From e549f26275921dc6dbfed2d0069b167c1acc3dbe Mon Sep 17 00:00:00 2001 From: alexander Date: Wed, 18 Feb 2026 00:33:32 +0100 Subject: [PATCH] Added pictures --- src/cheatsheets/Digitaltechnik.typ | 828 ++++++++++++--------- src/images/digitaltechnik/IMG_0538.jpg | Bin 0 -> 127738 bytes src/images/digitaltechnik/IMG_0549.jpg | Bin 0 -> 55689 bytes src/images/digitaltechnik/IMG_0550.jpg | Bin 0 -> 85558 bytes src/images/digitaltechnik/IMG_0555.jpg | Bin 0 -> 25283 bytes src/images/digitaltechnik/cmosPower.jpg | Bin 0 -> 156470 bytes src/images/digitaltechnik/dlatch.jpg | Bin 0 -> 49720 bytes src/images/digitaltechnik/dlatch2.jpg | Bin 0 -> 176834 bytes src/images/digitaltechnik/gateWidth.jpg | Bin 0 -> 142236 bytes src/images/digitaltechnik/literalMenge.jpg | Bin 0 -> 74244 bytes src/images/digitaltechnik/literalmenge.png | Bin 0 -> 67474 bytes src/images/digitaltechnik/logicGates.jpg | Bin 0 -> 100705 bytes src/images/digitaltechnik/nmos1.jpg | Bin 0 -> 75129 bytes src/images/digitaltechnik/nmos2.jpg | Bin 0 -> 61711 bytes src/images/digitaltechnik/nmos3.jpg | Bin 0 -> 60495 bytes src/images/digitaltechnik/parallel.jpg | Bin 0 -> 51115 bytes src/images/digitaltechnik/pipeline1.jpg | Bin 0 -> 93869 bytes src/images/digitaltechnik/pipeline2.jpg | Bin 0 -> 85801 bytes src/images/digitaltechnik/pmos1.jpg | Bin 0 -> 164105 bytes src/images/digitaltechnik/pmos2.jpg | Bin 0 -> 68887 bytes src/images/digitaltechnik/pmos3.jpg | Bin 0 -> 61567 bytes src/images/digitaltechnik/qmc1.jpg | Bin 0 -> 149539 bytes src/images/digitaltechnik/qmc2.jpg | Bin 0 -> 149539 bytes src/images/digitaltechnik/qmc3.jpg | Bin 0 -> 144675 bytes src/images/digitaltechnik/qmc4.jpg | Bin 0 -> 131535 bytes src/images/digitaltechnik/qmc5.jpg | Bin 0 -> 130189 bytes src/images/digitaltechnik/qmc6.jpg | Bin 0 -> 194289 bytes 27 files changed, 460 insertions(+), 368 deletions(-) create mode 100644 src/images/digitaltechnik/IMG_0538.jpg create mode 100644 src/images/digitaltechnik/IMG_0549.jpg create mode 100644 src/images/digitaltechnik/IMG_0550.jpg create mode 100644 src/images/digitaltechnik/IMG_0555.jpg create mode 100644 src/images/digitaltechnik/cmosPower.jpg create mode 100644 src/images/digitaltechnik/dlatch.jpg create mode 100644 src/images/digitaltechnik/dlatch2.jpg create mode 100644 src/images/digitaltechnik/gateWidth.jpg create mode 100644 src/images/digitaltechnik/literalMenge.jpg create mode 100644 src/images/digitaltechnik/literalmenge.png create mode 100644 src/images/digitaltechnik/logicGates.jpg create mode 100644 src/images/digitaltechnik/nmos1.jpg create mode 100644 src/images/digitaltechnik/nmos2.jpg create mode 100644 src/images/digitaltechnik/nmos3.jpg create mode 100644 src/images/digitaltechnik/parallel.jpg create mode 100644 src/images/digitaltechnik/pipeline1.jpg create mode 100644 src/images/digitaltechnik/pipeline2.jpg create mode 100644 src/images/digitaltechnik/pmos1.jpg create mode 100644 