added complex komonent list

.gitea/workflows/build-script.yaml

@@ -43,6 +43,11 @@ jobs:
         continue-on-error: true
         run: typst compile --root src src/cheatsheets/Digitaltechnik.typ "build/sem1-Digitaltechnik.pdf"
 
+      - name: Compile CT
+        continue-on-error: true
+        run: typst compile --root src src/cheatsheets/CT.typ "build/sem1-Computertechnik.pdf"
+
+
       - name: Create Gitea Release
         continue-on-error: true
         uses: akkuman/gitea-release-action@v1

src/cheatsheets/Analysis1.typ

@@ -1,9 +1,7 @@
-#import "../lib/common_rewrite.typ" : *
 #import "@preview/mannot:0.3.1"
 
-#show math.integral: it => math.limits(math.integral)
+#import "../lib/common_rewrite.typ" : *
-#show math.sum: it => math.limits(math.sum)
+#import "../lib/mathExpressions.typ" : *
-#let lim = $limits("lim")$
 
 #set text(7.5pt)
 
@@ -106,9 +104,8 @@
   // Complex Zahlen
   #bgBlock(fill: colorAllgemein)[
     #subHeading(fill: colorAllgemein)[Complexe Zahlen]
-    $z = r dot e^(phi i) = r (cos(phi) + i sin(phi))$
 
-    $z^n = r^n dot e^(phi i dot n) = r^n (cos(n phi) + i sin(n phi))$
+    #ComplexNumbersSection()
 
     #grid(
       columns: (1fr, 1fr),

src/cheatsheets/CT.typ

@@ -0,0 +1,154 @@
+#import "../lib/styles.typ" : *
+#import "../lib/common_rewrite.typ" : *
+#import "@preview/cetz:0.4.2"
+
+#set page(
+  paper: "a4", 
+  margin: (
+    bottom: 10mm,
+    top: 5mm,
+    left: 5mm,
+    right: 5mm
+  ),
+  flipped:true,
+  numbering: "— 1 —",
+  number-align: center
+)
+
+#set text(size: 8pt)
+
+#place(top+center, scope: "parent", float: true, heading(
+  [Computer Technik/Programmierpraktikum EI]
+))
+
+#let Allgemein = color.hsl(105.13deg, 92.13%, 75.1%)
+#let colorProgramming = color.hsl(330.19deg, 100%, 68.43%)
+#let colorNumberSystems = color.hsl(202.05deg, 92.13%, 75.1%)
+// #let colorVR = color.hsl(280deg, 92.13%, 75.1%)
+// #let colorAbbildungen = color.hsl(356.92deg, 92.13%, 75.1%)
+// #let colorGruppen = color.hsl(34.87deg, 92.13%, 75.1%)
+
+
+#let SeperatorLine = line(length: 100%, stroke: (paint: black, thickness: 0.3mm))
+#let MathAlignLeft(e) = {
+  align(left, block(e))
+}
+#columns(2, gutter: 2mm)[
+  #bgBlock(fill: colorNumberSystems)[
+    #subHeading(fill: colorNumberSystems)[ASCII Ranges]
+
+    #table(
+      columns: (1fr, 1fr, 1fr),
+      [Range], [Hex], [Bits],
+      [Upper Case], raw("0x41-0x5A"), [#raw("010XXXXX") (bit 6)],
+      [Lower Case], raw("0x61-0x7A"), [#raw("011XXXXX") (bit 6)],
+      [Numbers (0-9)], raw("0x30-0x39"), [#raw("0011XXXX")],
+      [Ganz ASCII], raw("0x00-0x7F"), [#raw("0XXXXXXX")],
+    )
+  ]
+
+  #bgBlock(fill: colorNumberSystems)[
+    #subHeading(fill: colorNumberSystems)[Einer-Kompilment, Zweier-Kompliment, Float (IEEE 754)]
+
+    *Float (IEEE 754)*
+
+    #cetz.canvas({
+      import cetz.draw : *
+      let cell_size = 0.3;
+      
+      let manntise_stop = 22;
+      let exponent_start = 23;
+      let exponent_stop = 30;
+      let sign_bit = 31;
+      let total_bits = sign_bit + 1;
+
+
+      for i in range(total_bits) {
+        let bit = 31 - i;
+
+        rect((i*cell_size, 0), (i*cell_size+cell_size, 0.5),
+          fill: if bit == sign_bit { rgb("#8fff57") } else { 
+            if ( bit >= exponent_start and bit <= exponent_stop) { rgb("#ffe057") } else { if (bit <= manntise_stop) {rgb("#57a5ff")} else { white } }
+          },
+          stroke: (thickness: 0.2mm)
+        )
+  
+        content((i*cell_size + 0.5*cell_size, 0.25), raw(str(0)))
+      }
+
+      content((cell_size, 0.7), [sign], anchor: "east")
+      content((5*cell_size, 0.7), [Exponent (#str(exponent_stop - exponent_start + 1) bit)])
+      content((20*cell_size, 0.7), [Mantisse/Wert (#str(manntise_stop+1) bit)])
+
+      rect((0,0), (32*cell_size, 0.5))
+
+      content((cell_size*(total_bits - sign_bit), -0.2), anchor: "south", raw(str(sign_bit)), angle: 90deg)
+
+      content((cell_size*(total_bits - exponent_stop), -0.2), anchor: "south", raw(str(exponent_stop)), angle: 90deg)
+
+      content((cell_size*(total_bits - exponent_start), -0.2), anchor: "south", raw(str(exponent_start)), angle: 90deg)
+
+      content((cell_size*(total_bits - manntise_stop), -0.2), anchor: "south", raw(str(manntise_stop)), angle: 90deg)
+
+      content((cell_size*(total_bits), -0.2), anchor: "south", raw(str(0)), angle: 90deg)
+    })
+
+    #cetz.canvas({
+      import cetz.draw : *
+      let cell_size = 0.21;
+      
+      let manntise_stop = 51;
+      let exponent_start = 52;
+      let exponent_stop = 62;
+      let sign_bit = 63;
+      let total_bits = sign_bit + 1;
+
+
+      for i in range(total_bits) {
+        let bit = sign_bit - i;
+
+        rect((i*cell_size, 0), (i*cell_size+cell_size, 0.5),
+          fill: if bit == sign_bit { rgb("#8fff57") } else { 
+            if ( bit >= exponent_start and bit <= exponent_stop) { rgb("#ffe057") } else { if (bit <= manntise_stop) {rgb("#57a5ff")} else { white } }
+          },
+          stroke: (thickness: 0.2mm)
+        )
+  
+        content((i*cell_size + 0.5*cell_size, 0.25), raw(str(0)))
+      }
+
+      content((cell_size, 0.7), [sign], anchor: "east")
+      content((7*cell_size, 0.7), [Exponent (#str(exponent_stop - exponent_start + 1) bit)])
+      content((20*cell_size, 0.7), [Mantisse/Wert (#str(manntise_stop+1) bit)])
+
+      rect((0,0), (total_bits*cell_size, 0.5))
+
+      content((cell_size*(total_bits - sign_bit), -0.2), anchor: "south", raw(str(sign_bit)), angle: 90deg)
+
+      content((cell_size*(total_bits - exponent_stop), -0.2), anchor: "south", raw(str(exponent_stop)), angle: 90deg)
+
+      content((cell_size*(total_bits - exponent_start), -0.2), anchor: "south", raw(str(exponent_start)), angle: 90deg)
+
+      content((cell_size*(total_bits - manntise_stop), -0.2), anchor: "south", raw(str(manntise_stop)), angle: 90deg)
+
+      content((cell_size*(total_bits), -0.2), anchor: "south", raw(str(0)), angle: 90deg)
+    })
+  ]
+
+  #bgBlock(fill: colorProgramming)[
+    #subHeading(fill: colorProgramming)[C]
+
+    #table(
+      columns: (auto, 1fr),
+      fill: white,
+      raw("restrict", lang: "c"), [
+        Funktions Argument modifier
+
+        Gibt compiler den hint, das eine Pointer nur in der Funktion verwedent wird. Kann besser optimiert werden
+      ],
+      raw("volatile", lang: "c"), [
+        Zwingt Compiler den Funktion/Variable nicht wegzuoptimieren
+      ]
+    )
+  ]
+]

src/cheatsheets/Digitaltechnik.typ

@@ -1,6 +1,10 @@
-#import "../lib/common_rewrite.typ" : *
 #import "@preview/mannot:0.3.1"
 #import "@preview/cetz:0.4.2"
+#import "@preview/zap:0.5.0"
+
+#import "../lib/common_rewrite.typ" : *
+#import "../lib/truthtable.typ" : *
+#import "../lib/fetModel.typ" : *
 
 #show math.integral: it => math.limits(math.integral)
 #show math.sum: it => math.limits(math.sum)
@@ -20,11 +24,15 @@
       columns: (1fr, 1fr, 1fr),
       [#align(left, datetime.today().display("[day].[month].[year]"))], 
       [#align(center, counter(page).display("- 1 -"))], 
+      [Thanks to Daniel for the circuit Symbols],
       [#align(right, image("../images/cc0.png", height: 5mm,))]
     )
   ],
 )
 
+#let pTypeFill = rgb("#dd5959").lighten(10%);
+#let nTypeFill = rgb("#5997dd").lighten(10%);
+
 #place(top+center, scope: "parent", float: true, heading(
   [Digitaltechnik]
 ))
@@ -173,18 +181,290 @@
     *KDNF:* Kanonische DNF\
     *KKNF:* Kanonische KNF
 
+    *DMF:* Disjunktive #underline("Minimal")-Form: \ 
+    $ --> LNot(x_0)x_1 + LNot(x_1)$\
+
+    *KMF:* Konjunktive #underline("Minimal")-Form: \
+    $ --> (LNot(x_0) + x_1) dot LNot(x_1)$
+
     $f(underline(x)) -->$ *KKNF* / *KDNF* mit Boolsche Expansion
 
   ]
 
