [i]) + let opts = (x-tick-step: none, y-tick-step: none, size: (3, 2), x-label: [u], y-label: [i]) + plot.plot(axis-style: "school-book", ..opts, name: "plot", { - - plot.add(((-1, -1), (1, 1)), style: (stroke: red)) + plot.add(((-1, -1), (2, 2)), style: (stroke: red)) }) + + line((1.7, 0.666 + 0.48), (1.7, 0.666), stroke: (paint: rgb("#009e22"))) + line((1, 0.666), (1.7, 0.666), stroke: (paint: rgb("#009e22"))) + + let offset_x = 0.7 + let offset_y = 0.6 + line((1.7 -offset_x, 0.666 + 0.58-offset_y), (1.7-offset_x, 0.666-offset_y), stroke: (paint: rgb("#009e22"))) + line((0.8-offset_x, 0.666-offset_y), (1.7-offset_x, 0.666-offset_y), stroke: (paint: rgb("#009e22"))) + + content((1.15,0.35), $1$) + content((1.40,0.48), $1$) + content((0.56,-0.1), $Omega$) + content((1.9,0.9), $S$) + })) ], align(left+top)[ @@ -2220,26 +2233,13 @@ ]), [ - ], - [], - - // Tunneldiode - [ - Tunneldiode - #scale(x: 100%, y: 100%, zap.circuit({ - import zap: * - import cetz.draw: content, line - tunnel("b1", (0, 0), (1., 0), stroke: black, fill: black) - })) - ], - [ - - ], - [ - - ], - [], + ], [], + + // Konkaver Wiederstand + + table.cell(colspan: 4, image("../images/schaltungstheorie/kw1.png", height: 1cm)), + table.cell(colspan: 4, image("../images/schaltungstheorie/kw2.png", height: 1cm)), ); ] ] @@ -2533,7 +2533,7 @@ content((0.8, -0.8), text([Input $cal(F)$], fill: rgb("#00318b"))) }) $ u_1 = - R_d i_2 &quad i_1 = 1/R_d u_2 \ - u_2 = R_d i_1 &quad u_2 = - 1/R_d u_1 + u_2 = R_d i_1 &quad i_2 = - 1/R_d u_1 $ ], [#align(center+horizon, image("../images/schaltungstheorie/knotenpotenzial/gyraptorESD.png", height: 3cm))], @@ -2665,12 +2665,23 @@ $A_"NII" = mat(0, R; -1/R, 0)$ ], + [Idealer Zirkulator \ (Drei-Tor)], + [#image("../images/schaltungstheorie/knotenpotenzial/zirkulatorBild.png", height: 3cm)], + [#image("../images/schaltungstheorie/knotenpotenzial/circulator.png", height: 3cm)], + [ + - NICHT Reziprok + - Verlustlos + ], + [$ G = mat(0, R, -R; -R, 0, R; R, -R, 0) quad quad quad G = mat(0, G, -G; -G, 0, G; G, -G, 0) \ + u_1 = (i_2 - i_3) R \ + u_2 = (i_3 - i_1) R \ + u_3 = -(u_1 + u_2) $] + ) ] ] // Knoten Spannungs Analyse -#pagebreak() // Tor Eigenschaften #bgBlock(fill: colorEigenschaften, width: 100%)[ #subHeading(fill: colorEigenschaften)[Tor Eigenschaften] From 7275984ab2fd7f8fff8f93ee82714a4cb11c59ed Mon Sep 17 00:00:00 2001 From: alexander Date: Mon, 9 Feb 2026 20:55:56 +0100 Subject: [PATCH 41/51] Swapped mayer Norton/Helmol Thevenin --- src/cheatsheets/Schaltungstheorie.typ | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index 8d92040..3cb82eb 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -372,10 +372,10 @@ inset: 3mm, align(center, [ *$u$-gesteuert* \ - Helmholz / Thévenin + Mayer / Norton ]), align(center, [ *$i$-gesteuert* \ - Mayer / Norton + Helmholz / Thévenin ]), [ From ffdcf7e0e8aa3088194f609377f4c3e48a76a15c Mon Sep 17 00:00:00 2001 From: levi Date: Mon, 9 Feb 2026 21:52:17 +0100 Subject: [PATCH 42/51] moore eintore 2 --- src/cheatsheets/Schaltungstheorie.typ | 41 +++++++++++++++++++++++---- 1 file changed, 35 insertions(+), 6 deletions(-) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index 3cb82eb..91ff301 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -2077,7 +2077,13 @@ }) })) ], - [], + align(left+top)[ + - Verlustlos + - Streng linear + - Linear + - Quellenfrei + - Reaktiv + ], // Kapazität [ @@ -2111,7 +2117,13 @@ }) })) ], - [], + align(left+top)[ + - Verlustlos + - Streng linear + - Linear + - Quellenfrei + - Reaktiv + ], table.hline(), @@ -2129,7 +2141,7 @@ ], align(horizon+center, [ $i=0$ falls $u<0$\ - $i>=0$. falls $u=0$ + $i>=0$ falls $u=0$ ]), [ /* @@ -2159,7 +2171,14 @@ }) })) ], - [], + align(left+top)[ + - Verlustlos + - Passiv + - Quellenfrei + - Gepolt + + + ], // reale/pn Diode [ @@ -2186,7 +2205,13 @@ plot.plot(axis-style: "school-book", ..opts, data, name: "plot") })) ], - [], + align(left+top)[ + - Quellenfrei + - Gepolt + - Passiv + - u-gest. + - i-gest. + ], // Photodiode [ @@ -2216,7 +2241,11 @@ }) })) ], - [], + align(left+top)[ + - Gepolt + //- u-gest. + - i-gest. + ], // Zenerdiode [ From 47ba4fe26748b267ace88be0dd1e3f8e5054c4eb Mon Sep 17 00:00:00 2001 From: levi Date: Mon, 9 Feb 2026 22:06:38 +0100 Subject: [PATCH 43/51] mehr dual --- src/cheatsheets/Schaltungstheorie.typ | 3 +++ 1 file changed, 3 insertions(+) diff --git a/src/cheatsheets/Schaltungstheorie.typ b/src/cheatsheets/Schaltungstheorie.typ index 91ff301..1fd8f14 100644 --- a/src/cheatsheets/Schaltungstheorie.typ +++ b/src/cheatsheets/Schaltungstheorie.typ @@ -292,6 +292,9 @@ $"Parallel" --> "Seriell"$, $"Seriell" --> "Parallel"$, + $"U-quelle" --> "I-quelle"\ "(polung = const.)"$, + $"I-quelle" --> "U-quelle"\ "(polung = const.)"$, + table.cell(colspan: 2)[ *Dualwandlung: Steurende & Ausgangs Größe* $ From 0bd2473b5ca869e4a47524390f02d155781398a9 Mon Sep 17 00:00:00 2001 From: alexander Date: Tue, 10 Feb 2026 23:06:36 +0100 Subject: [PATCH 44/51] Extend CT --- src/cheatsheets/CT.typ | 228 +++++++++++++++++++++++++++- src/images/ct/betragUndVorzeich.png | Bin 0 -> 96426 bytes src/images/ct/einerKomplement.png | Bin 0 -> 95922 bytes src/images/ct/zweierKomplement.png | Bin 0 -> 95984 bytes src/lib/bit_fields.typ | 40 +++++ 5 files changed, 265 insertions(+), 3 deletions(-) create mode 100644 src/images/ct/betragUndVorzeich.png create mode 100644 src/images/ct/einerKomplement.png create mode 100644 src/images/ct/zweierKomplement.png create mode 100644 src/lib/bit_fields.typ diff --git a/src/cheatsheets/CT.typ b/src/cheatsheets/CT.typ index ef4e18c..253af4b 100644 --- a/src/cheatsheets/CT.typ +++ b/src/cheatsheets/CT.typ @@ -1,5 +1,6 @@ #import "../lib/styles.typ" : * #import "../lib/common_rewrite.typ" : * +#import "../lib/bit_fields.typ" : * #import "@preview/cetz:0.4.2" #set page( @@ -24,8 +25,8 @@ #let Allgemein = color.hsl(105.13deg, 92.13%, 75.1%) #let colorProgramming = color.hsl(330.19deg, 100%, 68.43%) #let colorNumberSystems = color.hsl(202.05deg, 92.13%, 75.1%) -// #let colorVR = color.hsl(280deg, 92.13%, 75.1%) -// #let colorAbbildungen = color.hsl(356.92deg, 92.13%, 75.1%) +#let colorMMIX = color.hsl(280deg, 92.13%, 75.1%) +#let colorRandomShit = color.hsl(356.92deg, 92.13%, 75.1%) // #let colorGruppen = color.hsl(34.87deg, 92.13%, 75.1%) @@ -48,7 +49,98 @@ ] #bgBlock(fill: colorNumberSystems)[ - #subHeading(fill: colorNumberSystems)[Einer-Kompilment, Zweier-Kompliment, Float (IEEE 754)] + #subHeading(fill: colorNumberSystems)[Fixed Point] + + #table( + columns: 17, + fill: (x, y) => if calc.rem(x, 2) == 1 { tableFillLow } else { tableFillHigh }, + + .. for i in range(0,17) { + ([$2^#i$],) + }, + .. for i in range(0,17) { + ($#calc.pow(2,i)$,) + } + ) + + #columns(2, [ + *Vorzeichen und Betrag:* + + #grid( + columns: (2fr, 1fr), + [ + $x = (-1)^"sign-bit" dot "Betrag"$ + + $0 -> "positiv", 1 -> "negativ"$ + + Range: \ $(-2^(n-1) - 1) dot 