Merge branch 'main' of https://gitea.mintcalc.com/alexander/TUM-Formelsammlungen

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 @@
 
         }))
       ],
-      [
+      align(horizon+center, [
-        $u = 0$
+        $u = 0 \
-
+        i = "bel."$
-        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),
           )
         }))
       ],
-      [
+      align(horizon+center, [
-        $u = U_0$
+        $u = U_0 \
-        
+        i = "bel."$
-        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),
           )
         }))
       ],
-      [
+      align(horizon+center, [
-        u = bel.
+        $u = "bel." \
-
+        i = I_0$
-        $i = I_0$
+      ]),
-      ],
       [
         #scale(x: 75%, y: 75%, cetz.canvas({
           import cetz.draw: *
@@ -1565,14 +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)
         }))
       ],
-      [
+      align(horizon+center, [
-        
+        $u=0 &"falls" i>0 \
-        $i=0$ falls $u<0$\
+        i=0 &"falls" u<0$
-        $i>=0$. falls $u=0$
+      ]),
-      ],
       [
         /*
         #scale(x: 50%, y: 50%,
@@ -1613,10 +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: *
@@ -1639,7 +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({
@@ -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({
+    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),
+    columns: (auto, auto, auto, auto, auto),
-    [*Name*], [*Schaltbild*], [*Ersatz-Schaltbild*], [*Eigenschaften*], [*Beschreibung*], [*Knotenspannungs Analyse*],
+    [*Name*], [*Schaltbild*], [*Ersatz-Schaltbild*], [*Eigenschaften*], [*Beschreibung*],
 
     [Nullor], [], [#scale(x: 50%, y: 50%, zap.circuit({
-          import zap: *
+      import zap: *
-          import cetz.draw: content, line
+      import cetz.draw: content, line, rect
-          joham.nullor("nullor", (0,0))
+      joham.nullor("nullor", (0,0))
-        }))], [], [$ A = mat(0, 0; 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({
+    [OpAmp \ $U_"sat+"$\ (4-polig)], opampSymbol, [], [], [],
-          import zap: *
-          import cetz.draw: content, line
-          zap.opamp("opamp", variant: "ieee",(0,0))
 
-          //-
+    [OpAmp \ $U_"sat+"$], opampSymbol, [#zap.circuit({
-          zap.wire((0,0.45),(-1.3,0.45))
+      import zap : wire, vsource, node
-          //+
+      import cetz.draw : line, rect
-          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", 
+      node("a", (0,1), fill: false, label: (content: text($alpha$, fill: rgb("#8b2000")), anchor: "west", distance: 0.05))
-          (0.2,0),(0.2,0), 
+      node("b", (0,0), fill: false, label: (content: text($beta$, fill: rgb("#8b2000")), anchor: "west", distance: 0.05))
-          scale: .4)
 
-        }))], [], [], [], [],
+      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({
+      vsource("v", (1,1), (1,0), scale: 0.4, fill: none)
-          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"))
+      wire((1,1), (1.3,1))
-          node("n2_1", (-1.75, 2.5), f:$f$)
+      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
+    [OpAmp \ $U_"sat-"$], opampSymbol, [#zap.circuit({
-          zap.dvsource("dv1", 
+      import zap : wire, vsource, node
-          (0,2.5),(0,0), u:$alpha u_1$, i:$i_2$)
+      import cetz.draw : line, rect
-          
 
-          wire((0,0), (1.3,0))
+      node("a", (0,1), fill: false, label: (content: text($alpha$, fill: rgb("#8b2000")), anchor: "west", distance: 0.05))
-          node("n2_1", (1.3, 0))
+      node("b", (0,0), fill: false, label: (content: text($beta$, fill: rgb("#8b2000")), anchor: "west", distance: 0.05))
-          wire((0,2.5), (1.3,2.5))
+      node("c", (1.3,1), fill: false, label: (content: text($gamma$, fill: rgb("#00318b")), anchor: "east", distance: 0.05))
-          node("n2_2", (1.3,2.5), n:"o-o")
+      node("d", (1.3,0), fill: false, label: (content: text($delta$, fill: rgb("#00318b")), anchor: "east", distance: 0.05))
-          
-        }))], [], [], [$ 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) $], [],
+      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], [], [], 
+      wire((1,1), (1.3,1))
-    [], 
+      wire((1,0), (1.3,0))
-    [$ H = mat(0, ü; -ü, 0) quad
+    })], [], [],
+
+    [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
+      - Verlustlos
-      - Auch Positiv-Immitanz-Inverter
+      - 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)
+    [$ 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],
-    [],
+    [#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) $],
+    [$ 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],
-    [],
-    [],
-    [
-
-    ],
   )
 ]
+]
 
 // Knoten Spannungs Analyse
 
@@ -1835,8 +1992,9 @@
     [*passiv*\ (nimmt Energie auf)\ $not$aktiv],
     [$forall (u,i) in cal(F): u dot i >= 0$],
     [
-      $jMat(U)^T jMat(I) + jMat(I)^T jMat(U)$\
+      $jMat(U)^T jMat(I) + jMat(I)^T jMat(U) = 0$\
-      $forall vec(jVec(u), jVec(v)) in cal(F) : jVec(u)^T jVec(i) >=0$
+      $forall vec(jVec(u), jVec(v)) in cal(F) : jVec(u)^T jVec(i) >=0 \
+      jMat(G) = - jMat(G)^T quad jMat(R) = - jMat(R)^T$
     ],
     [],
 
@@ -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
 
       $jMat(U)^T jMat(I) - jMat(I)^T jMat(U) = 0 \
       jMat(R)^T = jMat(R), quad jMat(G)^T = jMat(G) quad h_21 = -h_12 \ det(jMat(A)) = 1 quad det(jMat(A')) = 1 quad h'_21 = -h'_12$],

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)
+      )
+    },
+  )
+}