+  // Dotierung
+  #bgBlock(fill: colorRealsierung)[
+    #table(
+      columns: (auto, 1fr),
+      [N-Type],
+      [
+        - Dotierung: Phosphor (V)
+        - Negative Ladgunsträger ($e^-$)
+        - mehr Elektron als Si
+      ],
+      [P-Type],
+      [
+        - Dotierung:  Bor (III)
+        - Postive Landsträger (Löcher)
+        - mehr Löcher als Si
+      ]
+    )
+
+
+    #zap.circuit({
+      import cetz.draw : *
+      import zap : *
+
+      diode("A", (0,1.7), (3,1.7), fill: black, i: (content: $i_d$, anchor: "south"))
+
+
+      rect((0,0),(1,1), fill: pTypeFill, stroke: none)
+      rect((2,0),(3,1), fill: nTypeFill, stroke: none)
+      rect((1,0), (1.5,1), fill: color.lighten(pTypeFill, 50%), stroke: none)
+      rect((1.5,0), (2,1), fill: color.lighten(nTypeFill, 50%), stroke: none)
+      line((2, 0), (2, 1), stroke: (dash: "dotted"))
+      line((1, 0), (1, 1), stroke: (dash: "dotted"))
+      line((1.5, 0), (1.5, 1), stroke: (dash: "densely-dotted"))
+
+      cetz.decorations.brace((2,-0.1),(1,-0.1))
+      content((1.5, -0.6), "RLZ")
+      content((2.5, 0.5), "N")
+      content((0.5, 0.5), "P")
+      content((1.25, 0.5), "-")
+      content((1.75, 0.5), "+")
+    })
+
+    #grid(
+      columns: (1fr, 1fr),
+      column-gutter: 6mm,
+      align: center,
+      [#align(center)[*NMOS*]], [#align(center)[*PMOS*]],
+      grid.cell(inset: 2mm,
+        align(center, 
+          zap.circuit({
+            import "../lib/circuit.typ" : *
+
+            registerAllCustom();
+            fet("T", (0,0), type: "N", scale: 150%);
+          })
+        )
+      ),
+      grid.cell(inset: 2mm,
+        align(center, 
+          zap.circuit({
+            import "../lib/circuit.typ" : *
+
+            registerAllCustom();
+            fet("T", (0,0), type: "P", scale: 150%);
+          }),
+        )
+      ),
+      scale(
+        x: 75%, y: 75%,
+        zap.circuit({
+          import cetz.draw : *
+          import zap : *
+          rect((1.5,0),(4-1.5, 0.1), fill: rgb("#535353"), stroke: none)
+          rect((0,0),(4,-1), fill: pTypeFill, stroke: none)
+          rect((0.5,-0),(1.5, -0.5), fill: nTypeFill, stroke: none)
+          rect((4 - 1.5,-0),(4-0.5, -0.5), fill: nTypeFill, stroke: none)
+          rect((1.5,-0),(2.5, -0.5), fill: none, stroke: (paint: black, dash: "dotted", thickness: 0.06))
+
+          line((3, 0.3), (3, 0))
+          line((1, 0.3), (1, 0))
+          line((2, 0.3), (2, 0.1))
+
+          cetz.decorations.brace((2.5,-0.6),(1.5,-0.6))
+          content((2, -1.3), "Channel")
+          content((3, -0.25), $"n"^+$)
+          content((1, -0.25), $"n"^+$)
+          content((0.5, -0.75), "p")
+
+          content((3, 0.5), "S")
+          content((1, 0.5), "D")
+          content((2, 0.5), "G")
+        })
+      ),
+      scale(
+        x: 75%, y: 75%,
+        zap.circuit({
+          import cetz.draw : *
+          import zap : *
+          rect((1.5,0),(4-1.5, 0.1), fill: rgb("#535353"), stroke: none)
+          rect((0,0),(4,-1), fill: nTypeFill, stroke: none)
+          rect((0.5,-0),(1.5, -0.5), fill: pTypeFill, stroke: none)
+          rect((4 - 1.5,-0),(4-0.5, -0.5), fill: pTypeFill, stroke: none)
+          rect((1.5,-0),(2.5, -0.5), fill: none, stroke: (paint: black, dash: "dotted", thickness: 0.06))
+
+          line((3, 0.3), (3, 0))
+          line((1, 0.3), (1, 0))
+          line((2, 0.3), (2, 0.1))
+
+          cetz.decorations.brace((2.5,-0.6),(1.5,-0.6))
+          content((2, -1.3), "Channel")
+          content((3, -0.25), $"p"^+$)
+          content((1, -0.25), $"p"^+$)
+          content((0.5, -0.75), "n")
+
+          content((3, 0.5), "S")
+          content((1, 0.5), "D")
+          content((2, 0.5), "G")
+        })
+      ),
+    )
+
+    *Drain Strom:*
+
+    NMOS: $I_"Dn" = cases(
+        gap: #0.6em,
+        0 & 0 < U_"GS" < U_t,
+        beta_n (U_"GS" - U_t - U_"DS" / 2) U_"DS" quad & cases(delim: #none, U_"GS" >= U_t, 0 < U_"DS" < U_"GS" - U_t),
+        beta_n/2 (U_"GS" - U_"th")^2 & cases(delim: #none, U_"GS" >= U_t, U_"DS" > U_"GS" - U_t)
+      )$
+
+    PMOS: $I_"Dp" = cases(
+        gap: #0.6em,
+        0 & 0 > U_"GS" > U_t,
+        beta_p (U_"GS" - U_t - U_"DS" / 2) U_"DS" quad & cases(delim: #none, U_"GS" <= U_t, 0 > U_"DS" > U_"GS" - U_t),
+        beta_p/2 (U_"GS" - U_"th")^2 & cases(delim: #none, U_"GS" <= U_t, U_"DS" < U_"GS" - U_t)
+      )
+    $
+  ]
+
+  // Quine McCluskey
   #bgBlock(fill: colorOptimierung)[
     #subHeading(fill: colorOptimierung)[Quine McCluskey]
   ]
 
+  // NMOS/PMOS
   #bgBlock(fill: colorRealsierung)[
-    #subHeading(fill: colorRealsierung)[NMOS/PMOS]
+    #subHeading(fill: colorRealsierung)[CMOS]
+    $hat(=)$ Complemntary MOS
+
+    #table(
+      columns: (1fr, 1fr),
+      zap.circuit({
+        import zap : *
+        import cetz.draw : content
+        import "../lib/circuit.typ" : *
+
+        set-style(wire: (stroke: (thickness: 0.025)))
+
+        registerAllCustom();
+        fet("N0", (0,0), type: "N", angle: 90deg);
+        fet("P0", (0,1), type: "P", angle: 90deg);
+        wire("N0.G", (rel: (-0.1, 0)), (horizontal: (), vertical: "P0.G"), "P0.G")
+
+        node("outNode", (0,0.5))
+        node("inNode", (-0.6,0.5))
+        wire((-1, 0.5), "inNode")
+        wire((0.2, 0.5), "outNode")
+
+        node("N2", (0,-0.5))
+        node("N2", (0,1.5))
+
+        wire((-1, -0.5), (0.5, -0.5))
+        wire((-1, 1.5), (0.5, 1.5))
+
+        content((-1, 0.5), scale($"X"$, 60%), anchor: "east")
+        content((0.45, 0.5), scale($overline("X")$, 60%), anchor: "east")
+        content((-0.9, 1.5), scale($"U"_"DD"$, 60%), anchor: "east")
+        content((-0.9, -0.5), scale($"GND"$, 60%), anchor: "east")
+      }),
+
+      [
+        *Inverter*
+        
+        $overline(X)$
+      ],
+
+      zap.circuit({
+        import zap : *
+        import cetz.draw : content
+        import "../lib/circuit.typ" : *
+
+        set-style(wire: (stroke: (thickness: 0.025)))
+
+        registerAllCustom();
+        fet("P0", (0.5,0.25), type: "P", angle: 90deg);
+        fet("P1", (0.5,1.25), type: "P", angle: 90deg);
+        fet("N0", (0,-1), type: "N", angle: 90deg);
+        fet("N1", (1,-1), type: "N", angle: 90deg);
+
+        content((-0.7, 1.75), scale($"V"_"DD"$, 60%), anchor: "east")
+        content((-0.7, -1.5), scale($"GND"$, 60%), anchor: "east")
+
+        content("N0.G", scale($"B"$, 60%), anchor: "east")
+        content("P0.G", scale($"B"$, 60%), anchor: "east")
+        content("N1.G", scale($"A"$, 60%), anchor: "east")
+        content("P1.G", scale($"A"$, 60%), anchor: "east")
+
+        wire((-0.75, -1.5), (1.5, -1.5))
+        wire((-0.75, 1.75), (1.5, 1.75))
+
+        wire("N0.S", "N1.S")
+        node("N2", "P0.D")
+        wire("N2", (horizontal: (), vertical: "N0.S"))
+        node("N3", "N0.D")
+        node("N4", "N1.D")
+        node("N5", "P1.S")
+        node("N6", (horizontal: (), vertical: "N0.S"))
+
+        wire("N2", (horizontal: (rel: (0.5, 0)), vertical: "N2"))
+        
+        content((horizontal: (rel: (0.65, 0)), vertical: "N2"), scale($"Y"$, 60%))
+      }),
+
+      [
+        *NOR*
+
+        $overline(A +B) = Y$
+      ],
+
+      zap.circuit({
+        import zap : *
+        import cetz.draw : content
+        import "../lib/circuit.typ" : *
+
+        set-style(wire: (stroke: (thickness: 0.025)))
+
+        registerAllCustom();
+        content((-0.7,  0.5), scale($"V"_"DD"$, 60%), anchor: "east")
+        content((-0.7, -2.75), scale($"GND"$, 60%), anchor: "east")
+
+        fet("P0", (0, 0), type: "P", angle: 90deg);
+        fet("P1", (1, 0), type: "P", angle: 90deg);
+        fet("N0", (0.5,-1.25), type: "N", angle: 90deg);
+        fet("N1", (0.5,-2.25), type: "N", angle: 90deg);
+
+        wire((-0.75, 0.5), (1.5, 0.5))
+        wire((-0.75, -2.75), (1.5, -2.75))
+        wire("P0.D", "P1.D")
+
+        node("N2", (horizontal: "N1.D", vertical: "P0.D"))
+        node("N3", "N0.S")
+        wire("N2", "N3")
+        wire("N3", (rel: (0.5, 0)))
+
+        content((horizontal: (rel: (0.65, 0)), vertical: "N3"), scale($"Z"$, 60%))
+        node("4", "P0.S")
+        node("4", "P1.S")
+        node("4", "N1.D")
+
+        content("N0.G", scale($"B"$, 60%), anchor: "east")
+        content("P0.G", scale($"B"$, 60%), anchor: "east")
+        content("N1.G", scale($"A"$, 60%), anchor: "east")
+        content("P1.G", scale($"A"$, 60%), anchor: "east")
+      }),
+
+      [
+        *NAND*
+
+        $overline(A dot B) = Z$
+      ],
+    )
   ]
 
+  // CMOS
   #bgBlock(fill: colorRealsierung)[
     #subHeading(fill: colorRealsierung)[CMOS Verzögerung]
 
@@ -287,10 +567,7 @@
         (cycle_start,signal_hight), (cycle_time*(t_setup + 2), signal_hight), 
         (cycle_time*(t_setup + 2) + switch_offset, 0), (cycle_end + switch_offset, 0), stroke: signal_storke
       )
-    
-
     })
-
   ]
 
