feat(etit-es): example exercise for 3dB and Arbeitspunkt + formatting

etit-es/summary.typ

@@ -0,0 +1,666 @@
+#import "@preview/zap:0.2.1"
+#import "@preview/cetz-plot:0.1.2": plot, chart
+
+#set columns(gutter: 5pt)
+#set rect(outset: 0pt)
+#set figure(supplement: "", numbering: none)
+// #set block(spacing: 5pt)
+#let section(..args) = block(width: 100%, fill: silver, spacing: 5pt, below: 5pt, breakable: false, ..args)
+#set page(
+  // columns: 2, 
+  numbering: "1",
+  margin: 1cm,
+  header: rect(width: 100%, stroke: (bottom: 1pt), inset: (left: 0pt, right: 0pt))[
+    #smallcaps[Elektronische Schaltungen]
+    #h(1fr)
+    Gero Beckmann
+  ]
+)
+
+#let out(name, pos) = {
+  import zap.cetz.draw: *
+  on-layer(1, {
+  circle(pos, name: name, radius: .1, fill: white)
+  })
+}
+
+#let arrow(a,b,..args) = {
+  import zap.draw: *
+  line((a,.2,b), (b, .2, a), name: "line", mark: (end: (symbol: ">", fill: black)))
+  content("line", anchor: "east", padding: .2, ..args)
+}
+
+
+
+#columns(2, [
+
+#section[
+== E 24 Reihe
+#{range(24)
+  .map(n => calc.pow(calc.root(10,24),n))
+  .map(e => str(calc.round(e, digits: 1) + calc.pow(10,-10)).slice(0,3))
+  .join(" | ")
+}
+
+#let units = (
+  ([Giga], $10^9$),
+  ([Mega], $10^6$),
+  ([Kilo], $10^3$),
+  ([Milli], $10^(-3)$),
+  ([Mikro $mu$], $10^(-6)$),
+  ([Nano], $10^(-9)$),
+  ([Piko], $10^(-12)$),
+  ([Femto], $10^(-15)$),
+)
+
+#text(size: 8pt)[#table(columns: units.len() * (1fr,), inset: 3pt, table.header(..units.map(array.first)), ..units.map(array.last))
+]
+
+#grid(columns: 2 * (1fr,), align: (right, left), gutter: 10pt,
+[Knotenregel, $sum I = 0$], [Maschenregel $sum U = 0$],
+[Parallelwiderstände], $R_1 || R_2 = 1 / (1 / R_1 + 1 / R_2) = (R_1 dot R_2) / (R_1 + R_2)$,
+[Spannungsteiler], $U_2 = U dot R_2 / (R_1 + R_2)$,
+[Stromteiler], $I_1 = I dot R_2 / (R_1 + R_2)$, [3 dB-Grenzfrequenz], $f_"3dB" =
+1 / (2 pi dot C dot R)$
+)
+Übertragungsfunktion normiert: $1/(1+j omega K)$ bzw $(j omega K)/(1 + j omega K)$ \
+$omega_"3dB" = 1 / K => f_"3dB" = 1 / (2 pi K)$
+$Z_L = j omega L, Z_C = 1 / (j omega C)$ \
+$abs(H(omega)) = abs(a+b j) = sqrt(a^2 + b ^2)$
+
+]
+#colbreak()
+
+#section[
+== Diode #box(zap.canvas({zap.diode("d", (0,0),(1,0))}))
+
+#v(-.5cm)
+#grid(columns: 2 * (1fr,), align: (right, left), gutter: 10pt,
+[], $" mit " U_T = (k_B dot T)/mono(e) approx 26"mv"$,  
+[Diodenstrom], $I_D &= I_s dot (e^(U_D/U_T) -1)$,
+[Diodenspannung], $U_D &= U_T dot ln(I_D/I_S)$ ,
+[Kleinsignal], $r_D &= U_T / I_D$
+ )
+
+  #zap.canvas({
+    import zap: *
+    import zap.cetz.draw: *
+
+    scale(.6)
+    content((-5,-.3), [Kleinsignalersatzschaltbild])
+    out("A", (0,0))
+    out("K", (3,0))
+    resistor("rd", "A", "K", label: (content: $r_D$, anchor: "south", distance: 0pt))
+
