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

src/cheatsheets/Schaltungstheorie.typ

@@ -54,6 +54,8 @@
   [Schaltungstheorie],
 ))
 
+#set text(8.5pt)
+
 #columns(4, gutter: 2mm)[
   // Allgemein
   #bgBlock(fill: colorAllgemein)[
@@ -73,7 +75,7 @@
       [
         KCL: $sum_(k=1)^n i_k =0$ (Knotenregel)
       ],
-      [
+      /*[
         #cetz.canvas(length: 8mm, {
           import cetz.draw: *
 
@@ -88,12 +90,12 @@
           line((angle: 120deg, radius: 1.2), (angle: 120deg, radius: 0.4), stroke: red)
           line((angle: 240deg, radius: 1.2), (angle: 240deg, radius: 0.4), stroke: red)
         })
-      ],
+      ],*/
 
       [
         KVL: $sum_(k=1)^n u_k =0$ (Maschenregel)
       ],
-      [
+      /*[
         #zap.circuit({
           import zap: wire
           import cetz.draw: *
@@ -113,7 +115,7 @@
           translate((0, -2mm))
           mark((angle: 0deg, radius: 4mm), 270deg, symbol: "straight", stroke: blue, scale: 0.75)
         })
-      ],
+      ],*/
     )
 
     $u dot i > 0$: Nimmt Energie auf\
@@ -121,7 +123,7 @@
     $u dot i < 0$: Gibt Energie ab\
   ]
 
-  // Eintrag
+  // Verschaltung
   #bgBlock(fill: colorAllgemein)[
     #subHeading(fill: colorAllgemein)[Verschaltung]
 
@@ -178,7 +180,6 @@
     )
   ]
 
-  // 
 
   // Quell Wandlung
   #bgBlock(fill: colorEineTore)[
@@ -206,6 +207,7 @@
     )
   ]
 
+
   // Lineare Quelle
   #bgBlock(fill: colorEineTore)[
     #subHeading(fill: colorEineTore)[Lineare Quelle]
@@ -407,6 +409,106 @@
   ]
   */
 