 
@@ -323,9 +600,6 @@
     - Leckstom (weil Diode)
     - Gatestrom 
 
-
-
-
     *Schaltrate*
 
     $alpha_"clk" = 100%$
@@ -334,3 +608,18 @@
 
   ]
 ]
+
+#place(bottom,
+  truth-table(
+    outputs: (
+      ("NAND", (1, 1, 1, 0)),
+      ("NOR",  (1, 0, 0, 0)),
+      ("XNOR", (1, 0, 0, 1)),
+      ("XOR",  (0, 1, 1, 0)),
+      ("AND",  (0, 0, 0, 1)),
+      ("OR",   (0, 1, 1, 1)),
+    ),
+    inputs: ("A", "B")
+  ),
+  float: true
+)

src/cheatsheets/LinearAlgebra.typ

@@ -1,7 +1,11 @@
 #import "@preview/biceps:0.0.1" : *
 #import "@preview/mannot:0.3.1"
+#import "@preview/fletcher:0.5.8"
+#import "@preview/cetz:0.4.2"
+
 #import "../lib/styles.typ" : *
 #import "../lib/common_rewrite.typ" : *
+#import "../lib/mathExpressions.typ" : *
 
 #set page(
   paper: "a4", 
@@ -23,8 +27,9 @@
 ))
 
 #let colorAllgemein = color.hsl(105.13deg, 92.13%, 75.1%)
+#let colorMatrixVerfahren = color.hsl(330.19deg, 100%, 68.43%)
 #let colorMatrix = color.hsl(202.05deg, 92.13%, 75.1%)
-#let colorReihen = color.hsl(280deg, 92.13%, 75.1%)
+#let colorVR = color.hsl(280deg, 92.13%, 75.1%)
 #let colorAbbildungen = color.hsl(356.92deg, 92.13%, 75.1%)
 #let colorGruppen = color.hsl(34.87deg, 92.13%, 75.1%)
 
@@ -35,9 +40,11 @@
 }
 #columns(4, gutter: 2mm)[
     #bgBlock(fill: colorAllgemein)[
-        #subHeading(fill: colorAllgemein)[Notation]
+        #subHeading(fill: colorAllgemein)[Komplexe Zahlen]
         
+        #ComplexNumbersSection()
         
+        #sinTable
     ]
 
     #bgBlock(fill: colorGruppen)[
@@ -75,8 +82,6 @@
         - $(R, dot)$ Halbgruppe
         - $(a + b) dot c = (a dot c) + (a dot b) space$ (Distributiv Gesetz)
 
-        #colbreak()
-
         *Körper:* Menge $K$ mit:
         - $(K, +), (K without {0} , dot)$ kommutativ Gruppe \
             ($0$ ist Neutrales Element von $+$)
@@ -84,8 +89,8 @@
         _Beweiß durch Überprüfung der Eigneschaften_
     ]
 
-    #bgBlock(fill: colorReihen)[
+    #bgBlock(fill: colorVR)[
-        #subHeading(fill: colorReihen)[Vektorräume (VR)]
+        #subHeading(fill: colorVR)[Vektorräume (VR)]
         $(V, plus.o, dot.o)$ ist ein über Körper $K$
         - $+: V times V -> V, (v,w) -> v + w$
         - $dot: K times V -> V, (lambda,v) -> lambda v$
@@ -102,8 +107,8 @@
         - $(U inter W) subset V$
     ]
 
-    #bgBlock(fill: colorReihen)[
+    #bgBlock(fill: colorVR)[
-        #subHeading(fill: colorReihen)[Basis und Dim]
+        #subHeading(fill: colorVR)[Basis und Dim]
         *Linear Abbildung:* $Phi: V -> V$ 
         - $Phi(0) = 0$
         - $Phi(lambda v + w) = lambda Phi(v) + Phi(w)$
@@ -154,6 +159,7 @@
         *Vektorraum-Homomorphismus:* linear Abbildung zwischen VR
     ]
 
+    // Spann und Bild, Kern
     #bgBlock(fill: colorAbbildungen)[
         #subHeading(fill: colorAbbildungen)[Spann und Bild]
         *Spann:* 
@@ -173,131 +179,252 @@
 
         *Rang*
         $op("Rang") f := dim op("Bild") f$
+
+        *Dimensionssatz:* Sei $A$ lineare Abbildung \
+        $dim(V) = dim(kern(A)) + dim(Bild(A))$ \
+        $dim(V) = dim(kern(A)) + Rang(A)$ \
+
+        $dim(V) = dim(Bild(A)) "oder" dim(kern(A)) = 0 \ <=> A "bijektiv" <=> "invertierbar"$
     ]
 
+    #bgBlock(fill: colorAbbildungen)[
+        #subHeading(fill: colorAbbildungen)[Determinate und Bilinearform]
+    ]
+
+    #bgBlock(fill: colorVR)[
+        #subHeading(fill: colorVR)[Eukldische Vektorräume]
+    ]
+
+    #bgBlock(fill: colorVR)[
+        #subHeading(fill: colorVR)[Unitair Vektorräume ]
+    ]
+
+
+    // Matrix Typem
     #bgBlock(fill: colorMatrix)[
+        #let colred(x) = text(fill: red, $#x$)
+        #let colblue(x) = text(fill: blue, $#x$)
+
         #subHeading(fill: colorMatrix)[Matrix Typen]
+        #align(center, scale($colred(m "Zeilen") colblue(n "Splate")\ A in KK^(colred(m) times colblue(n))$, 120%)) #grid(columns: (1fr, 1fr),
+        $quad mat(
+                a_11, a_12, ..., a_(1n);
+                a_21, a_22, ..., a_(2n);
+                dots.v, dots.v, dots.down, dots.v;
+                a_(m 1), a_(m 2), ..., a_(m n)
+            )
+        $,
             
-        *Einheits Matrix* $I,E$
+            cetz.canvas({
+                    import cetz.draw : *
 
-        *Diagonalmatrix*
+                    rect((0, 0), (1, 1), fill: rgb("#9292926b"))
 
-        *Symetrisch* $S$: \
+                    set-style(mark: (end: (symbol: "straight")))
-        $A A^T$ ist symetrisch
+                    line((0, -0.2), (1, -0.2), stroke: (paint: blue, thickness: 0.3mm))
+                    line((-0.2, 1), (-0.2, 0), stroke: (paint: red, thickness: 0.3mm))
 
-        *Orthogonal* $O$:
+                    content((-0.45, 0.5), $colred(bold(m))$)
+                    content((0.5, -0.35), $colblue(bold(n))$)
+                    content((0.5, 0.5), $A$)
+                })
+        )
 
-        *Unitair:*
+        #table(
+            columns: (auto, 1fr),
+            inset: 2mm,
+            fill: (x, y) => if (calc.rem(y, 2) == 0) { tableFillLow } else { tableFillHigh },
+            [*Einheits Matrix*\ $I,E$], [],
+            [*Diagonalmatrix* \ $Sigma,D$], [
+                Nur Einträger auf Hauptdiagonalen \
+                $det(D) = d_00 dot d_11 dot d_22 dot ...$
+            ],
+            [*Symetrisch*\ $S$], [
+                $S = S^T$, $S in KK^(n times n)$\
+                $A A^T$, $A^T A$ ist symetrisch \
+                $S$ immer diagonaliserbar \
+                EW immer $in RR$, EV orthogonal
+            ],
+            [*Invertierbar*], [
+                $exists A^(-1) : A A^(-1) = A^(-1) A = E$ \
 
-        *postiv-semi-definit* \
+                *Invertierbar wenn:* \
-        $forall$ Eigenwerte $>= 0$
+                $A$ bijektiv, $det(A) = 0$ \
+                $"Spalten Vekoren lin. unabhänig"$ \
+                $det(A) = 0$ \                
+
+                *Nicht Invertierbar wenn:*\
+                $exists$ EW $!= 0 => not "invertierbar"$
+                Keine Qudratische Matrix
+            ],
+            [*Orthogonal*\ $O$], [
+                $O^T = O^(-1)$ \
+                $ip(O v, O w) = ip(v, w)$
+            ],
+            [*Unitair*], [
+                $V^* )$
+            ],
+            [*Diagonaliserbar*], [
+                $exists A = B D B^(-1)$, $D$ diagonal,
+
+                $B$: Splaten sind EV von $A$
+
+                - Selbst-Adujunkte diagonalisierbar
+                - Symetrisch Matrix
+                - $A in KK^(n times n) "AND" alg(lambda) = geo(lambda)$
+            ],
+            [*postiv-semi-definit*], [
+                $forall$ EW $>= 0$
+            ],
+        )
     ]
 
-    #colbreak()
+    #bgBlock(fill: colorMatrixVerfahren)[
 
-    #bgBlock(fill: colorMatrix)[
+        #subHeading(fill: colorMatrixVerfahren)[Eigenwert und Eigenvektoren ]
-
-        #subHeading(fill: colorMatrix)[Eigenwert und Eigenvektoren ]
 
         $A in CC^(n times n):$ $n$ Complexe Eigenwerte \
         $A in RR^(n times n)$
 
-        *Eigentwete bestimmen*
+        *1. Eigentwete bestimmen*
         
-        $A v = lambda v$
+        $A v = lambda v => det(A-E lambda) = 0$
 
-        Lösen: $0 = det mat(#mannot.markhl($x_11 - lambda_1$, color: red), x_12, ..., x_(1n);
+        $0 = det mat(#mannot.markhl($x_11 - lambda_1$, color: red), x_12, ..., x_(1n);
             x_21, #mannot.markhl($x_22 - lambda_2$, color: red), ..., x_(2n);
             dots.v, dots.v, dots.down,  dots.v;
             x_(n 1), x_(n 2), ..., #mannot.markhl($x_(n n) -lambda_n$, color: red)
         )$
 
-        Charakteristisches Polynom: $chi_(A)$
+        $--> chi_A = (lambda_0 - lambda)^(n_0) dot (lambda_1 - lambda)^(n_1) ... $
 
 
-        *Eigenvektor bestimmen*
+        $lambda_0, lambda_1, ... = $ Nst von $chi_A$
-        
-        Eigentwerte einsetzen: $lambda in {lambda_1, lambda_2, ... lambda}$
 
 
-        *Algebrasche Vielfacheit:* \
+        *2. Eigenvektor bestimmen*
-        $sum$ Häufikeit der Nsts von $chi_A$
         
-        *Geometrische Vielfacheit:*\
+        $Eig(lambda_k) = kern(A - lambda_k E)$
-        $dim(op("spann")(v_lambda_1, v_lambda_2 ..., v_lambda_n))$ \
         
-        Anzahl der linearunabhänige $v_lambda_i$ 
+        $mat(#mannot.markhl($x_11 - lambda_k$, color: red), x_12, ..., x_(1n);
+            x_21, #mannot.markhl($x_22 - lambda_k$, color: red), ..., x_(2n);
+            dots.v, dots.v, dots.down,  dots.v;
+            x_(n 1), x_(n 2), ..., #mannot.markhl($x_(n n) -lambda_k$, color: red)
+        ) vec(v_1, v_2, dots.v, v_n) = vec(0, 0, dots.v, 0)$
 