+    translate((0.8,-1.5))
+    content((-4.2,0), [Erweitertes Kleinsignalersatzschaltbild])
+    translate((2.4,.4))
+    scale(.6)
+    out("A", (0,0))
+    out("K", (5,0))
+    resistor("RB", "A", (3,0), label: (content: $R_B$, anchor: "south", distance: 0pt))
+    resistor("rd", (2,0), "K", label: (content: $r_D$, anchor: "south", distance: 0pt))
+    capacitor("CD", 
+    (rel: (0.5, 1), to: "rd.in"), 
+    (rel: (-.5, 1), to: "K"),
+    label: (content: $C_D$, anchor: "north", distance: 1pt))
+    wire("CD.in", (rel: (0,-1)))
+    wire("CD.out", (rel: (0,-1)))
+  })
+  #stack(dir: ltr,[
+  #zap.cetz.canvas({
+    import zap.draw: *
+    plot.plot(axis-style: "school-book", name: "plot", size: (2,2), x-label: $U(V)$, y-label:
+    $I(A)$, x-tick-step: none, y-tick-step: none, {
+      plot.add(domain: (-23,15), u => if (u > 0) {(u, calc.exp(u - 2))}
+      else {(u,-calc.exp(-u - 10))})
+      plot.add-anchor("brk", (-8,0))
+      plot.add-anchor("UBR", (-18,0))
+      plot.add-anchor("UF", (14,0))
+    })
+    content("plot.brk", text(fill: black, weight: "extrabold")[\/\/])
+    line((rel: (0,.2), to: "plot.UBR"), (rel: (0,-.4)))
+    content("plot.UBR", anchor: "south", padding: 8pt, $U_"Br" "/" U_Z$)
+    line((rel: (0,.2), to: "plot.UF"), (rel: (0,-.4)))
+    content("plot.UF", anchor: "north", padding: 8pt, $U_"F"$)
+  })
+],[
+$
+U_F & "Flussspannung" \
+U_"Br" "/" U_Z & "Durchbruchspannung /" \
+               & "Zenerspannung "
+$
+])
+]
+])
+
+#section[
+
+#stack(dir: ltr, spacing: 1fr, [
+== Bipolartransistor #box[#zap.canvas({
+import zap: *
+import zap.draw: *
+scale(.5)
+pnp("Q", (0,0))
+content("Q.b", "B", anchor: "east", padding: (right: 5pt))
+content("Q.c", "C", anchor: "west", padding: (left: 5pt))
+content("Q.e", "E", anchor: "west", padding: (left: 5pt))
+})]
+#grid(columns: 2, align: (right, left), gutter: 10pt,
+[Steilheit], $S = I_(C,A) / U_T$,
+[Kleinsignal-Eingangs-\ Widerstand], $r_"BE" = beta / S$,
+[Stromverstärkung], $beta = I_C / I_B$,
+[Ausgangswiderstand], $r_"CE" = (abs(U_A) + U_"CE") / I_C$,
+)
+],[
+#figure(zap.canvas({
+import zap: *
+import zap.cetz.draw: *
+scale(.7)
+out("UBEE", (0,0))
+out("UBEA", (0,-2))
+out("UCEE", (5,0))
+out("UCEA", (5,-2))
+
+node("B", (1,0))
+content("B", anchor: "south", padding: 5pt, [Basis])
+node("K", (3.5,0))
+content("K", anchor: "south", padding: 5pt, [Kollektor])
+node("E", (2.5,-2))
+content("E", anchor: "north", padding: 5pt, [Emitter])
+
+wire("UBEE", "B", i: "hi")
+wire("UCEE", "K")
+wire("UBEA", "UCEA")
+
+resistor("RBE", "B", ((), "|-", "E"), label: (content: $r_"BE"$, anchor: "south", distance: 0pt))
+isource("SUBE", "K", ((), "|-", "E"), label: (content: $S dot u_"BE"$, distance: 1pt))
+set-style(zap: (wires: (stroke: red)))
+wire("B", (2.5,0), stroke: red)
