Merge branch 'main' of https://gitea.mintcalc.com/alexander/TUM-Formelsammlungen
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This commit is contained in:
levi
@@ -266,6 +266,7 @@
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$R_i$: Innenwiderstand $R_i = U_0/I_0$
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*Quell Wandlung*
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#table(
|
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columns: (1fr, 1fr),
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fill: (x, y) => if calc.rem(x, 2) == 1 { tableFillLow } else { tableFillHigh },
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@@ -319,7 +320,7 @@
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))
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wire((0, -1.5), (1.75, -1.5))
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cetz.draw.content((0.62, -0.75), [$R_i$])
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cetz.draw.content((0.9, -0.4), [$R_i$])
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cetz.draw.set-style(mark: (end: ">", fill: black, scale: 0.6))
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cetz.draw.content((1.95, -0.75), [$u$])
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cetz.draw.line((1.75, -0.1), (1.75, -1.4), stroke: 0.5pt)
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@@ -334,9 +335,18 @@
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$i = G_i u - I_0$
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],
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align(center, text(size: 7mm, $-->$)), [$G_i = 1/R_i \ I_0 = U_0 G_i$],
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[$R_i = 1/G_i \ U_0 = I_0 R_i$], align(center, text(size: 7mm, $<--$)),
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table.cell(colspan: 2)[
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#align(center, [*$u"-gesteuert" --> i"-gestuert"$*])
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$ R_i = 1/G_i quad quad quad U_0 = -I_0 1/G_i $
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],
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table.cell(colspan: 2, fill: tableFillLow)[
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#align(center, [*$i"-gesteuert" --> u"-gestuert"$*])
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$ G_i = 1/R_i quad quad quad I_0 = -U_0 1/R_i $
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],
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)
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]
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@@ -513,6 +523,19 @@
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#bgBlock(fill: colorAnalyseVerfahren)[
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#subHeading(fill: colorAnalyseVerfahren)[Graphen und Matrizen]
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$n:$ Knotenanzahle (mit Referenzknoten)
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$b:$ Zweiganzahle
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*Lineare Unabhänige KCL/KVLs*
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Für $2b$ unbekannte ($b$ Ströme + $b$ Spannungen)
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KCLs: $n-1$\
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KVLs: $b-(n-1)$
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#line(length: 100%, stroke: (thickness: 0.2mm))
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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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@@ -590,15 +613,41 @@
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// Baumkonzept
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#bgBlock(fill: colorAnalyseVerfahren)[
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#subHeading(fill: colorAnalyseVerfahren)[Baumkonzept]
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KCLs: $n-1$\
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KVLs: $b-(n-1)$
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Baum einzeichnen (Keine Schleifen!)
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1. Baum einzeichnen (Keine Schleifen!) \
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Muss alle Knoten umfassen
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2. $n-1$ KCLs: \
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Superknoten mit NUR einer Baumkante \
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$jMat(A) = mat(jMat(1)_(n-1), jMat(A)_e)$ \
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3. $b - (n-1)$ KVLs: \
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Maschen mit NUR einer NICHT Baumkante \
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$jMat(B) = mat(jMat(B)_t, jMat(1)_(b-(n-1)))$
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*Nur bei Baumkonzept:* $B_t = - A_e^T$
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]
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// Tablauematrix
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#bgBlock(fill: colorAnalyseVerfahren)[
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#subHeading(fill: colorAnalyseVerfahren)[Tablauematrix]
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Alle Element Gleichungen in Nullraum + KVLs/KCLs in eine Matrix
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KCLs: $jMat(A) jVec(i) = jVec(0)$\
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KVLs: $jMat(B) jVec(u) = jVec(0)$\
