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

src/cheatsheets/Schaltungstheorie.typ

@@ -1260,11 +1260,6 @@
     )
   ]
 
-  #bgBlock(fill: colorAllgemein)[
-    #subHeading(fill: colorAllgemein)[Complex Zahlen]
-
-  ]
-
   // Complex AC
   #bgBlock(fill: colorComplexAC)[
     #subHeading(fill: colorComplexAC)[Komplex Wechselstrom Rechnnung]
@@ -1310,6 +1305,8 @@
 
     $P_w = U_m^2 / 2R = (I_m^2 R)/2$
 
+    $P = 1/2 U I^* = 1/2 abs(U)^2 Y^* = 1/2 abs(I)^2 Z^*$
+
     $U_"eff" = U_m/sqrt(2), I_"eff" = I_m / sqrt(2)$
   ]
 
@@ -1331,10 +1328,124 @@
 
 #pagebreak()
 
+#bgBlock(fill: colorZweiTore, width: 100%)[
+  #subHeading(fill: colorZweiTore)[Zwei-Tor-Übersichts]
+
+  #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*],
+    
+    [Nullor],
+    [],
+    [],
+    [],
+    [$A = mat(0, 0; 0, 0)$],
+    [],
+
+    [OpAmp \ lin],
+    [],
+    [],
+    [],
+    [],
+    [],
+
+    [OpAmp \ $U_"sat+"$],
+    [],
+    [],
+    [],
+    [],
+    [],
+
+    [OpAmp \ $U_"sat-"$],
+    [],
+    [],
+    [],
+    [],
+    [],
+
+    [VCVS],
+    [],
+    [],
+    [],
+    [$H' = mat(0, 0; mu, 0) quad A = mat(1/mu 0; 0, 0)$],
+    [],
+
+    [VCCS],
+    [],
+    [],
+    [], 
+    [$G = mat(0, 0; g, 0) quad A = mat(0, -1/g; 0, 0)$],
+    [],
+
+    [CCVS],
+    [],
+    [],
+    [],
+    [$R = mat(0, 0, r, 0) quad A = mat(0, 0; 1/r, 0)$],
+    [],
+
+    [CCCS],
+    [],
+    [],
+    [],
+    [$H = mat(0, 0; beta, 0) quad A = mat(0, 0; 0, -1/beta)$],
+    [],
+
+    [Übertrager],
+    [],
+    [],
+    [],
+    [],
+    [],
+
+    [Gyrator],
+    [],
+    [],
+    [
+      - Antireziprok, Antisymetrisch
+      - Auch Positiv-Immitanz-Inverter
+    ],
+    [$R = mat(0, -R_d; R_d, 0) quad G = mat(0, G_d; -G_d, 0) \ A = mat(0, R_d; 1/R_d, 0) quad A' = mat(0, -R_d; -1/R_d, 0)$],
+    [],
+
+    [NIK],
+    [],
+    [],
+    [],
+    [
+      - Akitv
+      - 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],
+    [],
+    [],
+    [
+
+    ]
+  )
+]
+
+
 // Tor Eigenschaften
-#place(
+#bgBlock(fill: colorEigenschaften, width: 100%)[
-  bottom, float: true, scope: "parent",
-  bgBlock(fill: colorEigenschaften, width: 100%)[
   #subHeading(fill: colorEigenschaften)[Tor Eigenschaften]
 
   #table(
@@ -1421,11 +1532,9 @@
     [Klar],
     [$det(M) != 0$, Alle Eintrag $!= 0$]
   )
-  ]
+]
-)
 
-#place(bottom+left, scope: "parent", float: true)[
+#bgBlock(fill: colorZweiTore)[
-  #bgBlock(fill: colorZweiTore)[
   #set text(size: 10pt)
 
   #subHeading(fill: colorZweiTore)[Umrechnung Zweitormatrizen]
@@ -1518,5 +1627,4 @@
       $bold(A') vec(u_1, -i_1) = vec(i_2, u_2)$,
     
     )
-  ]
 ]

src/lib/common_rewrite.typ

@@ -1,4 +1,4 @@
-#let bgBlock(body, fill: color, width: 100%) =    block(body, fill:fill.lighten(80%), width: width, inset: (bottom: 2mm))
+#let bgBlock(body, fill: color, width: 100%) = block(body, fill:fill.lighten(80%), width: width, inset: (bottom: 2mm, left: 2mm, right: 2mm,))
 
 #let SeperatorLine = line(length: 100%, stroke: (paint: black, thickness: 0.3mm))
 #let MathAlignLeft(e) = {
@@ -6,7 +6,7 @@
 }
 
 #let subHeading(body, fill: color) = {
-  box(
+  move(dx: -2mm, dy: 0mm, box(
     align(
       top+center,
       text(
@@ -17,10 +17,10 @@
       )
     ),
     fill: fill,
-    width: 100%,
+    width: 100% + 4mm,
     inset: 1mm,
     height: auto
-  )
+  ))
 }
 
 #let MathAlignLeft(e) = {
@@ -58,12 +58,14 @@
 #let ComplexNumbersSection(i: $i$) = [
   $1/#i = #i^(-1) = -#i quad quad #i^2=-1 quad quad sqrt(#i) = 1/sqrt(2) + 1/sqrt(2)#i$
 
-  $z in CC = a + b #i quad quad quad z = r dot e^(phi #i)$ \
+  $z in CC = a + b #i quad quad quad z = r dot e^(#i phi)$ \
   $z_0 + z_1 = (a_0 + a_1) + (b_0 + b_1) #i$\
   $z_0 dot z_1 = (a_1 a_2 - b_1 b_2) + #i (a_1b_2 + a_2 b_1) = r_0 r_1 e^(#i (phi_0 + phi_1))$\
   $z^x = r^x dot e^(phi #i dot x) quad x in RR$ \
   $z_0/z_1 = r_0/r_1 e^(#i (phi_0 - phi_1)) quad quad quad$ 
 
+  $z^* = a - #i b = r e^(-#i phi)$
+
   $r = abs(z) quad phi = cases(
     + arccos(a/r) space : space b >= 0,
     - arccos(a/r) space : space b < 0,