209 lines
6.3 KiB
Typst
209 lines
6.3 KiB
Typst
#import "../lib/common_rewrite.typ" : *
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#import "@preview/mannot:0.3.1"
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#import "@preview/zap:0.5.0"
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#show math.equation.where(block: true): it => math.inline(it)
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#set page(
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paper: "a4",
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margin: (
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bottom: 10mm,
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top: 5mm,
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left: 5mm,
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right: 5mm
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),
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flipped:true,
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footer: context [
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#grid(
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align: center,
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columns: (1fr, 1fr, 1fr),
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[#align(left, datetime.today().display("[day].[month].[year]"))],
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[#align(center, counter(page).display("- 1 -"))],
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[#align(right, image("../images/cc0.png", height: 5mm,))]
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)
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],
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)
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#let colorAllgemein = color.hsl(105.13deg, 92.13%, 75.1%)
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#let colorEineTore = color.hsl(202.05deg, 92.13%, 75.1%)
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#let colorZweiTore = color.hsl(235.9deg, 92.13%, 75.1%)
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#let colorAnalyseVerfahren = color.hsl(280deg, 92.13%, 75.1%)
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#let colorComplexAC = color.hsl(356.92deg, 92.13%, 75.1%)
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#let colorMathe = color.hsl(34.87deg, 92.13%, 75.1%)
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#place(top+center, scope: "parent", float: true, heading(
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[Schaltungstheorie]
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))
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#columns(4, gutter: 2mm)[
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#bgBlock(fill: colorEineTore)[
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#subHeading(fill: colorEineTore)[Quelle Wandlung]
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#zap.circuit({
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import zap: *
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set-style(scale: (x: 0.75, y:0.75), fill: none)
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resistor("R1", (-2, 0), (0, 0))
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vsource("V1", (-2, 0), (-2, -2))
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wire((-2, -2), (0, -2))
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node("n1", (0, 0), label: "1")
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node("n2", (0, -2), label: "2")
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})
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]
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#bgBlock(fill: colorAnalyseVerfahren)[
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#subHeading(fill: colorAnalyseVerfahren)[Graphen und Matrizen]
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$bold(i_b)$ (oder $bold(i)$): Zweigstrom-Vektor \
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$bold(u_b)$ (oder $bold(u)$): Zweigspannungs-Vektor \
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$bold(i_m)$ : Maschenstrom-Vektor \
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#text(rgb(20%, 20%, 20%))[(Strom in einer viruellen Masche)] \
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$bold(u_k)$ : Kontenspannungs-Vektor \
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#text(rgb(20%, 20%, 20%))[(Spannung zwischen Referenzknoten und Knoten k)] \
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#line(length: 100%, stroke: (thickness: 0.2mm))
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Knotenzidenzmatrix $bold(A)$
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$bold(A) : bold(i_k) -> text("Knotenstrombianz") = 0$ \
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$bold(A^T) : bold(u_b)-> bold(u_k)$
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$
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bold(A) = quad mannot.mark(mat(
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a_11, a_12, ..., a_(1m);
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a_21, a_22, ..., a_(2m);
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dots.v, dots.v, dots.down, dots.v;
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a_(n 1), a_(n 2), ..., a_(n m)
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), tag: #<1>)
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#mannot.annot(<1>, pos:left, text(rgb("#404296"))[#rotate(-90deg)[$<-$ Knoten]], dx: 5mm)
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#mannot.annot(<1>, pos:bottom, text(rgb("#404296"))[Zweige $->$], dy: -0.5mm)
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a in {-1, 0, 1}
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$
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#line(length: 100%, stroke: (thickness: 0.2mm))
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Mascheninsidenz Matrix $bold(B)$\
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$bold(B) : bold(u_b) -> text("Zweigspannungsbilanz") = 0$ \
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$bold(B^T) : bold(i_m) -> i_b$
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$
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bold(B) = quad mannot.mark(mat(
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b_11, b_12, ..., b_(1m);
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b_21, b_22, ..., b_(2m);
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dots.v, dots.v, dots.down, dots.v;
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b_(n 1), b_(n 2), ..., b_(n m)
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), tag: #<1>)
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#mannot.annot(<1>, pos:left, text(rgb("#404296"))[#rotate(-90deg)[$<-$ Maschen]], dx: 6mm)
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#mannot.annot(<1>, pos:bottom, text(rgb("#404296"))[Zweige $->$], dy: -0.5mm)
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b in {-1, 0, 1}
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$
