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

src/cheatsheets/Schaltungstheorie.typ

@@ -205,8 +205,62 @@
         $i_(cal(F),2) = i_(cal(F),1)$
       ],
     )
+
+    *Kennline Addition* \
+
+    #grid(
+      columns: (1fr, auto, 1fr),
+      row-gutter: 2mm,
+      column-gutter: 3mm,
+      [Parallel-Schaltung], $-->$, [$i$-Richtung],
+      [Reihe-Schaltung], $-->$, [$u$-Richtung],
+
+    )
   ]
 
+  #bgBlock(fill: colorAllgemein)[
+    #subHeading(fill: colorAllgemein)[Spannungs Teiler/Strom Teiler]
+
+    #table(
+      columns: (1fr, 1fr),
+      fill: (x, y) => if calc.rem(x, 2) == 1 { tableFillLow } else { tableFillHigh },
+      [*Spannungsteiler*],
+      [*Stromteiler*],
+      zap.circuit({
+        import zap : *
+
+        node("N1", (0,1.5))
+        node("N2", (0,0))
+        node("N3", (0,-1.5))
+
+        resistor("R1", "N1", "N2", label: (content: $R_2$, distance: 0.1), scale: 0.7, fill: none)
+        resistor("R2", "N2", "N3", label: (content: $R_1$, distance: 0.1), scale: 0.7, fill: none)
+
+        joham.voltage((-0.4, 0), (-0.4, -1.5), $u_"out"$)
+        joham.voltage((0.8, 1.5), (0.8, -1.5), $u_"ges"$, anchor: "west")
+
+        wire((-0.6, 1.5),(0.8, 1.5))
+        wire((-0.6, -1.5),(0.8, -1.5))
+        wire((-0.6, 0),(0,0))
+      }),
+      zap.circuit({
+        import zap : *
+
+        node("N1", (0,0))
+        node("N2", (0,2))
+
+        resistor("R1", "N1", "N2", label: (content: $R_1$, distance: 0.1), scale: 0.7, fill: none, i: (content: $i_"out"$, anchor: "south", distance: 0.25, invert: true))
+        resistor("R2", (1,0), (1,2), label: (content: $R_2$, distance: 0.1), scale: 0.7, fill: none)
+
+        wire((-1, 0), "R2.in")
+        wire((-1, 2), "R2.out")
+        wire((-1, 2), "N2", i: (content: $i_"ges"$, distance: 0.1))
+
+      }),
+      $ u_"out" = R_1/(R_1 + R_2) $, $ i_"out" = R_2/(R_1 + R_2) i_"ges" $,
+      $ u_"out" = G_2/(G_1 + G_2) $, $ i_"out" = G_1/(G_1 + G_2) i_"ges" $
+    )
+  ]
 
   // Lineare Quelle
   #bgBlock(fill: colorEineTore)[
@@ -440,6 +494,7 @@
       $L --> C^d = L / R_d^2$,
 
       $"KS" --> "LL"$, $"LL" -> "KS"$,
+      $"Nullator" --> "Nullator"$, $"Norator" -> "Norator"$,
 
       $"Parallel" --> "Seriell"$,
       $"Seriell" --> "Parallel"$,
@@ -447,20 +502,10 @@
       table.cell(colspan: 2)[
       *Dualwandlung: Steurende & Ausgangs Größe*  
       $
-        "VCVS": u_"out" = mu dot u_"in" &--> i_"out" R_d = mu dot i_"in" R_d \
+        "VCVS" &: u_"out" &= mu dot u_"in"   &--> i_"out"^d = mu i_"in"^d\
-        "VCCS": u_"out" = g dot i_"in" &--> \
+        "VCCS" &: i_"out" &= g dot u_"in"    &--> u_"out"^d = g R_d^2 dot i_"in"^d \
-        "CCVS": u_"out" = r dot i_"in" &--> \
+        "CCVS" &: u_"out" &= r dot i_"in"    &--> i_"out"^d = r/R_d^2 dot u_"in"\
-        "CCCS": i_"out" = beta dot i_"in" &--> \
+        "CCCS" &: i_"out" &= beta dot i_"in" &--> u_"out"^d = beta u_"in"^d\
-      $
-      ],
-
-      table.cell(colspan: 2)[
-      *Dualwandlung: Nur Ausgangs Größe*  
-      $
-        "VCVS": u_"out" = mu dot u_"in" &-->  \
-        "VCCS": u_"out" = g dot i_"in" &--> \
-        "CCVS": u_"out" = r dot i_"in" &--> \
-        "CCCS": i_"out" = beta dot i_"in" &--> \
       $
       ],
 