-        $"Geometrische" <= "Algebrasche"$
+
+
+        *Algebrasche Vielfacheit:* $alg(lambda) = n_0 + n_1 + ...$ \
+        *Geometrische Vielfacheit:* $geo(lambda) = dim("Eig"_A (lambda))$ \
+
+        $1 <= geo(lambda) <= alg(lambda)$
 
     ]
 
-    #bgBlock(fill: colorMatrix)[
+    #bgBlock(fill: colorMatrixVerfahren)[
-        #subHeading(fill: colorMatrix)[Diagonalisierung]
+        #subHeading(fill: colorMatrixVerfahren)[Gram-Schmit ONB]
+
 
-        $A = R D R^T$
 
-        $D$: Diagonalmatrix
     ]
 
-    #bgBlock(fill: colorMatrix)[
+    #bgBlock(fill: colorMatrixVerfahren)[
-        #subHeading(fill: colorMatrix)[Schur-Zerlegung]
+        #subHeading(fill: colorMatrixVerfahren)[Diagonalisierung]
+        $A = R D R^(-1)$
+
+        *Rezept Diagonalisierung*
+
+        1. EW bestimmen: $det(A - lambda I) = 0$  \
+            $=> chi_A = (lambda_1 - lambda)^(m 1) (lambda_2 - lambda)^(m 2) ...$ 
+        2. EV bestimmen: $spann(kern(A - lambda_i I))$: $r_0, r_1, ...$
+        3. \
+            #grid(columns: (1fr, 1fr),
+            [
+                Diagnoalmatrix: $D$
+                $mat(
+                        lambda_1, 0, 0,...;
+                        0, lambda_1, 0, ...;
+                        0, 0, lambda_2, ...;
+                        dots.v, dots.v, dots.v, dots.down
+                    )
+                $
+            ],
+            [
+                Basiswechselmatrix: $R$
+                $mat(
+                    |, | , ..., |;
+                    r_0, r_1, ..., r_n;
+                    |, |, ..., |
+                )$
+            ]
+        )
+     ]
+
+
+    #bgBlock(fill: colorMatrixVerfahren)[
+        #subHeading(fill: colorMatrixVerfahren)[Schur-Zerlegung]
         immer anwendbar; 
-
-        $A in RR^(n times n)\/CC^(n times n)$ zerlegbar in $O^T R O$
-    
-        Orthogonal $O,O^T$, Dreiecksmatrix $R$
-
-        $R = mat(lambda_1, *, *,..., *;
-            0, lambda_2, *, ..., *;
-            0, 0, lambda_3, ..., *;
-            dots.v, dots.v, dots.v, dots.down, dots.v;
-            0, 0, 0, ..., lambda_n;
-        )$
-
-        1. Eigenwerte bestimmen $lambda_1, lambda_2, ... lambda_n$
-        2. Eigenvektor $v_lambda_1, v_lambda_2 ..., v_lambda_n$
-        3. 
     ]
 
-    #colbreak()
+    #bgBlock(fill: colorMatrixVerfahren)[
+        #subHeading(fill: colorMatrixVerfahren)[SVD]
+
+        $A in RR^(m times n)$ zerlegbar in $A = L S R^T$ \
+
+
+        $L in RR^(m times m)$ Orthogonal \
+        $S in RR^(m times n)$ Diagonal \
+        $R in RR^(n times n)$ Orthogonal
+
+
+        1. $A A^T$ berechnen $A A^T in RR^(m times m)$
+
+        2. $A A^T$ diagonalisieren in $R$, $D$
+
+        3. Singulärwere berechen: $sigma_i = sqrt(lambda_i) $
+        
+        4. $l_i = 1/sigma_i A v_(lambda i) quad quad L = mat( |, |, ..., |; l_0, l_1, ..., l_m; |, |, ..., |)$ \
+            (Evt. zu ONB ergenze mit Gram-Schmit/Kreuzprodukt)
+
+        5. $S in RR^(n times m)$ (wie $A$): \
+            $S = mat(sigma_0, 0; 0, sigma_1; dots.v, dots.v; 0, 0) quad quad quad S = mat(sigma_0, 0, dots, 0; 0, sigma_1, ..., 0)$
+    ]
+
     #bgBlock(fill: colorMatrix)[
-        #subHeading(fill: colorMatrix)[SVD]
+        #subHeading(fill: colorMatrix)[Matrix Normen]
 
-        $A in RR^(n times m)$ zerlegbar in $A = L S R^T$ \
+        $|| dot ||_M$ Matrix Norm, $|| dot ||_V$ Vektornorm
-        $L$ Orthogonal, $S$ Diagonalmatrix, $R$ Orthogonal \
-        $A^T = R S^T L^T$
 
+        Generisch Vektor Norm: $|| v ||_p = root(p, sum_(k=1)^n (x_k)^p)$
 
-        *1. $A A^T$ berechnen* $A A^T in RR^(n times n) $
+        - submultiplikativ: $||A B||_"M" <= ||A||||B||$
+        - verträglich mit einer Vektornorm: $||A v||_"V" <= ||A||_"M" ||v||_"V"$
 
-        *2. Eigenwerte von $A A^T$ bestimmen* $lambda_1, lambda_2, ... lambda_n$
+        *Frobenius-Norm* $||A||_"M" = sqrt(sum_(i=1)^m sum_(j=1)^n a_(m n)^2)$
 
-        *3. $S$ aufstellen* ($S$ hat gleiche Form wie $A$)
+        *Induzierte Norm* $||A||_"M" = sup_(v in V without {0}) (||A v||_V)/(||v||_V)$\
+        $ = sup_(||v|| = 1) (||A v||_V)/(||v||_V)$
+            - submultiplikativ
+            - verträglich mit einer Vektornorm $||dot||_V$
 
-        $sigma_i = sqrt(lambda_i) =  S in RR^(n x m) =\ mat(
+        *maximale Spaltensumme* $||A||_r = max_(1<= i <= n) sum_(j=1)^n |a_(j)|$
-            sigma_1, 0, 0, ..., 0, 0, ..., 0;
-            0, sigma_2, 0, ..., 0, 0, ..., 0;
-            0, 0, sigma_3, ..., 0, 0, ..., 0;
-            dots.v, dots.v, dots.v, dots.down, dots.v, dots.v, dots.down, dots.v;
-            0, 0, 0, ..., sigma_m, 0, ... , 0
-        )$
-
-        *4. $R$ bestimmen*
-
-        $op("Eig")(lambda_i) = op("kern")(A A^T - lambda_i) ->$
-
-        $A A^T - lambda_i = 0$ (Gaußverfahren)
-
-        $R = 1/sqrt(lambda_i)$
-
-        *5. $L$ bestimmen*
-        
-        $L = 1/sqrt(lambda_i) $
     ]
 
+    #bgBlock(fill: colorMatrix)[
+        #subHeading(fill: colorMatrix)[Rekursive Folgen]
 
+        E.g: $a_1 x_(n-1) + a_2 x_(n) = x_(n+1)$
 
+        1. Als Matrix Schreiben $F: vec(x_(n-1), x_(n)) = vec(x_n, x_(n+1))$ \
+            $F s_(n-1) = s_(n)$
+
+        2. Diagonaliseren: $F = R D R^(-1) $ \
+        3. Wiederholte Anwendung: $F^n = R D^n R^(-1)$
 
     ]
 
+    #bgBlock(fill: colorMatrix)[
+        #subHeading(fill: colorMatrix)[Differenzialgleichungen]
+    ]
+]
+

src/cheatsheets/Schaltungstheorie.typ

@@ -1,9 +1,13 @@
-#import "../lib/common_rewrite.typ" : *
 #import "@preview/mannot:0.3.1"
 #import "@preview/zap:0.5.0"
-#import "@preview/cetz:0.4.2"
+#import "@preview/cetz:0.4.2" :*
+#import "@preview/cetz-plot:0.1.3"
 #import "../lib/circuit.typ" : *
 #import "@preview/unify:0.7.1": num,qty,unit
+#import "@preview/cetz-plot:0.1.3"
+
+#import "../lib/common_rewrite.typ" : *
+#import "../lib/circuit.typ" : *
 
 #set math.mat(delim: "[") 
 #show math.equation.where(block: true): it => math.inline(it)
@@ -108,7 +112,70 @@
   #bgBlock(fill: colorAllgemein)[
     #subHeading(fill: colorAllgemein)[Verschaltung]
 
+    $1/x_"ges" = 1/x_1 + 1/x_2 + 1/x_3 + ...$
 
+    $x_1 parallel x_2 = 1/(1/x_1 + 1/x_2) = (x_1 x_2)/(x_1 + x_2)$
+
+    $x_1 parallel x_2 parallel x_3 = (x_1 x_2 x_3)/(x_1 x_2 + x_2 x_3 + x_1 x_3)$
+
+    #table(
+      columns: (1fr, 1fr),
+      fill: (x, y) => if calc.rem(x, 2) == 1 { tableFillLow } else { tableFillHigh },
+
+      [*Serie*],
+      [*Reihe/Parrallel*], 
+      
+      
+      align(
+        horizon+center,
+        scale(100%,
+          zap.circuit({
+            import zap : *
+
+            resistor("R1", (0,0.375), (1.5,0.375), fill: none, width: 1, height: 0.4)
+            resistor("R2", (1.5,0.375), (3,0.375), fill: none, width: 1, height: 0.4)
+          })
+        )
+      ),
+      align(
+        horizon+center,
+        scale(
+          100%,
+          zap.circuit({
+            import zap : *
+
+            resistor("R1", (0,0), (2,0), fill: none, width: 1, height: 0.4)
+            resistor("R2", (0,0.75), (2,0.75), fill: none, width: 1, height: 0.4)
+            wire("R1.in", "R2.in")
+            wire("R1.out", "R2.out")
+
+            node("N2", (0,0.375))
+            node("N3", (2,0.375))
+
+            wire("N2", (rel: (-0.3, 0)))
+            wire("N3", (rel: (0.3, 0)))
+          }),
+        )
+      ),
+
+
+
+      $R_"ges" = R_1+R_2$,
+      $R_"ges" = R_1 parallel R_2$,
+      $G_"ges" = G_1 parallel G_2$,
+      $G_"ges" = G_1 + G_2$,
+      $L_"ges" = L_1 + L_2$,
+      $L_"ges" = L_1 parallel L_2$,
+      $C_"ges" = C_1 parallel C_2$,
+      $C_"ges" = C_1 + C_2$,
+
+      $U_"ges" = U_1 + U_2$,
+      $U_"ges" = U_1 = U_2$,
+      $I_"ges" = I_1 = I_2$,
+      $I_"ges" = I_1 + I_2$,
+      [In $U$-Richtung Addieren],
+      [In $I$-Richtung Addieren],
+    )
   ]
 
   // Quell Wandlung
@@ -133,7 +200,107 @@
     )
   ]
 