2^r$ bis $(2^(n-1) - 1) dot 2^r$ + + Achtung: $plus.minus 0$ + ], + image("../images/ct/betragUndVorzeich.png", width: 2cm) + ) + + #line(length: 100%, stroke: (thickness: 0.2mm)) + + *Einer-Komplement* + + #grid( + columns: (2fr, 1fr), + [ + $x = (-1)^"sign-bit" dot "Betrag"$ + + $0 -> "positiv normaler Betrag"$ + + $1 -> "negativ INVERT. Betrag"$ + + Range: \ + $(-2^(n-1) - 1) dot 2^r$ bis $(2^(n-1) - 1) dot 2^r$ + + Achtung: $plus.minus 0$ + ], + image("../images/ct/einerKomplement.png", width: 2cm) + ) + #colbreak() + + *Zweier-Komplement* + + #grid( + columns: (2fr, 1fr), + [ + $x = (-1)^"sign-bit" dot "Betrag"$ + + $0 -> "positiv"$ + + $1 -> "negativ"$ + + Range: \ $(-2^(n-1)) dot 2^r$ bis $(2^(n-1) - 1) dot 2^r$ + + Positiv: Normal Binär Kodierung + + Negativ: #raw("Invertiert(Binär) + 1") + + ], + image("../images/ct/zweierKomplement.png", width: 2cm) + ) + + #line(length: 100%, stroke: (thickness: 0.2mm)) + + *Radix / Fixed Point* + + $r = 0$ Normal Falle, nix änder sich + + $r > 0$ : Komma nach Rechts und Nullen auffüllen \ + Bsp. $r = 3 quad ->$ #raw("xxxxxxx000.") + + $r < 0$ : Komma nach Links verschieben \ + Bsp: $r = -4 quad ->$ #raw("xxxxx.xxxx") + + ]) + ] + + #colbreak() + #bgBlock(fill: colorNumberSystems)[ + #subHeading(fill: colorNumberSystems)[Float (IEEE 754)] *Float (IEEE 754)* @@ -133,11 +225,46 @@ content((cell_size*(total_bits), -0.2), anchor: "south", raw(str(0)), angle: 90deg) }) + + $x = (-1)^"sign" dot #raw("1.[mantisse]") dot 2^(("exponent" - k))$ + + #grid( + columns: (auto, auto), + column-gutter: 5mm, + row-gutter: 2mm, + $"float32"&, k = 127 &= #raw(" 111 1111") "(7 x Einser)" \ + "float64"&, k = 1023 &= #raw("11 1111 1111") "(10 x Einser)"$ + ) + + *Spezial Cases* + #table( + columns: (auto, auto), + [$0$], [exponent = 0 \ mantisse = 0], + [$plus.minus infinity$], [exponent = alle 1 \ mantisse = 0], + [NaN], [exponent = alle 1 \ mantisse > 0], + [denormalisierte Float], [exponent = 0 \ mantisse > 0], + [normalisierter Float], [0 < exponent < 255/2047] + ) ] #bgBlock(fill: colorProgramming)[ #subHeading(fill: colorProgramming)[C] + #table( + columns: (auto, auto, auto), + fill: (x, y) => if calc.rem(y, 2) == 0 { tableFillLow } else { tableFillHigh }, + + [*C-Type*], [*min size*], [*typ. size*], + raw("char"), raw("1 byte"), raw("1 byte"), + raw("short (int)"), raw("2 byte"), raw("2 byte"), + raw("int"), raw("2 byte"), raw("4 byte"), + raw("long (int)"), raw("4 byte"), raw("8 byte"), + raw("long long"), raw("4 byte"), raw("8 byte"), + raw("float"), raw("4 byte"), raw("4 byte"), + raw("double"), raw("8 byte"), raw("8 byte"), + + ) + #table( columns: (auto, 1fr), fill: white, @@ -151,4 +278,99 @@ ] ) ] + + #bgBlock(fill: colorProgramming)[ + #subHeading(fill: colorProgramming)[#raw("scanf/printf") Format Specifier] + + #columns(2)[ + *printf* + #table( + columns: (auto, auto), + fill: (x, y) => if calc.rem(y, 2) == 0 { tableFillLow } else { tableFillHigh }, + raw("%s"), [*String*], + raw("%d"), [*Decimal: #raw("int/short/long"))*], + raw("%f"), [*Float*], + raw("%f"), [*Float*], + raw("%lf"), [*Double*], + raw("%x"), [* Hexdecimal #raw("int/short/long")*], + ) + + Allgemeiner Syntax: #raw("%[flags][width][.precision]type") + + Flags: + - #raw("0") Prepend With left aligned + - #raw("-") Left-aligned + + #table(columns: (auto, auto), + fill: (x, y) => if calc.rem(y, 2) == 0 { tableFillLow } else { tableFillHigh }, + raw("\\n"), [New Line], + raw("\\t"), [Tab], + raw("\\0"), [Null