@@ -476,8 +521,6 @@
 
     2. Ableitung $g_cal(F)(u)$/$r_cal(F)(i)$ bilden \ $g'_cal(F)(u)$/$r'_cal(F)(i)$
 
-    #colbreak()
-
     #line(length: 100%)
 
     *Stromgesteuert* $quad r(i) = u$
@@ -521,7 +564,7 @@
 
     #linebreak()
 
-    *Klein-Signal* $quad i_"lin" = g_"lin" (u) = g'(u_"AP")u$
+    *Klein-Signal* $quad Delta i_"lin" = g_"lin" (Delta u) = g'(u_"AP") Delta u$
 
     #line(length: 100%)
 
@@ -562,7 +605,7 @@
       })),
     );
     #linebreak()
-    *Klein-Signal* $quad u_"lin" = r_"lin" (i) = r'(i_"AP")i$
+    *Klein-Signal* $quad Delta u_"lin" = r_"lin" (Delta i) = r'(i_"AP") Delta i$
   ]
 
   // Graphen und Matrizen
@@ -984,6 +1027,26 @@
     )
   ],
 
+  // KS/LL  
+  #bgBlock(fill: colorZweiTore)[
+    #subHeading(fill: colorZweiTore)[Kurzschluss/Leerlauf Methode für Zweitore]
+
+    1. Was sind die Input-Größen/Output-Größen? \
+      $u"-gesteuert:" u = 0 &--> "Kurzschluss (KS)" \
+      i"-gesteuert:" i = 0 &--> "Leerlauf (LL)"$ \
+
+    2. Steuernde Größe 1 beschalten KS/LL \
+      $-->$ BEIDE gesteuerten Größe errechen \
+      (2. Spalte der Matrix)
+    3. Steuernde Größe 2 beschalten KS/LL \
+      $-->$ BEIDE gesteuerten Größe errechen \
+      (1. Spalte der Matrix)
+     
+    4. Matrix/Gleichung aufstellen \
+      Addition der Beschreibung pro gesteuerter Größe \
+      (Superpositions Prinzip)
+  ]
+
   // Linearsierung (N-Tore)
   #bgBlock(fill: colorAnalyseVerfahren)[
     #subHeading(fill: colorAnalyseVerfahren)[Linearisierung (N-Tore)]
@@ -1406,14 +1469,19 @@
     *Cramersche Regel:* $u_(k i) = (det jMat(G)_(k i))/(det jMat(G)_k)$ ($jMat(G)_(k i)$ entshet aus $G_k$ durch ersetzen der $i$-ten Splate mit $jVec(i)_q$)
 
     #table(
+      columns: (1fr, 1fr),
+      fill: (x, y) => if calc.rem(y, 2) == 0 { tableFillHigh } else { tableFillLow },
+
       grid(
         columns: 3,
+        column-gutter: 5mm,
+        row-gutter: 3mm,
         zap.circuit({
           import zap : *
           
           vsource("V", (0,0), (0,1.5), scale: 0.4, fill: none)
           joham.voltage((-0.3,1), (-0.3,0), $U_0$)
-          resistor("G", (0,1.5), (1,1.5), scale: 0.4, fill: none)
+          resistor("G", (0,1.5), (1,1.5), scale: 0.4, fill: none, label: (content: $G$, distance: 0.6mm, anchor: "south"))
           wire("V.in", (1,0))
         }),
         align(center+horizon, $==>$),
@@ -1422,12 +1490,204 @@
 
           isource("V", (0,0), (0,1.5), scale: 0.4, fill: none, i: (content: $G U_0 space$, invert: false, distance: 0.2, anchor: "east"))
 