-  #colbreak()
+  // Lineare Quelle
+  #bgBlock(fill: colorEineTore)[
+    #subHeading(fill: colorEineTore)[Lineare Quelle]
+
+    #align(
+      center+horizon,
+      cetz.canvas({
+        import cetz.draw: *
+        import cetz-plot: *
+        plot.plot(size: (3, 3), name: "plot",
+            axis-style: "school-book",
+            x-label: "u", y-label: "i",
+            x-tick-step: none, y-tick-step: none,
+            axes: ("u", "i"),
+            x-min: -1, x-max: 2, x-grid: "both",
+            y-min: -2, y-max: 1, y-grid: "both", {
+          plot.add(((-2, -3), (3,2)))
+          plot.add-anchor("u0", (1,0))
+          plot.add-anchor("i0", (0,-1))
+        })
+
+        content("plot.u0", $U_0$, anchor: "south", padding: .2)
+        content("plot.i0", $-I_0$, anchor: "east", padding: .2)
+
+        mark("plot.u0", 0deg, symbol: "+", fill: black)
+        mark("plot.i0", 0deg, symbol: "+", fill: black)
+
+        line("plot.i0", (horizontal: "plot.u0", vertical: "plot.i0"), "plot.u0", stroke: (dash: "dashed", paint: rgb("#005c00")))
+
+        content((horizontal: "plot.u0", vertical: "plot.i0"), anchor: "south-west", text(rgb("#005c00"))[$R$], padding: 0.1)
+      })
+    )
+
+    $U_0$: LL-Spannung ($i = 0 => u = U_0$) \
+    $I_0$: KS-Strom ($u = 0 => i = -I_0$)
+
+    $R_i$: Innenwiderstand $R_i = U_0/I_0$ 
+
+    #table(
+      columns: (1fr, 1fr),
+      fill: (x, y) => if calc.rem(x, 2) == 1 { tableFillLow } else { tableFillHigh },
+      inset: 3mm,
+      align(center, [*$u$-gesteuert*]),
+      align(center, [*$i$-gesteuert*]),
+      
+      align(
+        horizon+center,
+        zap.circuit({
+          import zap : *
+          import cetz.draw
+
+          zap.resistor("R1", (1, 0), (1, -1.5), fill: none, width: 0.8, height: 0.3)
+          zap.isource("I0", (0, 0), (0, -1.5), fill: none, scale: 0.6, i: (content: $-I_0$, distance: 6pt, label-distance: -11pt, anchor: "west", invert: true))
+          node("N0", "R1.in")
+          node("N0", "R1.out")
+
+          wire("I0.out", "R1.out", (rel: (0.5, 0)))
+          wire("I0.in", "R1.in")
+          wire("R1.in", (rel: (0.5, 0)), i: (content: $i$, invert: true))
+
+          cetz.draw.content((0.62, -0.75), [$R$])
+          cetz.draw.set-style(mark: (end: ">", fill: black, scale: 0.6))
+          cetz.draw.content((1.7, -0.75), [$u$])
+          cetz.draw.line((1.5, -0.1), (1.5, -1.4), stroke: 0.5pt)
+        })
+      ),
+      align(
+        horizon+center,
+        zap.circuit({
+          import zap : *
+          import cetz.draw
+
+          zap.vsource("U0", (0, 0), (0, -1.5), fill: none, scale: 0.6, u: (content: $U_0$, distance: -4pt, label-distance: -8pt, anchor: "south-west", invert: true))
+          zap.resistor("R1", (0, 0), (1.75, 0), fill: none, width: 0.8, height: 0.3,
+            i: (content: $i$, invert: true, distance: 0.3)
+          )
+          wire((0, -1.5), (1.75, -1.5))
+      
+          cetz.draw.content((0.62, -0.75), [$R$])
+          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)
+        })
+      ),
+
+      [
+        $u = R_i i + u_0$ \
+
+      ],
+      [
+        $i = 1/R_i u - I_0$
+      ],
+
+      table.cell(colspan: 2)[
+        #align($-->$)
+      ],
+      table.cell(colspan: 2)[
+        $<--$
+      ],
+    )
+  ]
 
   // Quell Wandlung
   #bgBlock(fill: colorEineTore)[
@@ -191,14 +358,14 @@
         
         $R_i=1/G_i$
 
-        $r(i) = R_i i + U_0$
+        $u = r(i) = R_i i + U_0$
       ],
       [
         $I_0 = U_0 G_i$
 
         $G_i=1/R_i$
 
-        $g(u) = G_i u + I_0$
+        $i = g(u) = G_i u + I_0$
       ]
     );
   ]
@@ -207,15 +374,353 @@
     #subHeading(fill: colorEineTore)[Bauelemente]
      #table(
       columns: (1fr, 1fr, 1fr ),
+      stroke: none,
       align: center,
       table.header([*Zeichen*],[*Gleichung*], [*Abbildung*]),
 
-      scale(x: 100%, y: 100%,
+      // Dioden ://
+      // 
+      // ideale Diode
+      [      
+      ideale Diode
+      #scale(x: 100%, y: 100%,
         zap.circuit({
           import zap : *
           import cetz.draw : line, content
-            diode("b1", (0, 0), (1., 0)) 
+            diode("b1", (0, 0), (1., 0), stroke: black, fill: white) 
-      })),
+
+      }))      
+      ],
+      [      
+        $u=0$ falls $i>0$
+        $i=0$ falls $u<0$
+      ],
+      [
+      /*
+      #scale(x: 50%, y: 50%,  
+        cetz.canvas({
+          import cetz.draw: *
+            line((-1.5, 0), (1.5, 0), mark: (end: "straight"))
+            line((0, -1.5), (0, 1.5), mark: (end: "straight"))
+
+            content( (1.55, 0), $u$, anchor: "west")
+            content( (0.15, 1.4), $i$, anchor: "west")
+
+            line((-1.5, 0), (0, 0), stroke: red)      // u = 0
+            line((0, 0), (0, 1.35), stroke: red)      // i = 0  
+
+      }))
+      */
+        #scale(x: 75%, y: 75%,  
+        cetz.canvas({
+          import cetz.draw: *
+          import cetz-plot: *
+
+          let opts = (x-tick-step: none, y-tick-step: none, size: (2,1), x-label: [u], y-label: [i])
+
+          plot.plot(axis-style: "school-book", ..opts, name: "plot",
+          {
+            plot.add(((-1,0), (0,0),), style: (stroke: red))
+            plot.add(((0,0), (0,1),), style: (stroke: red))
+          }
+          )
+      }))
+      ],
+      //table.hline(start: 1, end: 2),
+      
+      // reale/pn Diode
+      [      
+      reale/pn Diode
+      #scale(x: 100%, y: 100%,
+        zap.circuit({
+          import zap : *
+          import cetz.draw : line, content
+            diode("b1", (0, 0), (1., 0), stroke: black, fill: black) 
+
+      }))      
+      ],
+
+      [      
+        $u_D = u_T*ln((i_D/I_S)+1)$
+        $i_D = I_S*(e^(u_D/U_T)-1)$ 
+      ],
+      [
+      #scale(x: 75%, y: 75%,  
+        cetz.canvas({
+          import cetz.draw: *
+          import cetz-plot: *
+
+          let opts = (x-tick-step: none, y-tick-step: none, size: (2,1), x-label: [u], y-label: [i])
+          let data = plot.add(x => calc.exp(x)-1, 
+             domain: (-2, 2), style: (stroke: red))
+
+          plot.plot(axis-style: "school-book", ..opts, data, name: "plot")
+      }))
+      ],
+
+      // Photodiode
+      [      
+      Photodiode
+      #scale(x: 100%, y: 100%,
+        zap.circuit({
+          import zap : *
+          import cetz.draw : line, content
+            photodiode("b1", (0, 0), (1., 0), stroke: black, fill: black) 
+      }))      
+      ],
+      [      
+        $i = I_S*(e^(u_D/U_T)-1)- i_L$ 
+      ],
+      [
+      #scale(x: 75%, y: 75%,  
+        cetz.canvas({
+          import cetz.draw: *
+          import cetz-plot: *
+
+          let opts = (x-tick-step: none, y-tick-step: none, size: (2,1), x-label: [u], y-label: [i])
+
+          plot.plot(axis-style: "school-book", ..opts, name: "plot",
+          {
+            plot.add(x => calc.exp(x)-1, 
+             domain: (-2, 2), style: (stroke: red))
+            
+            plot.add(x => calc.exp(x)-2, 
+             domain: (-2, 2), style: (stroke: red))
+             
+            plot.add(x => calc.exp(x)-3, 
+             domain: (-2, 2), style: (stroke: red))
+             }
+
+          )
+      }))
+      ],
+
+      // Zenerdiode
+      [      
+      Zenerdiode
+      #scale(x: 100%, y: 100%,
+        zap.circuit({
+          import zap : *
+          import cetz.draw : line, content
+                  zener("b1", (0, 0), (1., 0), stroke: black, fill: black) 
+      }))      
+      ],
+      [      
+        Durchbruch bei $u=U_Z$ :
+        $u<=U_Z$ stark leitend
+      ],
+      [      
+        
+      ],
+
+      // Tunneldiode
+      [      
+      Tunneldiode
+      #scale(x: 100%, y: 100%,
+        zap.circuit({
+          import zap : *
+          import cetz.draw : line, content
+                  tunnel("b1", (0, 0), (1., 0), stroke: black, fill: black) 
+      }))      
+      ],
+      [
+
+      ],
+      [
+        
+      ],
+
+      // Quellen: //
+      // Spannungs-quelle
+      [
+        Spannungs-quelle
+      #scale(x: 100%, y: 100%,
+        zap.circuit({
+          import zap : *
+          import cetz.draw : line, content
+                  vsource(
+                    "b1", 
+                  (0, 0), 
+                  (1.75, 0)
+                  ) 
+      }))      
+      ],
+      [
+
+      ],
+      [
+        
+      ],
+
+      // Strom-quelle
+      [
+        Strom-quelle
+      #scale(x: 100%, y: 100%,
+        zap.circuit({
+          import zap : *
+          import cetz.draw : line, content
+                  isource(
+                    "b1", 
+                  (0, 0), 
+                  (1.75, 0)
+                  ) 
+      }))      
+      ],
+      [
+
+      ],
+      [
+        
+      ],
+
+      // Wiederstand
+      [
+      Wiederstand
+      #scale(x: 100%, y: 100%,
+        zap.circuit({
+          import zap : *
+          import cetz.draw : line, content
+                  resistor(
+                    "b1", 
+                  (0, 0), 
+                  (2, 0)
+                  ) 
+      }))      
+      ],
+      [
+
+      ],
+      [
+        
+      ],
+
+      // Induktivität
+      [
+      Induktivität
+      #scale(x: 100%, y: 100%,
+        zap.circuit({
+          import zap : *
+          import cetz.draw : line, content
+                  inductor(
+                    "b1", 
+                  (0, 0), 
+                  (2, 0),
+                  variant: "ieee"
+                  ) 
+      }))      
+      ],
+      [
+
+      ],
+      [
+        
+      ],
+
+      // Kapazität
+      [
+      Kapazität
+      #scale(x: 100%, y: 100%,
+        zap.circuit({
+          import zap : *
+          import cetz.draw : line, content
+                  capacitor(
+                    "b1", 
+                  (0, 0), 
+                  (2, 0)
+                  ) 
+      }))      
+      ],
+      [
+
+      ],
+      [
+        
+      ],
+
+      // Kurzschluss
+      [
+      Kurzschluss
+      #scale(x: 100%, y: 100%,
+        zap.circuit({
+          import zap : *
+          import cetz.draw : line, content
+                  capacitor(
+                    "b1", 
+                  (0, 0), 
+                  (2, 0)
+                  ) 
+      }))      
+      ],
+      [
+
+      ],
+      [
+        
+      ],
+
+      // Leerlauf
+      [
+      Leerlauf
+      #scale(x: 100%, y: 100%,
+        zap.circuit({
+          import zap : *
+          import cetz.draw : line, content
+                  capacitor(
+                    "b1", 
+                  (0, 0), 
+                  (2, 0)
+                  ) 
+      }))      
+      ],
+      [
+
+      ],
+      [
+        
+      ],
+
+      // Nullator
+      [
+      Nullator
+      #scale(x: 100%, y: 100%,
+        zap.circuit({
+          import zap : *
+          import cetz.draw : line, content
+                  capacitor(
+                    "b1", 
+                  (0, 0), 
+                  (2, 0)
+                  ) 
+      }))      
+      ],
+      [
+
+      ],
+      [
+        
+      ],
+
+      // Norator
+      [
+      Norator
+      #scale(x: 100%, y: 100%,
+        zap.circuit({
+          import zap : *
+          import cetz.draw : line, content
+                  capacitor(
+                    "b1", 
+                  (0, 0), 
+                  (2, 0)
+                  ) 
+      }))      
+      ],
+      [
+
+      ],
+      [
+        
+      ],
+
 