+capacitor("CBE", ("E"), (rel: (0,2)), stroke: red, label: (content: text(fill:red, $C_"BE"$), anchor: "west", distance: 5pt))
+capacitor("", ("K"), (rel: (-1,0)), stroke: red)
+content((rel: (-1.5,0), to: "K"), text(fill: red, $C_"BC"$))
+}),
+caption: [#text(fill:red)[vollständiges] \ Kleinsignalersatzschaltbild])
+], [
+#figure(zap.canvas({
+import zap: *
+import zap.cetz.draw: *
+scale(.7)
+out("UBEE", (0,0))
+out("UBEA", (0,-2))
+out("UCEE", (5,0))
+out("UCEA", (5,-2))
+
+node("B", (1.5,0))
+content("B", anchor: "south", padding: 5pt, [Basis])
+node("K", (3.5,0))
+content("K", anchor: "south", padding: 5pt, [Kollektor])
+node("E", (2.5,-2))
+content("E", anchor: "north", padding: 5pt, [Emitter])
+
+wire("UBEE", "B", i: "hi")
+wire("UCEE", "K")
+wire("UBEA", "UCEA")
+
+diode("RBE", "B", ((), "|-", "E"))
+isource("SUBE", "K", ((), "|-", "E"), label: (content: $S dot u_"BE"$, distance: 1pt))
+}),caption: [Großsignalersatzschaltbild])
+])
+#align(right + horizon, stack(dir: ltr, [
+#figure(zap.canvas({
+import zap: *
+import zap.cetz.draw: *
+scale(.7)
+out("U1E", (0,0))
+out("U1A", (0,-2))
+out("U2E", (5,0))
+out("U2A", (5,-2))
+set-style(zap: (wires: (stroke: green)))
+resistor("Z1", (1.5,0), (1.5,-2), stroke: green, label: (content: text(fill: green, $Z/(1-A)$), distance: 1pt))
+resistor("Z2", (5-1.5,0), (5-1.5,-2), stroke: green, label: (content: text(fill: green, $(A Z)/(A-1)$), distance: 1pt))
+wire("U1E", "Z1.in")
+wire("U2E", "Z2.in")
+wire("U1A", "U2A")
+set-style(zap: (wires: (stroke: red)))
+resistor("Z","Z1.in", "Z2.in", stroke: red, label: (content: text(fill: red, $Z$), distance: 1pt))
+
+arrow("U1E", "U1A", $u_1$, anchor: "west")
+arrow("U2E", "U2A", $u_2$, anchor: "west")
+}),caption: [
+])
+], [
+  Miller-Theorem: $A = u_2/u_1$\
+  #text(fill: red)[verbundene Impedanz $Z$] wird \
+  zu #text(fill: green)[zwei getrennte Impedanzen]
+]))
+
+#table(columns: 3 * (1fr,), align: center, 
+table.header([Ermitterschaltung], [Basisschaltung], [Kollektorschaltung]),[
+#set text(size: 9pt)
+#zap.canvas({
+import zap: *
+import zap.cetz.draw: *
+
+
+scale(.8)
+out("e", (0,0))
+out("a", (2.5,1))
+out("eg", (0,-1))
+out("ag", (2.5,-1))
+
+pnp("n1", (1.5,0))
+wire("e", "n1.b")
+wire("n1.c", ((), "|-", "a"), "a")
+wire("n1.e", ((), "|-", "ag"), "ag")
+wire("n1.e", ((), "|-", "eg"), "eg")
+
+scale(.3)
+resistor("", "n1.e", (rel: (0,-2)), stroke: red, label: (content: text(fill: red, size:8pt,$R_E$), distance: 1pt))
+
+line(("e",.2,"eg"), ("eg", .2, "e"), name: "line", mark: (end: (symbol: ">", fill: black)))
+content("line", anchor: "east", padding: .2, $U_e$)
+
+line(("a",.2,"ag"), ("ag", .2, "a"), name: "line", mark: (end: (symbol: ">", fill: black)))
+content("line", anchor: "east", padding: .2, $U_a$)
+})
+],