+
+  // Linearsierung
+  #bgBlock(fill: colorEineTore)[
+    #subHeading(fill: colorEineTore)[Linearisierung (Ein-Tore)]
+
+    1. Arbeitspunkt bestimmen \ $"AP" =(u_"AP", i_"AP")$
+
+    2. Ableitung $g_cal(F)(u)$/$r_cal(F)(i)$ bilden \ $g'_cal(F)(u)$/$r'_cal(F)(i)$
+
+    #colbreak()
+
+    #line(length: 100%)
+
+    *Stromgesteuert* $quad r(i) = u$
+
+    *Groß-Signal* \
+    #grid(columns: (1fr, 1fr),
+      column-gutter: 4mm,
+      $I_0 = i_"AP" - g'_cal(F)(u_"AP")u_"AP"$,
+      $g_0 = g'_cal(F)(u_"AP")u$
+    )
+
+    #linebreak()
+
+    $i_"lin" = g_"lin" (u) = g'_cal(F)(u_"AP")(u-u_"AP") + i_"AP"\
+    i_"lin" = g_"lin" (u) = g_0 u + I_0$
+
+    #block(
+      height: 20mm,
+      scale(x: 75%, y: 75%, zap.circuit({
+        import zap: *
+        import cetz.draw: content, line
+
+        isource("I0", (0, 1.5), (0, -1.5), fill: none)
+        node("n0", (2, 1.5))
+        node("n1", (2, -1.5))
+
+        node("n2", (3.5, 1.5), fill: false)
+        node("n3", (3.5, -1.5), fill: false)
+
+        resistor("g0", "n1", "n0", fill: none, label: (content: $g_0$, anchor: "south", distance: 0.2))
+        wire("I0.in", "n0", "n2")
+        wire("I0.out", "n1", "n3")
+        wire("n0", "n2", i: (content: $i_"lin"$, anchor: "south", invert: true))
+        wire((0, 0.6), "I0.in", i: (content: $I_0$, anchor: "east", invert: true))
+
+        set-style(mark: (end: ">", fill: black))
+        line((3.5, 1.2), (3.5, -1.2), stroke: 0.5pt)
+        content((3.9, 0), $u$)
+      })),
+    );
+
+    #linebreak()
+
+    *Klein-Signal* $quad i_"lin" = g_"lin" (u) = g'(u_"AP")u$
+
+    #line(length: 100%)
+
+
+    *Spannungsgesteuert* $quad g(u) = i$
+
+    *Groß-Signal* \
+    #grid(columns: (1fr, 1fr),
+      column-gutter: 4mm,
+      $U_0 = u_"AP" - r'(i_"AP") i_"AP"$,
+      $r_0 = r'(i_"AP")$
+    )
+    #linebreak()
+    $u_"lin" = r_"lin" (i) = r'(i_"AP")(i-i_"AP") + u_"AP"\
+    u_"lin" = r_"lin" (i) = r_0 i + U_0$
+    #block(
+      height: 25mm,
+      scale(x: 75%, y: 75%, zap.circuit({
+        import zap: *
+        import cetz.draw: content, line
+
+        vsource("U0", (0, 1.5), (0, -1.5), fill: none)
+
+        node("n2", (3.5, 1.5), fill: false)
+        node("n3", (3.5, -1.5), fill: false)
+
+        resistor("R0", "U0.in", "n2", fill: none, label: (content: $r_0$, anchor: "south", distance: 0.1))
+        wire("U0.out", "n3")
+
+        wire((2.49, 1.5), "n2", i: (content: $i$, anchor: "south", invert: true))
+
+        set-style(mark: (end: ">", fill: black))
+        line((3.5, 1.2), (3.5, -1.2), stroke: 0.5pt)
+        content((3.9, 0), $u_"lin"$)
+
+        line((0.7, 0.5), (0.7, -0.5), stroke: 0.5pt)
+        content((1.2, 0), $U_0$)
+      })),
+    );
+    #linebreak()
+    *Klein-Signal* $quad u_"lin" = r_"lin" (i) = r'(i_"AP")i$
+  ]
+
+
+  #colbreak()
   // Graphen und Matrizen
   #bgBlock(fill: colorAnalyseVerfahren)[
     #subHeading(fill: colorAnalyseVerfahren)[Graphen und Matrizen]
@@ -425,7 +527,7 @@
     $bold(A) : bold(i_k) -> text("Knotenstrombilanz") = 0$ \
     $bold(A^T) : bold(u_b)-> bold(u_k)$
     $
-      bold(A) = quad mannot.mark(
+      bold(A) = quad space space mannot.mark(
         mat(
           a_11, a_12, ..., a_(1m);
           a_21, a_22, ..., a_(2m);
@@ -433,13 +535,13 @@
           a_(n 1), a_(n 2), ..., a_(n m)
         ), tag: #<1>
       )
-      #mannot.annot(<1>, pos: left, text(rgb("#404296"))[#rotate(-90deg)[$<-$ Knoten]], dx: 5mm)
+      #mannot.annot(<1>, pos: left, text(rgb("#404296"))[#rotate(-90deg)[$<-$ Knoten \ ($n-1$)]], dx: 2mm)
-      #mannot.annot(<1>, pos: bottom, text(rgb("#404296"))[Zweige $->$], dy: -0.5mm)
+      #mannot.annot(<1>, pos: bottom, text(rgb("#404296"))[Zweige ($b$) $->$], dy: -0.5mm)
       a in {-1, 0, 1}
     $
-
+    #linebreak()
-    $-1$: In Knoten rein \
+    $-1 &: "In Knoten rein" \
-    $1$: Aus Knoten raus \
+    1 &: "Aus Knoten raus"$
 
     #line(length: 100%, stroke: (thickness: 0.2mm))
 