Terminator], + raw("\\\\"), [#raw("\\")], + raw("\\\""), [#raw("\"")], + ) + + #colbreak() + + *scanf* + #table( + columns: (auto, auto), + fill: (x, y) => if calc.rem(y, 2) == 0 { tableFillLow } else { tableFillHigh }, + raw("%[size of String]s"), [*String* \ Size of String (without the #raw("\\0")) \ Terminates with Whitespace], + raw("%i"), [*#raw("int")*], + raw("%f"), [*#raw("float")*], + raw("%lf"), [*#raw("double")*], + raw("%x"), [*#raw("int")* als Hexadezimal], + raw("%c"), [*#raw("char")* ], + ) + + #raw("fgets(char * s, int count, stdin)") + ] + ] + + #bgBlock(fill: colorMMIX)[ + #subHeading(fill: colorMMIX)[MMIX] + - $32$ Speziel Register + - $256$ Allzwickregister + - $2^64$ Speicher + + Wort: $64$ Bit + + ] + + #bgBlock(fill: colorRandomShit)[ + #subHeading(fill: colorRandomShit)[Register Register Magista] + + *Zwei-Address-Maschine:* $quad X <-- X dot.o Y$, Parameter: $(X,Y)$ \ + *Drei-Address-Maschine:* $quad X <-- Y dot.o Z$, Parameter: $(X,Y,Z)$ \ + *Ein-Address-Maschine:* $quad "ACC" <-- X$, Parameter: $(X)$ + + *Register-Speicher-Architekture:* \ + Operanden können Register und Addressen sein + + *Register-Register-Archiektur/Load-Store-Architektur* \ + Operanden nur Register. Extra Befehle fürs Laden aus Speicher + + + *CISC*: Complex Instruction Set Architecture + - Eine Befehl kann viel $->$ Wenige Befehle + - Befehlslänge Variable (meistens) + - z.B. x86 + + *RISC*: Reduced Instruction Set Architecture + - Eine Befehl kann wenig $->$ Viel Befehle + - Befehlslänge fix (meistens) + - z.B. 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b/src/lib/bit_fields.typ new file mode 100644 index 0000000..464aa7f --- /dev/null +++ b/src/lib/bit_fields.typ @@ -0,0 +1,40 @@ +#import "@preview/cetz:0.4.2" + +#let bitFieldField(name, color, total) = { + (name: name, color: color, total: total) +} + +#let bitFieldGreen = rgb("#8fff57") +#let bitFieldYellow = rgb("#ffe057") +#let bitFieldBlue = rgb("#57a5ff") +#let bitFieldRed = rgb("#ff5757") + +#let bitField(fields: (), BitHeight: 0.5, BitWidth: 0.25) = { + cetz.canvas({ + import cetz.draw : * + let pos = 0; + + let total = 0; + + for f in fields { + total += f.at("total") + } + + for f in fields { + content(((pos + 0.5)*BitWidth, -0.1), raw(str(total - pos - 1)), angle: 90deg, anchor: "east") + + for i in range(f.at("total")) { + rect(((pos + i)*BitWidth, 0), ((pos+i+1)*BitWidth, BitHeight), fill: f.at("color", default: bitFieldBlue)) + content(((pos+i+0.5)*BitWidth, BitHeight*0.5), raw("0")) + } + + content(((pos*BitWidth + f.at("total")*BitWidth*0.5), BitHeight + 0.2), f.at("name"), anchor: f.at("anchor", default: "mid")) + + pos += f.at("total") + + content(((pos - 0.5)*BitWidth, -0.1), raw(str(total - pos)), angle: 90deg, anchor: "east") + + } + }) +} + From b90683421e48938bae3f1f472bedcc55ea405b6c Mon Sep 17 00:00:00 2001 From: alexander Date: Wed, 11 Feb 2026 15:27:23 +0100 Subject: [PATCH 45/51] added calling convesions --- src/cheatsheets/CT.typ | 69 +++++++++++++++++++++++++++++++++++++++++- 1 file changed, 68 insertions(+), 1 deletion(-) diff --git a/src/cheatsheets/CT.typ b/src/cheatsheets/CT.typ index 253af4b..9e57927 100644 --- a/src/cheatsheets/CT.typ +++ b/src/cheatsheets/CT.typ @@ -336,7 +336,74 @@ Wort: $64$ Bit - ] + *Calling Convensions* + + #cetz.canvas({ + import cetz.draw : * + + let cellHeight = 0.4 + let cellWidth = 2 + + let c(y, c, x: 0, number: "") = { + rect((x, cellHeight*y), (x + cellWidth, cellHeight*(y+1)), fill: white) + content((x+ cellWidth/2, cellHeight*(y+0.5)), c) + content((x - 0.2, cellHeight*(y+0.5)), number, anchor: "mid-east") + } + + c(0, "3.Param", number: raw("0x3FFFFFFFFFFFFFF8")) + c(1, "2.Param", number: raw("0x3FFFFFFFFFFFFFF0")) + c(2, "1.Param", number: raw("0x3FFFFFFFFFFFFFE8")) + c(3, "Sicherung $1", number: raw("0x3FFFFFFFFFFFFFE0")) + c(4, "Sicherung $2", number: raw("0x3FFFFFFFFFFFFFD8")) + + c(0, "Rückgabe wert", x: cellWidth) + }) + + #colbreak() + +#text(rgb("#1a00aa"))[ +*1. (Aufrufer) Parameter auf Stack ablegen*\ +#raw("SUB :SP,:SP,n*8 +STO $x0,:SP,0*8 +STO $x1,:SP,1*8 +... +STO $xn,:SP,n*8") + +*2. (Aufrufer) Funktions Aufruf*\ +#raw("GO $0,:Fkt") +] + +#text(rgb("#aa0000"))[ +*3. (Funktion) Sicherung der Register*\ +#raw("SUB :SP,:SP,n*8 +STO $y0,:SP,0*8 +STO $y1,:SP,1*8 +... +STO $yn,:SP,n*8") + +*4. (Funktion) Funktions Code*\ + +*5. (Funktion) Schreiben des Rückgabewerts*\ +#raw(" +STO $r,:SP,m*8 +") + +*6. (Funktion) Wiederherstellung der Register*\ +#raw("LDO $x0,:SP, 0*8 + k +LDO $x1,:SP, 1*8 + k +... +LDO $xn,:SP, n*8 + k +") + +*7. (Funktion) Rücksprung*\ +] + +#text(rgb("#1a00aa"))[ +*8. (Aufrufer) Lesen des Rückgabewerts*\ + + +] +] #bgBlock(fill: colorRandomShit)[ #subHeading(fill: colorRandomShit)[Register Register Magista] From 6c99d14825f6dc69ff7db37d960c207d23c40243 Mon Sep 17 00:00:00 2001 From: alexander Date: Fri, 13 Feb 2026 14:03:07 +0100 Subject: [PATCH 46/51] Finished analysis --- src/cheatsheets/Analysis1.typ | 149 ++++++++++++++++++++++------------ 1 file changed, 99 insertions(+), 50 deletions(-) diff --git a/src/cheatsheets/Analysis1.typ b/src/cheatsheets/Analysis1.typ index fd474f3..9a8b835 100644 --- a/src/cheatsheets/Analysis1.typ +++ b/src/cheatsheets/Analysis1.typ @@ -76,30 +76,19 @@ *Binomische Formel*\ $(a + b)^n = sum^(n)_(k=0) binom(n,k) a^(n-k) b^k $ \ ], - [ - *Bekannte Werte* \ - $e approx 2.71828$ ($2 < e < 3$) \ - $pi approx 3.14159$ ($3 < pi < 4$) - ], + [ *Gaußklammer*: \ $floor(x) = text("floor")(x)$ \ $ceil(x) = text("ceil")(x)$ \ ], [ - *Fakultäten* $0! = 1! = 1$ \ ], - [ - *Mitternachtsformel* - $x_(1,2) = (-b plus.minus sqrt(b^2 + 4a c))/(2a)$ - ], - [ - *Binomische Formel*\ - $(a + b)^2 = a^2 + 2a b + b^2$\ - $(a - b)^2 = a^2 - 2a b + b^2$\ - $(a + b)(a - b) = a^2 - b^2$\ - ] ) + + $bold("Fakultäten") 0! = 1! = 1\ + e approx 2.71828 quad quad quad pi approx 3.14159 + $ ] // Complex Zahlen @@ -144,22 +133,17 @@ gutter: 2mm, columns: (auto, auto, auto), $cos^2(x) = (1 + cos(2x))/2$, - $sin^2(x) = (1 - cos(2x))/2$, - $cos(-x) = cos(x)$, - $sin(-x) = -sin(x)$, - grid.cell(colspan: 2, $cos^2(x) + sin^2(x) = 1$) + $sin^2(x) = (1 - cos(2x))/2$ ) - Subsitution mit Hilfsvariable + $tan(x)=sin(x)/cos(x) = -cot(x + pi/2)$ + + $cot(x)=cos(x)/sin(x)=-tan(x + pi/2)$ #grid( gutter: 5mm, row-gutter: 3mm, columns: (auto, auto), - [$tan(x)=sin(x)/cos(x)$], - [$cot(x)=cos(x)/sin(x)$], - [$tan(x)=-cot(x + pi/2)$], - [$cot(x)=-tan(x + pi/2)$], [$cos(x - pi/2) = sin(x)$], [$sin(x + pi/2) = cos(x)$], @@ -377,13 +361,13 @@ *Reihendarstellungen* #grid( - columns: (1fr, 1fr), + columns: (1fr), gutter: 3mm, row-gutter: 3mm, - $e^x = limits(sum)_(n=0)^infinity (x^n)/(n!)$, - $ln(x) = limits(sum)_(n=0)^infinity (-1)^n x^(n+1)$, - $sin(x) = limits(sum)_(n=0)^infinity (-1)^n (z^(2n+1))/((2n + 1)!)$, - $cos(x) = limits(sum)_(n=0)^infinity (-1)^n (z^(2n))/((2n)!)