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Elementgleichungen: $jMat(N) jVec(u) + jMat(M) jVec(i) = jVec(e)$
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$ mat(
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jMat(B), jMat(0);
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jMat(0), jMat(A);
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jMat(M), jMat(N)
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) vec(jVec(u), jVec(i)) = vec(jVec(0), jVec(0), jVec(e)) $
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]
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// Machenstrom-/Knotenpotenzial-Analyse
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#bgBlock(fill: colorAnalyseVerfahren)[
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@@ -1209,32 +1258,6 @@
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#let NodeBlue = rgb("#6156ff")
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#let NodeYellow = rgb("#ffa856")
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#let nodeSymbol(s, center, color, ..style) = {
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import cetz.draw: *
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(
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ctx => {
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// Define a default style
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let def-style = (n: 5, inner-radius: .5, radius: 1, stroke: auto, fill: auto)
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// Resolve center to a vector
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let (ctx, center) = cetz.coordinate.resolve(ctx, center)
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// Resolve the current style ("star")
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let style = cetz.styles.resolve(ctx.style, merge: style.named(), base: def-style, root: "star")
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let paths = (
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cetz.drawable.ellipse(center.at(0), center.at(1), 0, 0.25, 0.25, fill: color, stroke: black),
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cetz.drawable.content((center.at(0),center.at(1) + 0.025), 1, 1, none, s),
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)
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(
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ctx: ctx,
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drawables: cetz.drawable.apply-transform(ctx.transform, paths)
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)
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},
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)
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}
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#columns(2)[
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#bgBlock(fill: colorAnalyseVerfahren)[
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#subHeading(fill: colorAnalyseVerfahren)[Knotenpotenzial-Analyse Komponetent]
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@@ -1322,10 +1345,10 @@
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joham.norator("norator1",(0,0), (-1.75,0))
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}))
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],
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[
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align(horizon+center, [
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$u = "bel." \
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i = "bel."$
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],
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]),
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[
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#scale(x: 75%, y: 75%, cetz.canvas({
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import cetz.draw: *
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@@ -1361,11 +1384,10 @@
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}))
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],
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[
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$u = 0$
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i = bel.
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],
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align(horizon+center, [
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$u = 0 \
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i = "bel."$
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]),
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[
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#scale(x: 75%, y: 75%, cetz.canvas({
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import cetz.draw: *
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@@ -1393,10 +1415,10 @@
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wire((1,0), (1.25,0))
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}))
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],
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[
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align(horizon+center, [
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$u = "bel." \
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i = 0$
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],
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||||
]),
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[
