From af26032d6ee6219094e6ae3ea121698abf0b0368 Mon Sep 17 00:00:00 2001 From: alexander Date: Mon, 9 Feb 2026 17:20:28 +0100 Subject: [PATCH] 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 b/src/images/schaltungstheorie/knotenpotenzial/gyraptorESD.png new file mode 100644 index 0000000000000000000000000000000000000000..9111cb6a11595a880bbaa2a61b2b94ec2d57bcbb GIT binary patch literal 68549 zcmd?RWn5L;8!e0qN~nNHm$Zs>x6&PgbT>+OqtY$ia1aC(lu|;vK?Fp)ySp3SXLHW~ 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