src/images/digitaltechnik/pmos2.jpg create mode 100644 src/images/digitaltechnik/pmos3.jpg create mode 100644 src/images/digitaltechnik/qmc1.jpg create mode 100644 src/images/digitaltechnik/qmc2.jpg create mode 100644 src/images/digitaltechnik/qmc3.jpg create mode 100644 src/images/digitaltechnik/qmc4.jpg create mode 100644 src/images/digitaltechnik/qmc5.jpg create mode 100644 src/images/digitaltechnik/qmc6.jpg diff --git a/src/cheatsheets/Digitaltechnik.typ b/src/cheatsheets/Digitaltechnik.typ index d7a2705..7afdfc6 100644 --- a/src/cheatsheets/Digitaltechnik.typ +++ b/src/cheatsheets/Digitaltechnik.typ @@ -30,6 +30,8 @@ ], ) +#set text(11pt) + #let pTypeFill = rgb("#dd5959").lighten(10%); #let nTypeFill = rgb("#5997dd").lighten(10%); @@ -37,7 +39,7 @@ [Digitaltechnik] )) -#let SeperatorLine = line(length: 100%, stroke: (paint: black, thickness: 0.3mm)) +#let SeperatorLine = line(length: 100%, stroke: (paint: black, thickness: 0.2mm)) #let MathAlignLeft(e) = { align(left, block(e)) } @@ -201,101 +203,108 @@ #bgBlock(fill: colorOptimierung)[ #subHeading(fill: colorOptimierung)[Quine McCluskey] + === Quine 1. KNF/DNF $->$ KKNF/KDNF 2. Primiplikant Bestimme \ 2.1. Terme nach positive Literal ($x_i$) soltieren\ 2.2. Abosbition zwischen zwei unterliegen Blöcken \ Eine Literal unterschied, #raw("X") müssen matchen \ 2.3. Abhacken was absorbiert wurde \ + + #image("../images/digitaltechnik/qmc6.jpg", height: 3cm) + #SeperatorLine - === MacCluskyn + === McClusky 1. Überdeckungstabelle aufstellen + #image("../images/digitaltechnik/qmc1.jpg", height: 3cm) + #SeperatorLine + 2. Kernprimimplikanten finden \ (Splaten mit nur einem Eintrag) \ und vom Kerprimiplaten übdeckte \ NICHT Kernprimstplaten Streichen + #image("../images/digitaltechnik/qmc3.jpg", height: 3cm) + #SeperatorLine 3. Splaten dominazen \ - (Dominierende Splate streichen) + (Dominierte Spalte streichend) + + #image("../images/digitaltechnik/qmc4.jpg", height: 3cm) + #SeperatorLine 4. Zeilen dominazen \ (Domenierete Zeile streiche) \ Kosten: D1 dominierte D2 \ D1 $<=$ D2 $->$ NUR dann streichen \ + #image("../images/digitaltechnik/qmc5.jpg", height: 3cm) + #SeperatorLine 5. Wiederhole 3.-5. solange noch was geht ] + #bgBlock(fill: colorState)[ + #subHeading(fill: colorState)[Latches, Flipflops und Register] + #image("../images/digitaltechnik/dlatch2.jpg", height: 6cm) + ] + #bgBlock(fill: colorState)[ + #subHeading(fill: colorState)[Pipeline/Parallele Verarbeitungseinheiten] - // Dotierung + #image("../images/digitaltechnik/pipeline1.jpg") + #image("../images/digitaltechnik/pipeline2.jpg") + #image("../images/digitaltechnik/parallel.jpg", height: 3cm) + ] + + #bgBlock(fill: colorState)[ + #subHeading(fill: colorState)[Zustandsautomaten] + ] +] +#pagebreak() +#columns(2, gutter: 2mm)[ + // Mosfet #bgBlock(fill: colorRealsierung)[ - #table( - columns: (auto, 1fr), - [N-Type], + #subHeading(fill: colorRealsierung)[FET/MOSFET Funktion] + + #grid(columns: (1fr, 