$ + $e^x = limits(sum)_(n=0)^m (x^n)/(n!) + O(x^(m+1))$, + $ln(x) = limits(sum)_(n=0)^m (-1)^n x^(n+1) + O(x^(m+1))$, + $sin(x) = limits(sum)_(n=0)^m (-1)^n (z^(2n+1))/((2n + 1)!) + O(x^(2m + 3))$, + $cos(x) = limits(sum)_(n=0)^m (-1)^n (z^(2n))/((2n)!) + O(x^(2m + 2))$ ) ] @@ -446,7 +430,7 @@ *Allgemein* $f(x)$ ist stetig wenn: \ - $ limits(lim)_(x->x_0-) f(x) = limits(lim)_(x->x_0+) f(x) = f(x_0) $ \ + $limits(lim)_(x->x_0-) f(x) = limits(lim)_(x->x_0+) f(x) = f(x_0)$ \ $x in DD$ Beachten! Definitionslücken $!=$ unstätig \ Definition gilt auch für $I subset RR$ @@ -613,12 +597,25 @@ *Subsitution* - $integral_(x_0)^(x_1) f\(underbrace(g(x), "t")\) dot g'(x) d x$ + $integral_(x_0)^(x_1) f\(underbrace(g(x), "t")\) d x = integral_g(x_0)^g(x_1) f(t) dot <1/(g'(x)) d t$ + + 1. Ersetzung: $t := g(x)$ 2. Umformen: - $(d y)/(d x) = g'(x)$ - 3. $x$-kürzen sich weg + $(d t)/(d x) = g'(x)$ + + *Weierstrass Subsitution/Brechstange* \ + Subsitution: $t = tan(x/2)$ + + #grid( + columns: (1fr, 1fr), + row-gutter: 2.8mm, + $d x = 2/(1+t^2) d t$, + $sin(x) = 2t / (1 + t^2)$, + $tan(x) = (2t)/(1-t^2)$, + $cos(x) = (1-t^2) / (1 + t^2)$, + ) ]) #bgBlock(fill: colorIntegral, [ @@ -653,11 +650,10 @@ *Subsitution* - $integral_(x_0)^(x_1) f\(underbrace(g(x), "t")\) dot 1/(g'(x)) d x$ + $integral_(x_0)^(x_1) f\(underbrace(g(x), "t")\) dot 1/(g'(x)) d t$ - 1. Ersetzung: $ d x := d t dot g'(x)$ und $t := g(x)$ + 1. Ersetzung: $ d x := 1/g'(x) dot d t$ und $t := g(x)$ 2. Grenzen: $t_0 = g(x_0)$, $t_1 = g(x_1)$ - 3. $x$-kürzen sich weg *Absolute "Konvergenz"* \ Wenn $g(x)$ konvergent, @@ -680,20 +676,13 @@ 5. $A,B,...$ : Nst einsetzen, dann Koeffizientenvergleich 6. *Intergral wiederzusammen setzen $+c$* - 7. Summen teile Integrieren - - $delta = 4a - b^2$ - #grid(columns: (auto, auto), - row-gutter: 2mm, - column-gutter: 2mm, - $integral 1/(x - x_0)$, $ln abs(x - x_0)$, - $integral 1/((x - x_0)^n)$, $-1/((n-1)(x-x_0)^(n-1))$, - $integral 1/(x^2 + b x + c)$, $2/sqrt(delta) arctan((2x + b)/sqrt(delta))$, - $integral 1/((x^2 + b x + c)^n)$, $(2x + b)/((n-1)(sigma)(x^2+b x +c)^(n-1)) + \ - (2(2n-3))/((n-1)(delta)) + (C ) - $, - ) + 7. *Summen teile Integrieren* + $integral 1/(x-a) d x = ln(x - a) + c\ + integral 1/(x-a)^n d x = - 1/(n-1) 1/(x - a)^(n-1) + c quad "für" n >= 2 \ + integral 1/((x - a)^2 + b^2) d x = 1/b arctan((x - a)/b) + c quad "für" n > 0\ + integral (x - a)/((x-a)^a + b^2) d x = 1/2 ln((x-a)^2 + b^2) + c + $ ]) @@ -703,6 +692,8 @@ #sinTable ]) + /* + // Notwending und Hinreichend #bgBlock(fill: colorAllgemein, [ #subHeading(fill: colorAllgemein)[Notwending und Hinreiched] @@ -718,4 +709,62 @@ $not "hin." arrow.r.double.not "Satz"$, ) ]) + */ + + // Taylor Reihen + #bgBlock(fill: colorAbleitung)[ + #subHeading(fill: colorAbleitung)[Taylorreihe] + + $T_m (x_0;x) = sum^m_(k=0) (f^((k))(x_0))/(k!) (x-x_0)^k$ + + $f(x) = T_m (x_0;x) + R_(m+1)(x_0;x)$ + + *Restglied* \ + $I = (a,b) quad x_0,x in I$ + + $R_(m+1) (x) = 1/(m!) integral_(x_0)^x (x-t)^m f^((m+1))(t) d t$ \ + + $forall x in I space space exists xi_x in I "sodass" \ + R_(m+1)(x_0;x) = (f^((m+1))(xi_x))/((m + 1)!) (x - x_0)^(m+1)\ + = f(x_0 + h) - T_m (x_0; x_0 + h) = o(h^m) = O(h^(m+1))$ + ] + + // Lamdauer Notation + #bgBlock(fill: colorFolgen, [ + #subHeading(fill: colorFolgen)[Landau Notation] + + $f(x) = o(g(x)) "wenn" lim_(x->a) f(x)/g(x) = 0 \ + f(x) = O(g(x)) "wenn" abs(f(x)) <= abs(g(g))$ + + *Rechen Regelen* \ + - $f = o(g) => f = O(g)$ + - $f_1 + f_2 = O\/o(f_1) + O\/o(f_2)$ + - $f_1 