     );
     
@@ -721,7 +1226,7 @@
     [],
     [
       $Phi(t) = L dot i(t)$\
-      $u(t) = C dot (d i)/(d t)$\
+      $u(t) = L dot (d i)/(d t)$\
       $[L] = H = unit("V s") / unit("A")$
     ],
     [
@@ -732,12 +1237,16 @@
       $E_L = Phi^2/2L = (L i^2)/2$
     ],
     [
-      $C$: Admetanze $hat(=) G$
+      $C$: Admittanz $hat(=) G$
     ], [],
     [
       $L$: Impedanz $hat(=) R$
     ]
     )
+
+    Admittanz: $Y = I/U$\
+    Impedanz: $Z = U/I$
+
   ]
 
   // Reaktive Dual Wandlung
@@ -751,16 +1260,13 @@
     )
   ]
 
-  #bgBlock(fill: colorAllgemein)[
-    #subHeading(fill: colorAllgemein)[Complex Zahlen]
-
-  ]
-
   // Complex AC
   #bgBlock(fill: colorComplexAC)[
     #subHeading(fill: colorComplexAC)[Komplex Wechselstrom Rechnnung]
     Im Eingeschwungenem Zustand
 
+    $u(t) =U_m "Re"{e^(j omega t + phi)}$
+
     $u(t) = U_m cos(omega t + alpha)$ \ 
     $i(t) = I_m cos(omega t + beta)$ 
 
@@ -780,8 +1286,60 @@
       U_"ges"^2 = U_1^2 + 2 U_1 U_2 + U_2^2 \
       tan(phi) = (U_2 sin(phi))/(U_1 + U_2 cos(phi))
     $
+  ]
+
+  // AC Components
+  #bgBlock(fill: colorComplexAC)[
+    #subHeading(fill: colorComplexAC)[Komplexe Komponent]
+    #table(
+      columns: (1fr, 2fr, 2fr, 2fr),
+      fill: (x, y) => if calc.rem(y, 2) == 1 { tableFillLow } else { tableFillHigh },
+      [], [*$Y = U/I$*], [*$Z = I/U$*], [*$phi$*],
+      [], [*$Omega$*], [*$S$*], [*rad*],
+      zap.circuit({
+        import zap : *
+        resistor("R", (0, 0), (0.6, 0), width: 3mm, height: 2mm, fill: none)
+      }), $R$, $1/G = R$, $0$,
+
+      zap.circuit({
+        import zap : *
+        capacitor("R", (0, 0), (0.6, 0), width: 4mm, height: 6mm, fill: none)
+      }), $1/(j w C)$, $j w C$, $-pi/2$,
+      zap.circuit({
+        import zap : *
+        inductor("R", (0, 0), (0.6, 0), width: 4mm, height: 2mm, fill: none, variant: "ieee")
+      }), $j w L$, $1/(j w L)$, $pi/2$
+    )
+  ]
+
+  #bgBlock(fill: colorComplexAC)[
+    #subHeading(fill: colorComplexAC)[*Levi's Lustig Leistung*]
+
+    $P = 1/2 U dot I^*$\
+
+    #table(
+      columns: (auto, 1fr, auto),
+      fill: (x, y) => if calc.rem(y, 2) == 0 { tableFillLow } else { tableFillHigh },
+      [Scheinleitsung], [$S = abs(P)$], [$["VA"]$],
+      [Wirkleistung], [$P_w = "Re"{P} $], [$["W"]$],
+      [Blindleistung], [$P_b = "Im"{P}$], [$["var"]$]
+    )
+
+    Bei Wiederstand: $R$
+
+    $P_w = U_m^2 / 2R = (I_m^2 R)/2$
+
+    $P = 1/2 U I^* = 1/2 abs(U)^2 Y^* = 1/2 abs(I)^2 Z^*$
+
+    $U_"eff" = U_m/sqrt(2), I_"eff" = I_m / sqrt(2)$
+  ]
+
+  // Komplexe Zahlen
+  #bgBlock(fill: colorAllgemein)[
+    #subHeading(fill: colorAllgemein)[Komplexe Zahlen]
+
+    #ComplexNumbersSection(i: $j$)
 
-    **
 
   ]
 
@@ -794,17 +1352,133 @@
 
 #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(
     columns: (auto, auto, auto, auto),
     inset: 2mm,
     align: horizon,
-      table.header([], [*Ein-Tor*], [*Zwei-Tor*], [*Complex AC*]),
+    fill: (x, y) => if calc.rem(y, 2) == 1 { rgb("#c5c5c5") } else { white },
+
+    table.header([], [*Ein-Tor*], [*Zwei-Tor*], [*Reaktive Elemente*]),
     [*passiv*\ (nimmt Energie auf)\ $not$aktiv],
     [$forall (u,i) in cal(F): u dot i >= 0$],
     [
@@ -883,9 +1557,7 @@
     [$det(M) != 0$, Alle Eintrag $!= 0$]
   )
 ]
-)
 
-#place(bottom+left, scope: "parent", float: true)[
 #bgBlock(fill: colorZweiTore)[
   #set text(size: 10pt)
 
@@ -980,4 +1652,3 @@
     
     )
 ]
-]

src/lib/circuit.typ

@@ -3,16 +3,6 @@
 #import zap: interface
 
 #let registerAllCustom() = {
-  cetz.draw.set-ctx(ctx => {
-    ctx.zap.style.insert("einTor", (
-      scale: auto,
-      fill: auto,
-      height: 3mm,
-      width: 6mm,
-    ))
-    ctx
-  })
-
   cetz.draw.set-ctx(ctx => {
     ctx.zap.style.insert("zweiTor", (
       scale: auto,
@@ -20,8 +10,39 @@
       height: 10mm,
       width: 10mm,
     ))
+
+    ctx.zap.style.insert("einTor", (
+      scale: auto,
+      fill: none,
+      height: 3mm,
+      width: 6mm,
+    ))
+
+    ctx.zap.style.insert("fet", (
+      scale: auto,
+      fill: none,
+      height: 5mm,
+      width: 10mm,
+    ))
+
+
+    for it in ("lnot", "land", "lnand", "lor", "lnor", "lxor", "lxnor") {
+        ctx.zap.style.insert(it, (
+          width: 0.7,
+          min-height: 0.9,
+          spacing: 0.4,
+          padding: 0.25,
+          fill: white,
+          stroke: auto,
+        )
+      )
+    }
+
     ctx
   })
+
+
+
 }
 
 #let einTor(name, node, flip: false, ..params) = {
@@ -84,3 +105,52 @@
   // Component call
   component("zweiTor", name, node, draw: draw, ..params)
 }
+
+#let fet(name, node, type: "N", scale: 1, angle: 0, thickness: 0.5pt, ..params) = {
+  import cetz.draw: line, circle, anchor, rotate
+  import zap: component
+  
+  // Drawing function
+  let draw(ctx, position, style) = {
+    let zap-style = ctx.zap.style
+
+    let height = style.height * scale;
+    let width = style.width * scale;
+
+    let wireThink = ctx.zap.style.wire.stroke.thickness;
+
+    rotate(angle);
+
+    if(type == "N") {
+      line((0, height), (0, height*(1-0.45)), stroke: (thickness: wireThink))
+    } else { 
+      line((0, height), (0, height*(1-0.2)), stroke: (thickness: wireThink))
+      circle((0, height*(1-0.3) - thickness/2), radius: (height/2)*0.2, stroke: (thickness: wireThink))
+    }
+
+    line(
+      (width/2, 0), 
+      (width*0.4/2, 0),
+      (width*0.4/2, 0), 
+      (width*0.4/2, height*(1-0.6)),
+      (-width*0.4/2, height*(1-0.6)),
+      (-width*0.4/2, 0),
+      (-width/2, 0), stroke: (thickness: wireThink)
+    )
+
+    line(
+      (width*0.42/2, height*(1-0.45)),
+      (-width*0.42/2, height*(1-0.45)),
+      stroke: (thickness: wireThink)
+    )
+
+    anchor("G", (0, height))
+    anchor("D", (-width/2, 0))
+    anchor("S", (width/2, 0))
+
+    interface((-width / 2, -height / 2), (width / 2, height / 2), io: true)
+  }
+
+  // Component call
+  component("fet", name, node, draw: draw, ..params)
+}

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(
@@ -17,16 +17,19 @@
       )
     ),
     fill: fill,
-    width: 100%,
+    width: 100% + 4mm,
     inset: 1mm,
     height: auto
-  )
+  ))
 }
 