+[ #zap.canvas({
+import zap: *
+import zap.cetz.draw: *
+scale(.8)
+out("e", (-1.25,0))
+out("a", (1.5,1))
+out("eg", (-1.25,-1))
+out("ag", (1.5,-1))
+
+rotate(x:180deg)
+rotate(z:-90deg)
+pnp("n1", (0,0))
+set-transform(none)
+
+wire("e", "n1.e")
+wire("n1.c", ((), "|-", "a"), "a")
+wire("n1.b", ((), "|-", "ag"), "ag")
+wire("n1.b", ((), "|-", "eg"), "eg")
+
+line(("e",.2,"eg"), ("eg", .2, "e"), name: "line", mark: (end: (symbol: ">", fill: black)))
+content("line", anchor: "east", padding: .2, $U_e$)
+
+line(("a",.2,"ag"), ("ag", .2, "a"), name: "line", mark: (end: (symbol: ">", fill: black)))
+content("line", anchor: "east", padding: .2, $U_a$)
+})
+],[
+
+#zap.canvas({
+import zap: *
+import zap.cetz.draw: *
+scale(.8)
+out("e", (0,0))
+out("a", (2.5,1))
+out("eg", (0,-1))
+out("ag", (2.5,-1))
+
+rotate(x: 180deg)
+pnp("n1", (1.5,0))
+wire("e", "n1.b")
+wire("n1.e", ((), "|-", "a"), "a")
+wire("n1.c", ((), "|-", "ag"), "ag")
+wire("n1.c", ((), "|-", "eg"), "eg")
+
+line(("e",.2,"eg"), ("eg", .2, "e"), name: "line", mark: (end: (symbol: ">", fill: black)))
+content("line", anchor: "east", padding: .2, $U_e$)
+
+line(("a",.2,"ag"), ("ag", .2, "a"), name: "line", mark: (end: (symbol: ">", fill: black)))
+content("line", anchor: "east", padding: .2, $U_a$)
+})
+]
+,[
+#text(size: 8pt)[
+  #grid(columns: 2 * (1fr,), [
+$
+A &= -S R_C \
+r_e &= r_"BE" \
+r_a &= r_"CE" || R_C
+$
+  ],text(fill: red)[
+Stromgegen-\kopplung $
+A &= -R_C / R_E \
+r_e &= r_"BE" \
+r_a &= r_"CE" || R_C
+$
+  ])
+]
+], [
+
+#text(size: 9pt, $
+A &= S R_C \
+r_e &= 1 / S \
+r_a &= r_"CE" || R_C
+$)
+], [
+#text(size: 9pt, $
+A &= 1 \
+r_e &= r_"BE" + beta R_E \
+r_a &= 1 / S
+$)
+])
+
+]
+
+== Übergangsfunktion und 3dB-Grenzfrequenz
+
+#grid(columns: 3*(1fr,), [
+#scale(80%, reflow: true)[
+#zap.canvas({
+  import zap: *
+  // acvsource("UE", (0,0), (1,0))
+  vsource("UE", (0,0), (0,-2), u: (label:$u_e$, position: bottom))
+  resistor("R1", (0,0), (3,0), label: (content: $R 1 = 250 Omega$))
+  wire((3,0), (5,0))
+  resistor("RL", (3,0), (3,-2), label: (content: $R_L = 500 Omega$, anchor: "south"), distance: 0pt)
+  inductor("L", (5,0), (5,-2), u: (label: $u_L$, position: bottom), i: $i_L$, label: (content: $L = 850 "pH"$))
+  wire((0,-2), (5,-2))
+})
+]
+$
+H(omega) =& u_l / u_e = (j omega L || R_2) / (R_1 + (j omega L || R_2)) \
+         =& (j omega L dot R_2) / (R_1 dot R_2 + j omega L dot (R_1 + R_2)) \
+         =& R_2 / (R_1 + R_2) (j omega K) / (1+j omega K) 
+$
+], [
+#v(.3cm)
+$
+" mit " K &= L dot (R_1 + R_2) / (R_1 dot R_2) = 5,1 "ps" \
+abs(H(omega)) =& R_2 / (R_1 + R_2) (omega K) / sqrt(1 + (omega K)^2) \
+        &=> f_"3dB" = omega_"3dB" / (2 pi) = 1 / ( 2 pi K) \
+        & = 1 / ( 2 pi * 5,1 "ps") = 31,2 "GHz" \
+H(omega -> oo) &= R_2 / (R_1 + R_2) = 2 / 3 | 20 log(x) \