dot f_2 = O\/o(f_1 dot f_2)$ + + + ]) + + // Kurven + #bgBlock(fill: colorAbleitung)[ + #subHeading(fill: colorAbleitung)[Kurven] + + Länge einer Kurve $k(t)$: $L(k) = integral_a^b norm(k'(t)) d t$ + + Umparametrisierung: $h(tau)$ *streng monoton steigended* \ + $h(tau): [a,b] -> [overline(a), overline(b)]$ + + $overline(k): [overline(a), overline(b)] -> R^n, quad overline(k) = k(h(tau))$ + + Parametriesierung nach Länge: \ + $s(t) = integral_a^t norm(k'(tau)) d tau quad overline(k)(tau) = k(s^(-1)(tau))$ + + Wenn $k$ nach Länge param.: $T(t) =k'(t)$ + + Tangentenvektor: $T(t) = (k'(t))/norm(k'(t))$ \ + Krümmung: $kappa(t) = 1/(s'(t)) norm(T'(t))$ + + + $RR^2: kappa(t) = abs(x'(t)y''(t) - y'(t)x''(t))/((x'(t)^2 + y'(r)^2)^(3/2))$ \ + Param Länge: $kappa(t) = abs(x'(t)y''(t) - y'(t)x''(t))$ + ] ] From d2417aa6fa79d871345022fb77d5b6bd27fdf894 Mon Sep 17 00:00:00 2001 From: alexander Date: Sat, 14 Feb 2026 12:23:56 +0100 Subject: [PATCH 47/51] fixed integrierbar bedinung --- src/cheatsheets/Analysis1.typ | 19 +++++-------------- 1 file changed, 5 insertions(+), 14 deletions(-) diff --git a/src/cheatsheets/Analysis1.typ b/src/cheatsheets/Analysis1.typ index 9a8b835..a97e420 100644 --- a/src/cheatsheets/Analysis1.typ +++ b/src/cheatsheets/Analysis1.typ @@ -163,26 +163,17 @@ - Beweiße: durch Induktion - Beweiße: Hat min. ein konvergent Teilefolge - (Beweiße: Ungleichung $abs(a_n) <= k$) - - *Monoton fallend/steigended* + + *Monoton fallend/steigended $a_(n+1) lt.eq.gt a_(n)$* - Beweise: Induktion - #grid(columns: (1fr, 1fr), - inset: 0.2mm, - align(top+center, [*Fallend*]), align(top+center, [*Steigend*]), - [$ a_(n+1) <= a_(n), quad a_(n+1) >= a_(n) $], - [$ a_(n+1)/a_(n) < 1, quad a_(n+1)/a_(n) > 1 $], - ) *Konvergentz Allgemein* $lim_(n -> infinity) a_n = a$ $forall epsilon > 0 space exists n_epsilon in NN$ sodass \ - Konvergent $-> a$: $a_n in [a - epsilon, a + epsilon] $ - - Divergent $-> infinity$: $a_n in [epsilon, infinity) $ - - Divergent $-> infinity$: $a_n in (-infinity, epsilon) $ - - $space forall n > n_epsilon$ - + - unbeschränkt $=>$ Divergent + *Konvergentz Häufungspunkte* - $a_n -> a <=>$ Alle Teilfolgen $-> a$ @@ -579,7 +570,7 @@ #bgBlock(fill: colorIntegral, [ #subHeading(fill: colorIntegral, [Integral]) - Wenn $f(x)$ stetig und monoton $=>$ integrierbar + Wenn $f(x)$ stetig oder monoton $=>$ integrierbar Summen: $integral f(x) + g(x) d x = integral f(x) d x + integral g(x)$ From 300e74cd0d4dbf659d580e83cef5b72493f85f11 Mon Sep 17 00:00:00 2001 From: alexander Date: Sat, 14 Feb 2026 17:24:37 +0100 Subject: [PATCH 48/51] fixed mistake in surjektiv definition --- src/cheatsheets/Analysis1.typ | 2 +- src/cheatsheets/LinearAlgebra.typ | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/src/cheatsheets/Analysis1.typ b/src/cheatsheets/Analysis1.typ index a97e420..4d2226d 100644 --- a/src/cheatsheets/Analysis1.typ +++ b/src/cheatsheets/Analysis1.typ @@ -372,7 +372,7 @@ $f(x) = f(y) <=> x = y quad$ *Surjectiv (Epimorhismis):* Output space coverered \ - - $forall x in B : exists x in A : f(x) = y$ + - $forall y in B : exists x in A : f(x) = y$ *Bijektiv* diff --git a/src/cheatsheets/LinearAlgebra.typ b/src/cheatsheets/LinearAlgebra.typ index 431d2f3..1c3ab02 100644 --- a/src/cheatsheets/LinearAlgebra.typ +++ b/src/cheatsheets/LinearAlgebra.typ @@ -141,7 +141,7 @@ *Surjectiv (Epimorhismis):* \ _Output space coverered_ \ - Zeigen das $f(f^(-1)(x)) = x$ für $x in DD$ - - $forall x