@@ -450,21 +552,22 @@
     $bold(B^T) : bold(i_m) -> i_b$
 
     $ 
-      bold(B) = quad mannot.mark(mat(
+      bold(B) = quad space space mannot.mark(mat(
         b_11, b_12, ..., b_(1m);
         b_21, b_22, ..., b_(2m);
         dots.v, dots.v, dots.down, dots.v;
         b_(n 1), b_(n 2), ..., b_(n m)
       ), tag: #<1>)
 
-      #mannot.annot(<1>, pos:left, text(rgb("#404296"))[#rotate(-90deg)[$<-$ Maschen]], dx: 6mm)
+      #mannot.annot(<1>, pos:left, text(rgb("#404296"))[#rotate(-90deg)[$<-$ Maschen \ $b-(n-1)$]], dx: 4mm)
-      #mannot.annot(<1>, pos:bottom, text(rgb("#404296"))[Zweige $->$], dy: -0.5mm)
+      #mannot.annot(<1>, pos:bottom, text(rgb("#404296"))[Zweige ($b$) $->$], dy: -0.5mm)
 
       b in {-1, 0, 1}
     $
 
-    $-1$: Gegen Maschenrichtung
+    #linebreak()
-    $1$: In Maschenrichtung
+    $-1 &: "Gegen Maschenrichtung" \
+    1 &: "In Maschenrichtung"$
 
     #line(length: 100%, stroke: (thickness: 0.2mm))
 
@@ -476,6 +579,9 @@
     KVL in Nullraum: $bold(B) bold(u_b) = bold(0)$ \
     KCL in Bildraum: $bold(B^T) bold(i_m) = bold(i_b)$ \
 
+    #line(length: 100%, stroke: (thickness: 0.2mm))
+
+
     *Tellegen'sche Satz* \
     $bold(A B^T) = bold(B^T A) = 0$ \
     $bold(u_b^T i_b) = 0$
@@ -729,88 +835,6 @@
     )
   ],
 