+        &= -3,51 "dB"
+$
+], [
+#zap.canvas({
+  import zap.draw: *
+  plot.plot(
+    x-tick-step: none, y-tick-step: none,
+    size: (4,3),
+    x-label: $f " in Hz"$,
+    y-label: $abs(H) " in dB"$,
+    legend: (-1,-1),
+    x-min: 100,
+    x-max: 150000,
+    y-min: -40,
+    x-mode: "log",
+    x-base: 10,
+    y-max: 0,
+    x-ticks: ((100,$100 M$), (1000,$1 G$), (10000,$10 G$), (100000,$100 G$)), 
+    y-ticks: (-40, -20, 0), {
+      plot.add-hline((-3.52), label: $H(omega -> oo) = -3,51 "dB"$)
+      plot.add-vline((31200), label: $f_"3dB" = 31,2 "GHz"$)
+      plot.add(((500, -40), (31200, -3.52), (150000,-3.52)))
+      plot.annotate({
+        line((1500,-30),(6000,-30),(6000,-18))
+        content((14000,-24), $20 "dB"/"Dek"$)
+      })
+  })
+})
+])
+
+#section[
+#grid(columns: (2fr, 3fr), [
+== Feldeffekttransistor (FET) #box[#zap.canvas({
+  import zap: *
+  import zap.draw: *
+  scale(.5)
+  pmos("Q", (0,0))
+  content("Q.gl", "G", anchor: "east", padding: (right: 5pt))
+  content("Q.d", "D", anchor: "west", padding: (left: 5pt))
+  content("Q.s", "S", anchor: "west", padding: (left: 5pt))
+})]
+
+$
+r_"DS" = (partial U_"DS") / (partial I_D) = (abs(U_A) + U_"DS") / I_D \
+S = (partial I_D) / (partial U_"DS") = beta (U_"GS" - U_"th") \
+beta = mu dot C'_"ox" dot omega / l
+$
+], [
+  #grid(columns: 2 * (1fr,), align: center, [
+    #scale(60%, reflow: true)[#table(columns: (auto, 1fr, 1fr), [], [n-Kanal], [p-Kanal],
+    rotate(-90deg, reflow: true)[normal\ leitend], 
+    zap.canvas({ zap.nmos("", (), mode: "depletion") }), 
+    zap.canvas({ zap.pmos("", (), mode: "depletion") }), 
+    rotate(-90deg, reflow: true)[normal\ sperrend], 
+    zap.canvas({ zap.nmos("", ()) }), 
+    zap.canvas({ zap.pmos("", ()) }), 
+  )]
+], [
+  #figure(scale(65%, reflow: true)[
+    #zap.canvas({
+      import zap: *
+      import zap.cetz.draw: *
+      scale(.9)
+      out("G", (0,0))
+      content("G", "G", anchor: "east", padding: 5pt)
+      out("S", (0,-2))
+      content("S", "S", anchor: "east", padding: 5pt)
+      out("D", (6,0))
+      content("D", "D", anchor: "west", padding: 5pt)
+      out("DA", (6,-2))
+      node("", (4,0))
+      node("", (2,-2))
+      node("", (4,-2))
+      isource("Su", (2,0), (2,-2), i: (label: [#h(.6cm)$S dot u_"GS"$], position: end + top ))
+      resistor("", (4,0), (4,-2), label: (content: $r_"DS"$, anchor: "south", distance: 3pt))
+      wire((2,0), "D")
+      wire("S", "DA")
+      line(("G",.2,"S"), ("S", .2, "G"), name: "line", mark: (end: (symbol: ">", fill: black)))
+      content("line", anchor: "east", padding: .2, $u_"GS"$)
+      line(("D",.2,"DA"), ("DA", .2, "D"), name: "line", mark: (end: (symbol: ">", fill: black)))
