From b0cdfdce51b416bb5b7a79603c14dc00376f4e32 Mon Sep 17 00:00:00 2001 From: alexander Date: Mon, 9 Feb 2026 08:59:03 +0100 Subject: [PATCH] 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) = 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