-  // Linearsierung
-  #bgBlock(fill: colorEineTore)[
-    #subHeading(fill: colorEineTore)[Linearisierung (Ein-Tore)]
-
-    1. Arbeitspunkt bestimmen \ $"AP" =(u_"AP", i_"AP")$
-
-    2. Ableitung $g_cal(F)(u)$/$r_cal(F)(i)$ bilden \ $g'_cal(F)(u)$/$r'_cal(F)(i)$
-
-    *Stromgesteuert $r(i) = u$*
-
-    Groß-Signal:
-
-    $i_"lin" = g_"lin" (u) = g'_cal(F)(u_"AP")(u-u_"AP") + i_"AP" = \
-    g'_cal(F)(u_"AP")u - g'_cal(F)(u_"AP")u_"AP" + i_"AP"$
-
-    $I_0 = i_"AP" - g'_cal(F)(u_"AP")u_"AP"$
-
-    $g_0 = g'_cal(F)(u_"AP")u$
-
-    #block(
-      height: 20mm,
-      scale(x: 75%, y: 75%, zap.circuit({
-        import zap: *
-        import cetz.draw: content, line
-
-        isource("I0", (0, 1.5), (0, -1.5), fill: none)
-        node("n0", (2, 1.5))
-        node("n1", (2, -1.5))
-
-        node("n2", (3.5, 1.5), fill: false)
-        node("n3", (3.5, -1.5), fill: false)
-
-        resistor("g0", "n1", "n0", fill: none, label: (content: $g_0$, anchor: "south", distance: 0.2))
-        wire("I0.in", "n0", "n2")
-        wire("I0.out", "n1", "n3")
-        wire("n0", "n2", i: (content: $i_"lin"$, anchor: "south", invert: true))
-        wire((0, 0.6), "I0.in", i: (content: $I_0$, anchor: "east", invert: true))
-
-        set-style(mark: (end: ">", fill: black))
-        line((3.5, 1.2), (3.5, -1.2), stroke: 0.5pt)
-        content((3.9, 0), $u$)
-      })),
-    );
-
-    #linebreak()
-
-    Klein-Signal:$i_"lin" = g_"lin" (u) = g'(u_"AP")u$
-
-    *Spannungsgesteuert $g(u) = i$*
-
-    $u_"lin" = r_"lin" (i) = r'(i_"AP")(i-i_"AP") + u_"AP"$
-
-    $U_0 = u_"AP" - r'(i_"AP") i_"AP"$
-
-    #block(
-      height: 25mm,
-      scale(x: 75%, y: 75%, zap.circuit({
-        import zap: *
-        import cetz.draw: content, line
-
-        vsource("U0", (0, 1.5), (0, -1.5), fill: none)
-
-        node("n2", (3.5, 1.5), fill: false)
-        node("n3", (3.5, -1.5), fill: false)
-
-        resistor("R0", "U0.in", "n2", fill: none, label: (content: $r_0$, anchor: "south", distance: 0.1))
-        wire("U0.out", "n3")
-
-        wire((2.49, 1.5), "n2", i: (content: $i$, anchor: "south", invert: true))
-
-        set-style(mark: (end: ">", fill: black))
-        line((3.5, 1.2), (3.5, -1.2), stroke: 0.5pt)
-        content((3.9, 0), $u_"lin"$)
-
-        line((0.7, 0.5), (0.7, -0.5), stroke: 0.5pt)
-        content((1.2, 0), $U_0$)
-      })),
-    );
-    Klein-Signal: $u_"lin" = r_"lin" (i) = r'(i_"AP")i$
-  ]
-  #colbreak()
-
   // Linearsierung (N-Tore)
   #bgBlock(fill: colorZweiTore)[
     #subHeading(fill: colorZweiTore)[Linearisierung (N-Tore)]
@@ -905,16 +929,32 @@
       columns: (1fr, 0pt, 1fr),
       row-gutter: 4mm,
       column-gutter: 2mm,
-      [
+      [*Kapazitiv*],
-        *Kapazitiv*
-      ],
       grid.vline(stroke: 0.75pt),
       [],
+      [*Induktivität*],
       [
-        *Induktivität*
+        $q = c(u) \ u = chi(q)$\
       ],
+      [],
       [
-        $q = c(u) \ chi(q) = u$\
+        $Phi = l(i) \ i = lambda(Phi)$
+      ],
+
+      [$u,q$ stetig und beschränkt],
+      [],
+      [$i,Phi$ stetig und beschränkt],
+
+      grid.hline(stroke: 0.75pt),
+      [],
+      [],
+      [],
+
+      [*Restiv*],
+      [],
+      [*Memristiv*],
+      [
+        $i = g(u) \ u = r(i)$\
       ],
       [],
       [
@@ -927,6 +967,8 @@
       [],
     )
 
+    #line(length: 100%, stroke: (thickness: 0.2mm))
+
     #align(center, [*Lineare Bauelemente*])
     #grid(
       columns: (1fr, 0pt, 1fr),
@@ -1198,7 +1240,7 @@
     #subHeading(fill: colorAnalyseVerfahren)[Knotenpotenzial-Analyse Komponetent]
     #import mannot: *
 
-    #let ImageHeight = 3.0cm
+    #let ImageHeight = 2.5cm
 
     #table(
       columns: (1fr, 1fr),
@@ -1222,6 +1264,10 @@
       align(center, image("../images/schaltungstheorie/knotenpotenzial/schaltKontenPotenziell1.png", height: ImageHeight, fit: "contain")),
 
       align(center, image("../images/schaltungstheorie/knotenpotenzial/schaltKontenPotenziell2.png", height: ImageHeight, fit: "contain")),
+    
+      align(center, image("../images/schaltungstheorie/knotenpotenzial/nullator.jpg", height: ImageHeight, fit: "contain")),
+    
+      align(center, image("../images/schaltungstheorie/knotenpotenzial/norator.jpg", height: ImageHeight, fit: "contain")),
 
     )
   ]
@@ -1231,6 +1277,7 @@
   // Bauelemente
   #bgBlock(fill: colorEineTore)[
     #subHeading(fill: colorEineTore)[Bauelemente]
+    
     #table(
       columns: (1fr, 1fr, 1fr),
       stroke: none,