+      content("line", anchor: "east", padding: .2, $u_"DS"$)
+    })
+  ], caption: [ Kleinsignalersatzschaltbild ])
+])
+
+$
+I_D &= cases(
+  0 & U_"GS" <= U_"th", 
+  beta dot ((U_"GS" - U_"th") - U_"th"^2 / 2) dot (1 + U_"DS" / U_A) & "linearer Bereich",
+  beta / 2 dot (U_"GS" - U_"th")^2 dot (1 + U_"DS" / U_A) & "Sättigungsbereich"
+)
+$
+])
+
+
+#table(columns: 3 * (1fr,), align: center, 
+table.header([Source-Schaltung], [Gate-Schaltung], [Drain-Schaltung]) ,[
+#zap.canvas({
+import zap: *
+import zap.cetz.draw: *
+
+scale(.8)
+out("e", (0,0))
+out("a", (2.5,1))
+out("eg", (0,-1))
+out("ag", (2.5,-1))
+
+scale(.5)
+nmos("n1", (3,0.5))
+wire("e", "n1.g")
+wire("n1.d", ((), "|-", "a"), "a")
+wire("n1.s", ((), "|-", "ag"), "ag")
+wire("n1.s", ((), "|-", "eg"), "eg")
+
+line(("e",.2,"eg"), ("eg", .2, "e"), name: "line", mark: (end: (symbol: ">", fill: black)))
+content("line", anchor: "east", padding: .2, $U_e$)
+
+line(("a",.2,"ag"), ("ag", .2, "a"), name: "line", mark: (end: (symbol: ">", fill: black)))
+content("line", anchor: "east", padding: .2, $U_a$)
+})
+],
+[
+#zap.canvas({
+import zap: *
+import zap.cetz.draw: *
+scale(.8)
+out("e", (-1.25,0))
+out("a", (1.5,1))
+out("eg", (-1.25,-1))
+out("ag", (1.5,-1))
+
+rotate(x:180deg)
+rotate(z:-90deg)
+scale(.5)
+nmos("n1", (0,0))
+set-transform(none)
+
+wire("e", "n1.s")
+wire("n1.d", ((), "|-", "a"), "a")
+wire("n1.g", ((), "|-", "ag"), "ag")
+wire("n1.g", ((), "|-", "eg"), "eg")
+
+line(("e",.2,"eg"), ("eg", .2, "e"), name: "line", mark: (end: (symbol: ">", fill: black)))
+content("line", anchor: "east", padding: .2, $U_e$)
+
+line(("a",.2,"ag"), ("ag", .2, "a"), name: "line", mark: (end: (symbol: ">", fill: black)))
+content("line", anchor: "east", padding: .2, $U_a$)
+})
+], [
+#zap.canvas({
+import zap: *
+import zap.cetz.draw: *
+scale(.8)
+out("e", (0,0))
+out("a", (2.5,1))
+out("eg", (0,-1))
+out("ag", (2.5,-1))
+
+rotate(x: 180deg)
+scale(.5)
+nmos("n1", (3,.5))
+wire("e", "n1.g")
+wire("n1.s", ((), "|-", "a"), "a")
+wire("n1.d", ((), "|-", "ag"), "ag")
+wire("n1.d", ((), "|-", "eg"), "eg")
+
+line(("e",.2,"eg"), ("eg", .2, "e"), name: "line", mark: (end: (symbol: ">", fill: black)))
+content("line", anchor: "east", padding: .2, $U_e$)
+
+line(("a",.2,"ag"), ("ag", .2, "a"), name: "line", mark: (end: (symbol: ">", fill: black)))
+content("line", anchor: "east", padding: .2, $U_a$)
+})
+],
+[
+#text(size: 9pt, $
+r_e &= oo \
+r_a &= R_D || r_"DS" \
+A &= -S dot (R_D || r_"DS")
+$)
+
+] ,[
+#text(size: 9pt, $
+r_e &= 1/S \
+r_a &= R_D || r_"DS" \
+A &= S dot (R_D || r_"DS")
+$)
+], [
+#text(size: 9pt, 
+$
+r_e &= oo \
+r_a &= 1 / S || R_S \
+A &= (S dot R_S) / (1 + S dot R_S)
+$
+)
+])
+]
+
+== Arbeitspunkt und Lastgerade
+
+#grid(columns: 3*(1fr,),[
+  #scale(80%, reflow: true, [
+#zap.canvas({