-          resistor("G", (0,1.5), (1,1.5), scale: 0.4, fill: none)
+          resistor("G", (1,0), (1,1.5), n: "*-*", scale: 0.4, fill: none, label: (content: $G$, distance: 0.6mm))
-          wire("V.in", (1,0))
+          wire("V.in", (1.5,0))
-        })
+          wire("V.out", (1.5,1.5))
+        }),
       ),
 
+      grid(
+        columns: 3,
+        column-gutter: 5mm,
+        row-gutter: 3mm,
+        zap.circuit({
+          import zap : *
           
+          vsource("V", (0,0), (0,1.5), scale: 0.4, fill: none)
+          joham.voltage((-0.3,1), (-0.3,0), $U_0$)
+          
+          wire("V.in", (1,0))
+          wire("V.out", (1,1.5))
+        }),
+        align(center+horizon, $==>$),
+        zap.circuit({
+          import zap : *
+
+          isource("V", (0,0), (0,1.5), scale: 0.4, fill: none, i: (content: $G U_0 space$, invert: false, distance: 0.2, anchor: "east"))
+
+          resistor("G", (1,0), (1,1.5), n: "*-*", scale: 0.4, fill: none, label: (content: $G$, distance: 0.6mm))
+          resistor("-G", (2.3,1.5), (1,1.5), scale: 0.4, fill: none, label: (content: $-G$, distance: 0.6mm))
+          wire("V.in", (2.3,0))
+          wire("V.out", "G.out")
+        }),
+      ),
+
+      grid(
+        columns: 3,
+        column-gutter: 5mm,
+        row-gutter: 3mm,
+        zap.circuit({
+          import zap : *
+          
+          vsource("V", (0,0), (0,1.5), scale: 0.4, fill: none)
+          joham.voltage((-0.3,1), (-0.3,0), $U_0$)
+          
+          wire("V.in", (1,0))
+          wire("V.out", (1,1.5))
+        }),
+        align(center+horizon, $==>$),
+        zap.circuit({
+          import zap : *
+          joham.gyrator("G", (0,0), scale: 0.4, constant: $G_d$, invert: true)
+          joham.ground("GND", "G.12")
+          node("A", "G.12")
+          node("B", (-0.75,0.67), label: (content: $alpha$, distance: 0.1))
+          isource("V", "G.12", "G.11", scale: 0.4, fill: none, i: (content: $G_d U_0 space$, invert: true, distance: 0.3, anchor: "east"))
+        }),
+      ),
+
+      [*Übertrager/NIK* siehe Zweitor-Tabelle],
+
+      scale(90%, grid(
+        columns: (auto, 0mm, 1fr),
+        column-gutter: 5mm,
+        row-gutter: 3mm,
+        
+        [
+          *VCVS + 1 Knoten* \
+          #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), $u_"out"$, anchor: "west")
+          })
+
+          $u_"out" = mu u_"in"$
+        ],
+        align(center+horizon, $==>$),
+        [
+          #zap.circuit({
+            import zap : vsource, node, disource, dvsource, wire
+            import cetz.draw : line, rect, mark, content
+
+            joham.gyrator("G0", (3,0), scale: 0.4, invert: true, constant: $G_d$)
+
+            disource("S", "G0.11", "G0.12", scale: 0.4, fill: none, i: (content: $i_"out"$, distance: 0.3, anchor: "west", invert: true))
+            node("N4", "G0.11", label: (content: $beta$, distance: 0.1),)
+            node("N3", "G0.12",)
+            joham.ground("GND1", "N3")
+
+            node("A", (1, 0.67), fill: false)
+            node("B", (1, -0.67), fill: false)
+            joham.voltage((1, 0.7), (1, -0.7), $u_"in"$, anchor: "west")
+
+          })
+          $i_"out" = mu G_d u_"in"$
+        ],
+      )),
+
+      scale(90%, grid(
+          columns: (auto, 0mm, 1fr),
+          column-gutter: 5mm,
+          row-gutter: 3mm,
+          
+          [
+            *CCCS + 1 Knoten* \
+            #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), $i_"out"$, anchor: "west")
+            })
+            $i_"out" = beta i_"in"$
+          ],
+          align(center+horizon, $==>$),
+        [
+          #zap.circuit({
+            import zap : vsource, node, disource, dvsource, wire
+            import cetz.draw : line, rect, mark, content
+
+            joham.gyrator("G1", (0,0), scale: 0.4, constant: $G_d$)
+
+            node("A", (1.8,-0.67))
+            node("B", (1.8,0.67))
+
+            disource("S", "A", "B", scale: 0.4, fill: none, i: (content: $i_"out"$, distance: 0.2, label-distance: -0.4, anchor: "east", invert: true))
+            node("N1", "G1.21", label: (content: $alpha$, distance: 0.1),)
+            node("N2", "G1.22",)
+            joham.ground("GND1", "N2")
+
+            joham.voltage("G1.21", "G1.22", $u_"in"$)
+          })
+          $i_"out" = beta G_d u_in$
+        ],
+      )),
+      
+      table.cell(
+        align(center+horizon, grid(
+          columns: (auto, 0mm, auto),
+          column-gutter: 5mm,
+          row-gutter: 3mm,
+          [
+            *CCVS + 2 Knoten* \
+            #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), $u_"out"$, anchor: "west")
+            })
+
+            $u_"out" = r i_"in"$
+          ],
+          align(center+horizon, $==>$),
+          [
+            #zap.circuit({
+              import zap : vsource, node, disource, dvsource, wire
+              import cetz.draw : line, rect, mark, content
+
+              joham.gyrator("G1", (0,0), scale: 0.4, constant: $G_d$)
+              joham.gyrator("G0", (3,0), scale: 0.4, invert: true, constant: $G_d$)
+
+              disource("S", "G0.11", "G0.12", scale: 0.4, fill: none, i: (content: $i_"out"$, distance: 0.3, anchor: "west", invert: true))
+              node("N1", "G1.21", label: (content: $alpha$, distance: 0.1),)
+              node("N4", "G0.11", label: (content: $beta$, distance: 0.1),)
+              node("N2", "G1.22",)
+              node("N3", "G0.12",)
+              joham.ground("GND1", "N3")
+              joham.ground("GND1", "N2")
+
+              joham.voltage("G1.21", "G1.22", $u_"in"$)
+            })
+            $i_"out" = r G_d^2 u_"in"$
+          ],
+        )),
+        colspan: 2
+      )
     )
     