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#scale(x: 75%, y: 75%, cetz.canvas({
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import cetz.draw: *
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@@ -1420,17 +1442,17 @@
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import zap: *
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import cetz.draw: content, line
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vsource(
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fill: none,
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"b1",
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(0, 0),
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(1.75, 0),
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)
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||||
}))
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],
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[
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$u = U_0$
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i = bel.
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],
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align(horizon+center, [
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||||
$u = U_0 \
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||||
i = "bel."$
|
||||
]),
|
||||
[
|
||||
#scale(x: 75%, y: 75%, cetz.canvas({
|
||||
import cetz.draw: *
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||||
@@ -1454,17 +1476,17 @@
|
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import zap: *
|
||||
import cetz.draw: content, line
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isource(
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fill: none,
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"b1",
|
||||
(0, 0),
|
||||
(1.75, 0),
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||||
)
|
||||
}))
|
||||
],
|
||||
[
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||||
u = bel.
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|
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$i = I_0$
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],
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align(horizon+center, [
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$u = "bel." \
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||||
i = I_0$
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||||
]),
|
||||
[
|
||||
#scale(x: 75%, y: 75%, cetz.canvas({
|
||||
import cetz.draw: *
|
||||
@@ -1565,14 +1587,13 @@
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#scale(x: 100%, y: 100%, zap.circuit({
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import zap: *
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import cetz.draw: content, line
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diode("b1", (0, 0), (1., 0), stroke: black, fill: white)
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diode("b1", (0, 0), (1., 0), stroke: black, fill: none)
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||||
}))
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||||
],
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||||
[
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||||
|
||||
$i=0$ falls $u<0$\
|
||||
$i>=0$. falls $u=0$
|
||||
],
|
||||
align(horizon+center, [
|
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$u=0 &"falls" i>0 \
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||||
i=0 &"falls" u<0$
|
||||
]),
|
||||
[
|
||||
/*
|
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#scale(x: 50%, y: 50%,
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@@ -1613,10 +1634,10 @@
|
||||
}))
|
||||
],
|
||||
|
||||
[
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align(horizon+center, [
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$u_D = u_T dot ln((i_D/I_S)+1) \
|
||||
i_D = I_S dot (e^(u_D/U_T)-1)$
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||||
],
|
||||
]),
|
||||
[
|
||||
#scale(x: 75%, y: 75%, cetz.canvas({
|
||||
import cetz.draw: *
|
||||
@@ -1639,7 +1660,7 @@
|
||||
}))
|
||||
],
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align(horizon+center,
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$i = I_S*(e^(u_D/U_T)-1)- i_L$
|
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$i = I_S dot (e^(u_D/U_T)-1)- i_L$
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),
|
||||
[
|
||||
#scale(x: 75%, y: 75%, cetz.canvas({
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||||
@@ -1667,10 +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
|
||||
],
|
||||
]),
|
||||
[
|
||||
|
||||
],
|
||||
@@ -1703,121 +1724,257 @@
|
||||
]
|
||||
|
||||
// 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({
|
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import zap : wire, node
|
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import cetz.draw : line, rect
|
||||
|
||||
joham.ideal-opamp("Op", (0,0), scale: 0.7, invert: true)
|
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|
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wire("Op.plus", (rel: (-0.25, 0)))
|
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wire("Op.minus", (rel: (-0.25, 0)))
|
||||
wire("Op.ground", (rel: (0, -0.3)))
|
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wire("Op.out", (rel: (0.2,0)))
|
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|
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node("a", (to: "Op.plus", rel: (-0.25, 0)), fill: false, label: (content: text($alpha$, fill: rgb("#8b2000")), anchor: "west", distance: 0.05))