in B: exists x in A : f(x) = y$ + - $forall y in B: exists x in A : f(x) = y$ NICHT surjektiv wenn $abs(a) < abs(b)$ *Bijektiv (Isomorphismus):* \ From 5e83a41b54ba4852748a2ea9cbeab3086c419876 Mon Sep 17 00:00:00 2001 From: alexander Date: Sat, 14 Feb 2026 17:45:12 +0100 Subject: [PATCH 49/51] Fix differenzen Qutient --- src/cheatsheets/Analysis1.typ | 3 +-- 1 file changed, 1 insertion(+), 2 deletions(-) diff --git a/src/cheatsheets/Analysis1.typ b/src/cheatsheets/Analysis1.typ index 4d2226d..70606d6 100644 --- a/src/cheatsheets/Analysis1.typ +++ b/src/cheatsheets/Analysis1.typ @@ -462,10 +462,9 @@ #subHeading(fill: colorAbleitung)[Ableitung] *Differenzierbarkeit* - $f(x)$ ist an der Stelle $x_0 in DD$ diffbar wenn \ - #MathAlignLeft($ f'(x_0) = lim_(x->x_0 plus.minus) (f(x_0 + h - f(x_0))/h) $) + $f'(x_0) = lim_(x->x_0^plus.minus) (f(x_0 + h) - f(x_0))/h$ - Tangente an $x_0$: $f(x_0) + f'(x_0)(x - x_0)$ - Beste #underline([linear]) Annäherung - - Tangente $t(x)$ von $f(x)$ an der Stelle $x_0$: $ lim_(x->0) (f(x) - f(x_0))/(x-x_0) -f'(x_0) =0 $ *Ableitung Regeln* From 51554e849416078a1189b71bd36e81502ac9801f Mon Sep 17 00:00:00 2001 From: alexander Date: Sun, 15 Feb 2026 18:40:52 +0100 Subject: [PATCH 50/51] Fixed small error in Ableitungs Table --- src/lib/ableitungs_tabelle.typ | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/lib/ableitungs_tabelle.typ b/src/lib/ableitungs_tabelle.typ index 41b3fa8..2979961 100644 --- a/src/lib/ableitungs_tabelle.typ +++ b/src/lib/ableitungs_tabelle.typ @@ -8,7 +8,7 @@ fill: (x, y) => if calc.rem(x, 3) == 0 { color.hsl(180deg, 89.47%, 88.82%) } else if calc.rem(x, 3) == 1 { color.hsl(180deg, 100%, 93.14%) } else { color.hsl(180deg, 81.82%, 95.69%) }, - [$1/(q + x) x^(q+1)$], [$x^q$], [$q x^(q-1)$], + [$1/(q + 1) x^(q+1)$], [$x^q$], [$q x^(q-1)$], [$ln abs(x)$], [$1/x$], [$-1/x^2$], [$x ln(a x) - x$], [$ln(a x)$], [$a / x$], [$2/3 sqrt(a x^3)$], [$sqrt(a x)$], [$a/(2 sqrt(a x))$], From 6c273eef2d2786562f6e1062a3d93480b44cd788 Mon Sep 17 00:00:00 2001 From: alexander Date: Sun, 15 Feb 2026 19:17:42 +0100 Subject: [PATCH 51/51] added some usefull integrals --- src/cheatsheets/Analysis1.typ | 21 ++++++++++++++++++++- 1 file changed, 20 insertions(+), 1 deletion(-) diff --git a/src/cheatsheets/Analysis1.typ b/src/cheatsheets/Analysis1.typ index 70606d6..66d9d03 100644 --- a/src/cheatsheets/Analysis1.typ +++ b/src/cheatsheets/Analysis1.typ @@ -606,6 +606,13 @@ $tan(x) = (2t)/(1-t^2)$, $cos(x) = (1-t^2) / (1 + t^2)$, ) + + *Tricks aus der Schule* + + $integral f(a x+b) d x = 1/a F(a x + b) +c \ + integral (f'(x))/f(x) d x = ln abs(f(x)) \ + integral f'(x) e^(f(x)) d x = e^(f(x)) +c \ + $ ]) #bgBlock(fill: colorIntegral, [ @@ -671,9 +678,21 @@ $integral 1/(x-a) d x = ln(x - a) + c\ integral 1/(x-a)^n d x = - 1/(n-1) 1/(x - a)^(n-1) + c quad "für" n >= 2 \ integral 1/((x - a)^2 + b^2) d x = 1/b arctan((x - a)/b) + c quad "für" n > 0\ - integral (x - a)/((x-a)^a + b^2) d x = 1/2 ln((x-a)^2 + b^2) + c + integral (x - a)/((x-a)^a + b^2) d x = 1/2 ln((x-a)^2 + b^2) + c \ $ + #grid( + columns: (1fr), + column-gutter: 2mm, + row-gutter: 4mm, + $integral 1/x d x = ln abs(x) +c$, + $integral 1/x^2 d x = - 1/x + c$, + $integral 1/(a + x) d x = ln abs(a + x) + c$, + $integral 1/(a + x)^2 d x = - 1/(a + x) + c$, + $integral 1/(a - x) d x = - ln abs(a - x) + c$, + $integral 1/(a - x)^2 d x = 1/(a - x) + c$ + ) + ])

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