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#line(length: 100%, stroke: (thickness: 0.2mm))
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*KCL und KVL* \
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KCL in Nullraum: $ bold(A) bold(i_b) = bold(0)$ \
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KVL in Bildraum: $ bold(A^T) bold(u_k) = bold(u_b)$
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KVL in Nullraum: $bold(B) bold(u_b) = bold(0)$ \
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KCL in Bildraum: $bold(B^T) bold(i_m) = bold(i_b)$ \
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*Tellegen'sche Satz* \
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$bold(A B^T) = bold(B^T A) = 0$ \
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$bold(u_b^T i_b) = 0$
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]
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#bgBlock(fill: colorAnalyseVerfahren)[
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#subHeading(fill: colorAnalyseVerfahren)[Baumkonzept]
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]
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#bgBlock(fill: colorAnalyseVerfahren)[
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#subHeading(fill: colorAnalyseVerfahren)[Machenstrom-/Knotenpotenzial-Analyse]
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]
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#bgBlock(fill: colorAnalyseVerfahren)[
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#subHeading(fill: colorAnalyseVerfahren)[Reduzierte Knotenpotenzial-Analyse]
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]
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]
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#pagebreak()
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#place(bottom+left, scope: "parent", float: true)[
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#bgBlock(fill: colorZweiTore)[
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#subHeading(fill: colorZweiTore)[Umrechnung Zweitormatrizen]
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#show table.cell: it => pad(),
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#table(
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columns: (auto, 1fr, 1fr, 1fr, 1fr, 1fr, 1fr),
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align: center,
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gutter: 0.1mm,
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[In $->$], $bold(R)$, $bold(G)$, $bold(H)$, $bold(H')$, $bold(A)$, $bold(A')$,
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$bold(R)$,
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$mat(r_11, r_12; r_21, r_22)$,
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$1/det(bold(G)) mat(g_22, -g_12; -g_21, g_11)$,
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$1/h_22 mat(det(bold(H)), h_12; -h_21, 1)$,
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$1/h'_11 mat(1, -h'_12; h'_21, det(bold(H')))$,
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$1/a_21 mat(a_11, det(bold(A)); 1, a_22)$,
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$1/a'_21 mat(a'_22, 1; det(bold(A')), a'_11)$,
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$bold(G)$,
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$1/det(bold(R)) mat(r_22, -r_12; -r_21, r_11)$,
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$mat(g_11, g_12; g_21, g_22)$,
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$1/h_11 mat(1, -h_12; h_21, det(bold(H)))$,
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$1/h'_22 mat(det(bold(H')), h'_12; -h'_21, 1)$,
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$1/a_12 mat(a_22, -det(bold(A)); -1, a_11)$,
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$1/a'_12 mat(a'_11, -1; -det(bold(A')), a'_22)$,
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$bold(H)$,
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$1/r_22 mat(det(bold(R)), r_12; -r_21, 1)$,
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$1/g_11 mat(1, -g_12; g_21, det(bold(G)))$,
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$mat(h_11, h_12; h_21, h_22)$,
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$1/det(bold(H')) mat(h'_22, -h'_12; -h'_21, h'_11)$,
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$1/a_22 mat(a_12, det(bold(A)); -1, a_21)$,
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$1/a'_11 mat(a'_12, 1; -det(bold(A')), a'_21)$,
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$bold(H')$,
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$1/r_11 mat(1, -r_12; r_21, det(bold(R)))$,
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$1/g_22 mat(det(bold(G)), g_12; -g_21, 1)$,
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$1/det(bold(H)) mat(h_22, -h_12; -h_21, h_11)$,
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$mat(h'_11, h'_12; h'_21, h'_22)$,
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$1/a_11 mat(a_21, -det(bold(A)); 1, a_12)$,
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$1/a'_22 mat(a'_21, -1; det(bold(A')), a'_12)$,
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$bold(A)$,
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$1/r_21 mat(r_11, det(bold(R)); 1, r_22)$,
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$1/g_21 mat(-g_22, -1; -det(bold(G)), -g_11)$,
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$1/h_21 mat(-det(bold(H)), -h_11; -h_22, -1)$,
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$1/h'_21 mat(1, h'_22; h'_11, det(bold(H')))$,
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$mat(a_11, a_12; a_21, a_22)$,
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$1/det(bold(A')) mat(a'_22, a'_12; a'_21, a'_11)$,
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$bold(A')$,
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$1/r_12 mat(r_22, det(bold(R)); 1, r_11)$,
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$1/g_12 mat(-g_11, -1; -det(bold(G)), -g_22)$,
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$1/h_12 mat(1, h_11; h_22, det(bold(H)))$,
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$1/h'_12 mat(-det(bold(H')), -h'_22; -h'_11, -1)$,
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$1/det(bold(A)) mat(a_22, a_12; a_21, a_11)$,
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$mat(a'_11, a'_12; a'_21, a'_22)$,
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)
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]
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]
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#place(bottom+left, scope: "parent", float: true)[
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#bgBlock(fill: colorAllgemein, [
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#subHeading(fill: colorAllgemein, [Sin-Table])
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#sinTable
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])
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]
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