 #let MathAlignLeft(e) = {
   align(left, block(e))
 }
 
+#let tableFillHigh = white
+#let tableFillLow = color.lighten(gray, 50%)
+
 #let sinTable = [
   #let data = json("../sintable.json")
   #table(
@@ -34,10 +37,11 @@
     rows: data.keys().len(),
     stroke: none,
     table.hline(stroke: (thickness: 0.3mm)),
-    fill: (x, y) => if (calc.rem(y, 2) == 0) { color.lighten(gray, 50%) } else { white },
+    fill: (x, y) => if (calc.rem(y, 2) == 0) { tableFillLow } else { tableFillHigh },
 
-    ..for (label) in data.keys() {
+    table.vline(),
-      ([*#eval(label, mode: "math")*], )
+    ..for (i, label) in data.keys().enumerate() {
+      ([*#eval(label, mode: "math")*], if i > 0 { table.vline() } else { table.vline(stroke: none) })
     },
 
     table.hline(stroke: (thickness: 0.3mm)),
@@ -46,6 +50,24 @@
     for (col) in data.keys() {
         (eval(data.at(col).at(i), mode: "math"),)
       }
-    }
+    },
+    table.hline(stroke: (thickness: 0.3mm)),
   )
 ]
+
+#let ComplexNumbersSection(i: $i$) = [
+  $1/#i = #i^(-1) = -#i quad quad #i^2=-1 quad quad sqrt(#i) = 1/sqrt(2) + 1/sqrt(2)#i$
+
+  $z in CC = a + b #i quad quad quad z = r dot e^(#i phi)$ \
+  $z_0 + z_1 = (a_0 + a_1) + (b_0 + b_1) #i$\
+  $z_0 dot z_1 = (a_1 a_2 - b_1 b_2) + #i (a_1b_2 + a_2 b_1) = r_0 r_1 e^(#i (phi_0 + phi_1))$\
+  $z^x = r^x dot e^(phi #i dot x) quad x in RR$ \
+  $z_0/z_1 = r_0/r_1 e^(#i (phi_0 - phi_1)) quad quad quad$ 
+
+  $z^* = a - #i b = r e^(-#i phi)$
+
+  $r = abs(z) quad phi = cases(
+    + arccos(a/r) space : space a >= 0,
+    - arccos(a/r) space : space a < 0,
+  )$
+]

src/lib/fetModel.typ

@@ -0,0 +1,290 @@
+#import "@preview/zap:0.5.0"
+#import "@preview/cetz-plot:0.1.3"
+
+
+#set page(width: auto, height: auto)
+
+#let FetModelSubstrate = zap.circuit({
+  import zap: *
+  import cetz.draw: *
+
+  rect(
+    (0, 0),
+    (12, 4),
+    fill: rgb("#ffb1b1"),
+    name: "p",
+  )
+  rect((0, -0.05), (12, -0.05), stroke: 3pt, name: "substrate")
+  earth("g1", (11.5, 0))
+
+  content("substrate", [Bulk], anchor: "north", padding: 0.2)
+})
+
+#let FetModel1 = zap.circuit({
+  import zap: *
+  import cetz.draw: *
+
+  rect(
+    (0, 0),
+    (12, 4),
+    fill: rgb("#ffb1b1"),
+    name: "p",
+  )
+  rect((0, -0.05), (12, -0.05), stroke: 3pt, name: "substrate")
+  earth("g1", (11.5, 0))
+
+  rect((2.75, 3), (5.25, 4), fill: rgb("#61ff9f"), name: "kanal1", radius: (
+    south: 0.2,
+  ))
+  rect((6.75, 3), (9.25, 4), fill: rgb("#61ff9f"), name: "kanal2", radius: (
+    south: 0.2,
+  ))
+
+  content("kanal1", [n+], anchor: "center", padding: 0.2)
+  content("kanal2", [n+], anchor: "center", padding: 0.2)
+  content("substrate", [Bulk], anchor: "north", padding: 0.2)
+})
+
+#let FetModel2 = zap.circuit({
+  import zap: *
+  import cetz.draw: *
+
+  rect(
+    (0, 0),
+    (12, 4),
+    fill: rgb("#ffb1b1"),
+    name: "p",
+  )
+  rect((0, -0.05), (12, -0.05), stroke: 3pt, name: "substrate")
+  earth("g1", (11.5, 0))
+
+  rect((2.75, 3), (5.25, 4), fill: rgb("#61ff9f"), name: "kanal1", radius: (
+    south: 0.2,
+  ))
+  rect((6.75, 3), (9.25, 4), fill: rgb("#61ff9f"), name: "kanal2", radius: (
+    south: 0.2,
+  ))
+
+  content("kanal1", [n+], anchor: "center", padding: 0.2)
+  content("kanal2", [n+], anchor: "center", padding: 0.2)
+  content("substrate", [Bulk], anchor: "north", padding: 0.2)
+
+
+  rect((0, 4), (12, 4.5), fill: rgb("#fffc61"), name: "isolator")
+  content("isolator.west", [Isolator ($"SiO"_2$)], anchor: "west", padding: .2)
+})
+
+#let FetModel3 = zap.circuit({
+  import zap: *
+  import cetz.draw: *
+
+  rect(
+    (0, 0),
+    (12, 4),
+    fill: rgb("#ffb1b1"),
+    name: "p",
+  )
+  rect((0, -0.05), (12, -0.05), stroke: 3pt, name: "substrate")
+  earth("g1", (11.5, 0))
+
+  rect((2.75, 3), (5.25, 4), fill: rgb("#61ff9f"), name: "kanal1", radius: (
+    south: 0.2,
+  ))
+  rect((6.75, 3), (9.25, 4), fill: rgb("#61ff9f"), name: "kanal2", radius: (
+    south: 0.2,
+  ))
+
+  content("kanal1", [n+], anchor: "center", padding: 0.2)
+  content("kanal2", [n+], anchor: "center", padding: 0.2)
+  content("substrate", [Bulk], anchor: "north", padding: 0.2)
+
+
+  rect((0, 4), (3, 4.5), fill: rgb("#fffc61"), name: "isolator2")
+  rect((5, 4), (7, 4.5), fill: rgb("#fffc61"))
+  rect((9, 4), (12, 4.5), fill: rgb("#fffc61"), name: "isolator")
+
+  rect((3, 4), (5, 4.25), fill: gray)
+  rect((7, 4), (9, 4.25), fill: gray)
+  rect((5.1, 4.5), (6.9, 4.75), fill: gray)
+
+  content("isolator", [$"SiO"_2$])
+  content("isolator2", [Isolator])
+})
+
+#let FetModel(type: "N", s: 100%) = zap.circuit({
+  import zap: *
+  import cetz.draw: rect, content
+
+  cetz.draw.scale(s)
+
+  let pTypeFill = rgb("#ffb1b1");
+  let pTypeFill = rgb("#ffb1b1");
+  let nTypeFill = rgb("#61ff9f")
+
+  rect(
+    (0, 0),
+    (12, 4),
+    fill: if(type == "N") { pTypeFill } else { nTypeFill },
+    name: "p",
+  )
+  rect((0, -0.05), (12, -0.05), stroke: 3pt, name: "substrate")
+  earth("g1", (11.5, 0))
+
+  wire((13, 5.5), (13, 0), mark: (end: ">"))
+  node("n-r1", (13, 5.75))
+
+  wire((6, 4.5), (6, 5.75))
+  node("n-g1", (6, 5.75))
+  wire("n-g1", "n-r1")
+
+  node("n-s1", (4, 5))
+  wire("n-s1", (4, 4.25))
+
+  node("n-d1", (8, 5))
+  wire("n-d1", (8, 4.25))
+
+  rect((0, 4), (3, 4.5), fill: rgb("#fffc61"), name: "isolator2")
+  rect((5, 4), (7, 4.5), fill: rgb("#fffc61"))
+  rect((9, 4), (12, 4.5), fill: rgb("#fffc61"), name: "isolator")
+
+  rect((3, 4), (5, 4.25), fill: gray)
+  rect((7, 4), (9, 4.25), fill: gray)
+  rect((5.1, 4.5), (6.9, 4.75), fill: gray)
+
+  content("n-g1", [*G*\ate], anchor: "south", padding: 0.2, auto-scale: true)
+  content("n-s1", [*S*\ource], anchor: "south", padding: 0.2)
+  content("n-d1", [*D*\rain], anchor: "south", padding: 0.2, auto-scale: true)
+  content("substrate", [Bulk], anchor: "north", padding: 0.2, auto-scale: true)
+  content("p", if type == "N" [p] else [n], auto-scale: true)
+  content("isolator", [$"SiO"_2$], auto-scale: true)
+
+  content("isolator2", [Isolator], auto-scale: true)
+
+  rect((2.75, 3), (5.25, 4), fill: if(type == "N") { nTypeFill }  else { pTypeFill }, name: "kanal1", radius: (
+    south: 0.2,
+  ))
+  rect((6.75, 3), (9.25, 4), fill: if(type == "N") { nTypeFill } else { pTypeFill }, name: "kanal2", radius: (
+    south: 0.2,
+  ))
+
+  content("kanal1", if type == "N" [n+] else [p+], anchor: "center", padding: 0.2, auto-scale: true)
+  content("kanal2", if type == "N" [n+] else [p+], anchor: "center", padding: 0.2, auto-scale: true)
+})
+
+#let FetModelConducting = zap.circuit({
+  import zap: *
+  import cetz.draw: *
+
+  rect(
+    (0, 0),
+    (12, 4),
+    fill: rgb("#ffb1b1"),
+    name: "p",
+  )
+  rect((0, -0.05), (12, -0.05), stroke: 3pt, name: "substrate")
+  earth("g1", (11.5, 0))
+
+  wire((13, 5.5), (13, 0), mark: (end: ">"))
+  node("n-r1", (13, 5.75))
+
+  wire((6, 4.5), (6, 5.75))
+  node("n-g1", (6, 5.75))
+  wire("n-g1", "n-r1")
+
+  node("n-s1", (4, 5))
+  wire("n-s1", (4, 4.25))
+
+  node("n-d1", (8, 5))
+  wire("n-d1", (8, 4.25))
+
+  rect((0, 4), (3, 4.5), fill: rgb("#fffc61"), name: "isolator2")
+  rect((5, 4), (7, 4.5), fill: rgb("#fffc61"))
+  rect((9, 4), (12, 4.5), fill: rgb("#fffc61"), name: "isolator")
+
+  rect((3, 4), (5, 4.25), fill: gray)
+  rect((7, 4), (9, 4.25), fill: gray)
+  rect((5.1, 4.5), (6.9, 4.75), fill: gray)
+
+  content("n-g1", [*G*\ate], anchor: "south", padding: 0.2)
+  content("n-s1", [*S*\ource], anchor: "south", padding: 0.2)
+  content("n-d1", [*D*\rain], anchor: "south", padding: 0.2)
+  content("substrate", [Bulk], anchor: "north", padding: 0.2)
+  content("p", [p])
+  content("isolator", [$"SiO"_2$])
+  content("isolator2", [Isolator])
+
+  rect((2.75, 3), (5.25, 4), fill: rgb("#61ff9f"), name: "kanal1", radius: (
+    south: 0.2,
+  ))
+  rect((6.75, 3), (9.25, 4), fill: rgb("#61ff9f"), name: "kanal2", radius: (
+    south: 0.2,
+  ))
+  rect((5.20, 3.99), (6.8, 3.9), fill: rgb("#61ff9f"), stroke: none)
+
+  content("kanal1", [n+], anchor: "center", padding: 0.2)
+  content("kanal2", [n+], anchor: "center", padding: 0.2)
+
+  rect((0.5, -1), (1, -0.70), fill: gray, stroke: none, name: "metal")
+  content("metal", [metal], anchor: "west", padding: 0.3)
+
+  rect((0.5, -1.2), (1, -1.5), fill: rgb("#61ff9f"), stroke: none, name: "n")
+  content("n", [n+], anchor: "west", padding: 0.3)
+
+  rect(
+    (2.5, -1),
+    (3, -0.7),
+    fill: rgb("#ffb1b1"),
+    stroke: none,
+    name: "p-substrate",
+  )
+  content("p-substrate", [p], anchor: "west", padding: 0.3)
+
+  rect((2.5, -1.2), (3, -1.5), fill: rgb("#fffc61"), stroke: none, name: "siO2")
+  content("siO2", [oxide], anchor: "west", padding: 0.3)
+})
+
+#let FetPlot() = {
+  let u_gs = 1
+  let beta = 1
+
+  cetz.canvas({
+    import cetz-plot: plot
+    import cetz: draw.content
+
+    cetz.draw.set-style(axes: (
+      shared-zero: false,
+      overshoot: 0.2,
+      x: (mark: (end: ">", fill: black, scale: 0.6)),
+      y: (mark: (end: ">", fill: black, scale: 0.6)),
+    ))
+
+    plot.plot(
+      size: (2, 2),
+      name: "plot",
+      axis-style: "school-book",
+      x-min: 0,
+      x-tick-step: none,
+      y-tick-step: none,
+      x-label: $U_"GS"$,
+      y-label: $U_"DS"$,
+      {
+        plot.add-fill-between(domain: (1, 6), ((1, 0), (1, 5)), u_gs => u_gs - u_t)
+
+        plot.add(domain: (0, 5), fill: true, axes: ("y", "x"), _ => 1)
+
+        plot.add(domain: (1, 6), fill: true, u_gs => u_gs - u_t)
+
+        plot.add-anchor("I", (0.5, 2.5))
+        plot.add-anchor("II", (4.5, 1.5))
+        plot.add-anchor("III", (2.5, 3.5))
+
+        plot.add-anchor("ut", (u_t, 0))
+      }
+    )
+    content("plot.ut", $U_t$, anchor: "north", padding: 0.1)
+
+    content("plot.I", [I])
+    content("plot.II", [II])
+    content("plot.III", [III])
+  })
+}