+  import zap: *
+  import zap.draw: *
+  
+  out("UEE", (0,0))
+  arrow((0,0), (0,-2), $u_e$)
+  ground("UEA", (0,-2))
+  out("", (0,-2))
+  capacitor("", (0,0), (2,0))
+  resistor("RG2", (2,0), (2,-2), label: (content: $R_"G2"$, anchor: "south"))
+  ground("", (2,-2))
+  resistor("RG1", (2,3),(2,0), i: (label: $i_a$, position: bottom), label: (content: $R_"G1"$, anchor: "south"))
+  wire((2,0), (3,0))
+  nmos("Q", (4,0.5))
+  wire("Q.s", (rel: (0,-2)))
+  ground("", (4,-2))
+  resistor("RD", (4,3), (4,1), i: $i_D$, label: (content: $R_D$))
+  wire((2,3), (6,3))
+  out("Ub", (6,3))
+  content((6,3), anchor: "west", padding: 5pt, $U_b = 2 V$)
+  capacitor("", (4,1), (6,1))
+  out("UAE", (6,1))
+  arrow((6,1),(6,-2), $U_a$)
+  ground("", (6,-2))
+  out("UAA", (6,-2))
+})
+  ])
+],[
+$
+U_b = U_"DS1" + R_D dot I_D \
+<=> I_D = (U_b - U_"DS1") / R_D
+$
+$
+P 1: I_D (U_"DS1" = 0) = U_D / R_D = 16"mA" \
+P 2: I_D (U_"DS1" = U_b = 2 V) = 0
+$
+
+],[
+  #v(-1cm)
+  #zap.canvas({
+    import zap.draw: *
+    plot.plot(name: "plot", size: (5,5), 
+    x-label: $U_"DS1" "in V"$,
+    y-label: $I_D "in mA"$,
+    y-tick-step: 4,
+    x-tick-step: .5,
+    y-min: 0, y-max: 16,
+    x-min: 0, x-max: 2.1,
+    {
+      plot.add-anchor("AP", (1,8))
+      plot.add-anchor("P1", (2,0))
+      plot.add(((0,16), (2,0)))
+      plot.add(domain: (0.00001,2.1), u => 2 * calc.log(u) + 2)
+      plot.add(domain: (0.00001,2.1), u => 1.5 * calc.log(u) + 5)
+      plot.add(domain: (0.00001,2.1), u => 1 * calc.log(u) + 8)
+      plot.add(domain: (0.00001,2.1), u => .5 * calc.log(u) + 11)
+      plot.add(domain: (0.00001,2.1), u => .2 * calc.log(u) + 14)
+      plot.annotate({
+        content((2.7,3),  anchor: "east", padding: 0, $U_"GS1" = 0,8 V$)
+        content((2.7,6),  anchor: "east", padding: 0, $U_"GS1" = 0,9 V$)
+        content((2.7,9),  anchor: "east", padding: 0, $U_"GS1" = 1,0 V$)
+        content((2.7,12), anchor: "east", padding: 0, $U_"GS1" = 1,1 V$)
+        content((2.7,15), anchor: "east", padding: 0, $U_"GS1" = 1,2 V$)
+      })
+      plot.annotate({
+        content((1,8), $times$)
+        content((1,8), anchor: "north", padding: 20pt, [AP])
+        content((2,0), $times$)
+        content((2,0), anchor: "north", padding: 20pt, [P1])
+        content((0,16), $times$)
+        content((0,16), anchor: "north", padding: 20pt, [P2])
+      })
+    })
+  })
+])
+#v(-1.3cm)
+$
+"Einstellen sodass " U_"GS1" = 1 V": " & R_"G1" + R_"G2" = U_D / I_D =^! (2 V) / (8"mA") = 25 k Omega \
+&R_"G1" / (R_"G1" + R_"G2") =^! U_"GS1" = 1 V \
+&R_"G2" / (R_"G1" + R_"G2") dot U_D =^! U_D - U_"GS1" = 1 V => R_"G1" = R_"G2" =
+&12,5 k Omega
+$
+
+NOT #box(align(horizon, stack(dir:ltr, rect[1],circle(radius: 3pt))))
+AND #box(rect[&])
+OR #box(rect[$>=1$])
+