|
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node("b", (to: "Op.minus", rel: (-0.25, 0)), fill: false, label: (content: text($beta$, fill: rgb("#8b2000")), anchor: "west", distance: 0.05))
|
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node("c", (to: "Op.out", rel: (0.25, 0)), fill: false, label: (content: text($gamma$, fill: rgb("#00318b")), anchor: "east", distance: 0.05))
|
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node("d", (to: "Op.ground", rel: (0, -0.3)), fill: false, label: (content: text($delta$, fill: rgb("#00318b")), anchor: "south", distance: 0.05))
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|
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joham.voltage((to: "Op.plus", rel: (-0.25, 0)), (to: "Op.minus", rel: (-0.25, 0)), $u_"in"$)
|
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|
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joham.voltage((to: "Op.out", rel: (0.25, 0)), (to: "Op.out", rel: (0.25, -0.7)), $u_"out"$, anchor: "west")
|
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})
|
||||
|
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#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: *
|
||||
import cetz.draw: content, line
|
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joham.nullor("nullor", (0,0))
|
||||
}))], [], [$ A = mat(0, 0; 0, 0) $], [],
|
||||
import zap: *
|
||||
import cetz.draw: content, line, rect
|
||||
joham.nullor("nullor", (0,0))
|
||||
|
||||
[OpAmp \ lin], [], [], [], [], [],
|
||||
}))],
|
||||
[
|
||||
- Verlustlos
|
||||
- Reziprok
|
||||
- Passiv
|
||||
- Symetrisch
|
||||
], [$ 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))
|
||||
[OpAmp \ $U_"sat+"$\ (4-polig)], opampSymbol, [], [], [],
|
||||
|
||||
//-
|
||||
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))
|
||||
[OpAmp \ $U_"sat+"$], opampSymbol, [#zap.circuit({
|
||||
import zap : wire, vsource, node
|
||||
import cetz.draw : line, rect
|
||||
|
||||
joham.norator("null-op",
|
||||
(0.2,0),(0.2,0),
|
||||
scale: .4)
|
||||
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))
|
||||
|
||||
}))], [], [], [], [],
|
||||
wire((0,1), (0.4, 1))
|
||||
wire((0,0), (0.4, 0))
|
||||
|
||||
[OpAmp \ $U_"sat-"$], [], [], [], [], [],
|
||||
joham.voltage((0.4, 1), (0.4, 0), $u_d$)
|
||||
joham.voltage((1.3, 1), (1.3, 0), $U_"sat"$, anchor: "west")
|
||||
|
||||
[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))
|
||||
vsource("v", (1,1), (1,0), scale: 0.4, fill: none)
|
||||
|
||||
wire((-1.75,2.5),(-1,2.5), i: (content: $i_1$, anchor: "south"))
|
||||
node("n2_1", (-1.75, 2.5), f:$f$)
|
||||
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))
|
||||
})], [], [],
|
||||
|
||||
//tor 2
|
||||
zap.dvsource("dv1",
|
||||
(0,2.5),(0,0), u:$alpha u_1$, i:$i_2$)
|
||||
|
||||
[OpAmp \ $U_"sat-"$], opampSymbol, [#zap.circuit({
|
||||
import zap : wire, vsource, node
|
||||
import cetz.draw : line, rect
|
||||
|
||||
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) $], [],
|
||||
node("a", (0,1), fill: false, label: (content: text($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$, fill: rgb("#00318b")), anchor: "east", distance: 0.05))
|
||||
|
||||
[VCCS], [], [], [], [$ G = mat(0, 0; g, 0) quad A = mat(0, -1/g; 0, 0) $], [],
|
||||
wire((0,1), (0.4, 1))
|
||||
wire((0,0), (0.4, 0))
|
||||
|
||||
[CCVS], [], [], [], [$ R = mat(0, 0; r, 0) quad A = mat(0, 0; 1/r, 0) $], [],
|
||||
joham.voltage((0.4, 1), (0.4, 0), $u_d$)
|
||||
joham.voltage((1.3, 1), (1.3, 0), $- U_"sat"$, anchor: "west")
|
||||
|
||||
[CCCS], [], [], [], [$ H = mat(0, 0; beta, 0) quad A = mat(0, 0; 0, -1/beta) $], [],
|
||||
vsource("v", (1,1), (1,0), scale: 0.4, fill: none)
|
||||
|
||||
[Übertrager], [], [],
|
||||
[],
|
||||
[$ H = mat(0, ü; -ü, 0) quad
|
||||
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],
|
||||
[],
|
||||
[#zap.circuit({
|
||||
joham.zweitor("NIK", (0,0), label: "NIK")
|
||||
})],
|
||||
[],
|
||||
[
|
||||
- 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) $],
|
||||
[],
|
||||
|
||||
[T-Glied],
|
||||
[],
|
||||
[],
|
||||
[],
|
||||
[
|
||||
|
||||
],
|
||||
[],
|
||||
|
||||
[$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
|
||||
|
||||
@@ -1835,8 +1992,9 @@
|
||||
[*passiv*\ (nimmt Energie auf)\ $not$aktiv],
|
||||
[$forall (u,i) in cal(F): u dot i >= 0$],
|
||||
[
|
||||
$jMat(U)^T jMat(I) + jMat(I)^T jMat(U)$\
|
||||
$forall vec(jVec(u), jVec(v)) in cal(F) : jVec(u)^T jVec(i) >=0$
|
||||
$jMat(U)^T jMat(I) + jMat(I)^T jMat(U) = 0$\
|
||||
$forall vec(jVec(u), jVec(v)) in cal(F) : jVec(u)^T jVec(i) >=0 \
|
||||
jMat(G) = - jMat(G)^T quad jMat(R) = - jMat(R)^T$
|
||||
],
|
||||
[],
|
||||
|
||||
@@ -1884,13 +2042,16 @@
|
||||
$jMat(G) = jMat(P) jMat(G) jMat(P), space jMat(R) = jMat(P) jMat(R) jMat(P), quad jMat(P) = mat(0, 1; 1, 0) \
|
||||
det(H) = 1,$
|
||||
|
||||
Für Eintore: Streng Linear $=>$ Umkehrbar
|
||||
|
||||
],
|
||||
[],
|
||||
|
||||
[*Reziprok*],
|
||||
[Immer Reziprok],
|
||||
[
|
||||
$cal(F)$ symetrisch $=> cal(F)$ reziprok
|
||||
Symetrisch $=>$ Reziprok \
|
||||
Für Eintore: Streng Linear $=>$ Reziprok
|
||||
|
||||
$jMat(U)^T jMat(I) - jMat(I)^T jMat(U) = 0 \
|
||||
jMat(R)^T = jMat(R), quad jMat(G)^T = jMat(G) quad h_21 = -h_12 \ det(jMat(A)) = 1 quad det(jMat(A')) = 1 quad h'_21 = -h'_12$],
|
||||
|
||||
@@ -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)
|
||||
)
|
||||
},
|
||||
)
|
||||
}
|
||||
Reference in New Issue
Block a user