src/lib/logic.typ

@@ -0,0 +1,62 @@
+#import "@preview/zap:0.5.0": *
+#import "@preview/cetz:0.4.2": (
+  draw.anchor, draw.arc-through, draw.circle, draw.content, draw.line, draw.rect, draw.rotate, draw.get-ctx, draw.bezier
+)
+
+#let logic(name, node, text: $"&"$, invert: false, mirror: false, invert-inputs: (), angle: 0deg, inputs: 2, ..params) = {
+  assert(inputs >= 1, message: "logic supports minimum one inputs")
+
+  let style = (
+    width: 0.7,
+    min-height: 0.9,
+    spacing: 0.4,
+    padding: 0.25,
+    fill: white,
+    stroke: auto,
+  )
+
+  // Drawing function
+  let draw(ctx, position, _) = {
+    rotate(angle)
+
+    let height = calc.max(style.min-height, (inputs - 1) * style.spacing + 2 * style.padding)
+    let width = style.width * if mirror { -1 } else { 1 }
+
+    interface((-width / 2, -height / 2), (width / 2, height / 2), io: false)
+
+    rect((-width / 2, -height / 2), (rel: (width, height)), fill: style.fill, stroke: style.stroke)
+    content((0, height / 2 - style.padding / 2), text, anchor: "north", angle: angle)
+
+    let ball-radius = calc.min(height, width) * 0.1
+
+    for input in range(1, inputs + 1) {
+      let pad = (height - (inputs - 1) * style.spacing) / 2
+      let y = height / 2 - pad - (input - 1) * style.spacing;
+
+      if input in invert-inputs {
+        circle((-width / 2 - ball-radius, y), radius: ball-radius, stroke: style.stroke, fill: style.fill)
+        anchor("in" + str(input), (-width / 2, y))
+      } else {
+        anchor("in" + str(input), (-width / 2, y))
+      }
+    }
+
+    if invert {
+      circle((width / 2 + ball-radius, 0), radius: ball-radius, stroke: style.stroke, fill: style.fill)
+      anchor("out", (width / 2, 0))
+    } else {
+      anchor("out", (width / 2, 0))
+    }
+  }
+
+  // Component call
+  component("logic", name, node, draw: draw, ..params)
+}
+
+#let lnot(name, node, ..params) = logic(name, node, ..params, text: $1$, invert: true)
+#let land(name, node, ..params) = logic(name, node, ..params, text: $"&"$)
+#let lnand(name, node, ..params) = logic(name, node, ..params, text: $"&"$, invert: true)
+#let lor(name, node, ..params) = logic(name, node, ..params, text: $>=1$)
+#let lnor(name, node, ..params) = logic(name, node, ..params, text: $>=1$, invert: true)
+#let lxor(name, node, ..params) = logic(name, node, ..params, text: $=1$)
+#let lxnor(name, node, ..params) = logic(name, node, ..params, text: $=1$, invert: true)

src/lib/mathExpressions.typ

@@ -0,0 +1,13 @@
+// Math macors
+#let kern(x) = $op("kern")(#x)$
+#let alg(x) = $op("alg")(#x)$
+#let geo(x) = $op("geo")(#x)$
+#let spann(x) = $op("spann")(#x)$
+#let Bild(x) = $op("Bild")(#x)$
+#let Rang(x) = $op("Rang")(#x)$
+#let Eig(x) = $op("Eig")(#x)$
+#let lim = $limits("lim")$
+#let ip(x, y) = $lr(angle.l #x, #y angle.r)$
+
+#show math.integral: it => math.limits(math.integral)
+#show math.sum: it => math.limits(math.sum)

src/lib/table.typ

@@ -0,0 +1,80 @@
+#import "@preview/zap:0.5.0"
+#import "logic.typ"
+
+#let circuit(body) = zap.circuit({
+  import zap: *
+
+  set-style(
+    node: (
+      radius: 0.04,
+    )
+  )
+
+  body
+})
+
+#table(
+  columns: (1fr, 1fr),
+  align: center + horizon,
+  stroke: (x, y) => (
+    left: if x > 0 { 0.5pt },
+    top: if y == 1 { 1pt } else if y > 0 { 0.5pt },
+  ),
+  table.header([DNF], [KNF]),
+  circuit({
+    import zap: *
+
+    logic.land("A1", (0, 0.75), invert-inputs: (1,))
+    logic.land("A2", (0, -0.75), invert-inputs: (2,))
+
+    logic.lor("O1", (1.25, 0))
+
+    zwire("A1.out", "O1.in1", ratio: 50%)
+    zwire("A2.out", "O1.in2", ratio: 50%)
+
+    wire((-1, 1.25), (-1, -1.25), name: "A")
+    wire((-0.75, 1.25), (-0.75, -1.25), name: "B")
+
+    cetz.draw.content("A.in", [a], anchor: "south", padding: 2pt)
+    cetz.draw.content("B.in", [b], anchor: "south", padding: 2pt)
+
+    node("N4", ("A1.in1", "-|", "A.in"))
+    wire("A1.in1", "N4")
+    node("N3", ("A1.in2", "-|", "B.in"))
+    wire("A1.in2", "N3")
+    node("N2", ("A2.in1", "-|", "A.in"))
+    wire("A2.in1", "N2")
+    node("N1", ("A2.in2", "-|", "B.in"))
+    wire("A2.in2", "N1")
+
+    wire("O1.out", (rel: (0.3, 0)))
+  }),
+  circuit({
+    import zap: *
+
+    logic.lor("A1", (0, 0.75))
+    logic.lor("A2", (0, -0.75), invert-inputs: (1,2))
+
+    logic.land("O1", (1.25, 0))
+
+    zwire("A1.out", "O1.in1", ratio: 50%)
+    zwire("A2.out", "O1.in2", ratio: 50%)
+
+    wire((-1, 1.25), (-1, -1.25), name: "A")
+    wire((-0.75, 1.25), (-0.75, -1.25), name: "B")
+
+    cetz.draw.content("A.in", [a], anchor: "south", padding: 2pt)
+    cetz.draw.content("B.in", [b], anchor: "south", padding: 2pt)
+
+    node("N4", ("A1.in1", "-|", "A.in"))
+    wire("A1.in1", "N4")
+    node("N3", ("A1.in2", "-|", "B.in"))
+    wire("A1.in2", "N3")
+    node("N2", ("A2.in1", "-|", "A.in"))
+    wire("A2.in1", "N2")
+    node("N1", ("A2.in2", "-|", "B.in"))
+    wire("A2.in2", "N1")
+
+    wire("O1.out", (rel: (0.3, 0)))
+  })
+)

src/lib/truthtable.typ

@@ -0,0 +1,35 @@
+#let truth-table(outputs: (), inputs: none) = {
+  let variables = calc.max(..outputs.map(output => calc.ceil(calc.log(output.at(1).len()) / calc.log(2))))
+
+  if inputs == none {
+    inputs = ($a$, $b$, $c$, $d$).slice(0, variables)
+  }
+
+  assert(outputs.len() >= 1, message: "There has to be at least one output")
+  assert(inputs.len() == variables, message: "There aren't enough variables to label")
+
+  let num-to-bin(x, digits) = {
+    let bits = ()
+
+    while x != 0 {
+      bits.push(calc.rem(x, 2))
+
+      x = calc.floor(x / 2)
+    }
+
+    range(digits).map(x => bits.at(digits - x - 1, default: 0))
+  }
+
+  table(
+    columns: (auto,) * (variables + outputs.len()),
+    stroke: (x, y) => (
+      left: if x == variables { 1pt } else if x > 0 { 0.5pt },
+      top: if y == 1 { 1pt } else if y > 0 { 0.5pt },
+    ),
+    inset: 4pt,
+    if inputs != none { table.header(..inputs.map(x => [#x]), ..outputs.map(((x, _)) => [#x])) },
+    ..range(calc.pow(2, variables))
+      .map(x => (..num-to-bin(x, variables).map(y => [#y]), ..outputs.map(((_, y)) => [#y.at(x, default: [])])))
+      .flatten()
+  )
+}