     #table(
@@ -2101,7 +2361,7 @@
       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")
+      content((0.9, 0.15), $i_"out" = g u_"in"$, anchor: "west")
 
     })], [], [
       - NICHT Verlustlos
@@ -2490,7 +2750,6 @@
     inset: (bottom: 4mm, top: 4mm),
     gutter: 0.1mm,
     fill: (x, y) => if x != 0 and calc.rem(x, 2) == 0 { rgb("#c5c5c5") } else { white },
-
     [],
     $bold(R) jVec(i) = jVec(u)$,
     $bold(G) jVec(u) = jVec(i)$,
@@ -2498,5 +2757,19 @@
     $bold(H') vec(u_1, i_2) = vec(i_1, u_2)$,
     $bold(A) vec(u_2, -i_2) = vec(i_1, u_1)$,
     $bold(A') vec(u_1, -i_1) = vec(i_2, u_2)$,
+    [],
+    [Stromge-steuert],
+    [Spannung-gesteuert],
+    [Hybrid-beschreibung],
+    [Inverse-Hybrid],
+    [Ketten-Beschreibung],
+    [Inverse-Ketten],
+    [],
+    $jVec(r)vec(i_1, i_2) = vec(u_1, u_2)$,
+    $jVec(g)vec(u_1, u_2) = vec(i_1, i_2)$,
+    $jVec(h) vec(i_1, u_2) = vec(u_1, i_2)$,
+    $jVec(h') vec(u_1, i_2) = vec(i_1, u_2)$,
+    $jVec(a) vec(u_2, -i_2) = vec(i_1, u_1)$,
+    $jVec(a') vec(u_1, -i_1) = vec(i_2, u_2)$,
   )
 ]