2fr), + image("../images/digitaltechnik/gateWidth.jpg", height: 3cm), + [ - - Dotierung: Phosphor (V) - - Negative Ladgunsträger ($e^-$) - - mehr Elektron als Si - ], - [P-Type], - [ - - Dotierung: Bor (III) - - Postive Landsträger (Löcher) - - mehr Löcher als Si + #grid(columns: (1fr, 1fr), + row-gutter: 2.5mm, + [$W$: Kanalweite], [$L$: Kanallänge], + [Löcherbeweglichkeit: $mu_"n/p"$], + [Oxdy Dicke: $t_"ox"$], + [Oxdy Dielektriukum: $epsilon_"ox"$], + [$mu_"n" = 1,6 mu_"p" "bis" 3,5 mu_"p"$], + ) + + $L$ wir immer so kleine wie möglich gewählt $= L_"min"$ + + $beta_"n/p" = (mu_"n/p" epsilon_0 epsilon_"ox")/(t_"ox") W/L = K'_"n/p" W/L$ + + $R_"on" = $ + ] ) + #table(columns: (1fr, 1fr), + fill: (x, y) => if (calc.rem(y, 2) == 1) { tableFillLow } else { tableFillHigh }, - #zap.circuit({ - import cetz.draw : * - import zap : * + [*NMOS*], [*PMOS*], - diode("A", (0,1.7), (3,1.7), fill: black, i: (content: $i_d$, anchor: "south")) + image("../images/digitaltechnik/nmos3.jpg"), + image("../images/digitaltechnik/pmos3.jpg"), + [ + - Source am *niedrigen* Potenzial (*GND*) + - Guter PULL-DOWN + ], + [ + - Source am *hohes* Potenzial (*$V_"DD"$*) + - Guter PULL-UP + ], - 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( + align(center+horizon, scale( x: 75%, y: 75%, zap.circuit({ import cetz.draw : * @@ -320,8 +329,8 @@ content((1, 0.5), "D") content((2, 0.5), "G") }) - ), - scale( + )), + align(center+horizon,scale( x: 75%, y: 75%, zap.circuit({ import cetz.draw : * @@ -346,36 +355,308 @@ content((1, 0.5), "D") content((2, 0.5), "G") }) - ), - ) + )), - *Drain Strom:* - - NMOS: $I_"Dn" = cases( + block( inset: (top: 2mm, bottom: 2mm),$ 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: $I_"Dp" = cases( + )$), + block( inset: (top: 2mm, bottom: 2mm), $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) - ) - $ + )$), + + grid( + columns: (auto, auto), + column-gutter: 2mm, + image("../images/digitaltechnik/nmos1.jpg", height: 2.5cm), + image("../images/digitaltechnik/nmos2.jpg", height: 2.5cm), + ), + grid( + columns: (auto, auto), + column-gutter: 2mm, + image("../images/digitaltechnik/pmos1.jpg", height: 2.5cm), + image("../images/digitaltechnik/pmos2.jpg", height: 2.5cm), + ), + ) ] + #colbreak() - // NMOS/PMOS - #bgBlock(fill: colorRealsierung)[ - #subHeading(fill: colorRealsierung)[CMOS] - $hat(=)$ Complemntary MOS + #columns(2, gutter: 2mm)[ + // Dotierung + #bgBlock(fill: colorRealsierung)[ + #subHeading(fill: colorRealsierung)[Dotierung] + #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 + ] + ) - #table( - columns: (1fr, 1fr), - zap.circuit({ + #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") + }) + ), + ) + */ + ] + + // CMOS Circits + #bgBlock(fill: colorRealsierung)[ + #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* + + $overline(A dot B) = Z$ + ], + ) + ] + + #bgBlock(fill: colorRealsierung)[ + #subHeading(fill: colorRealsierung)[Verlustleistung/Verzögerung] + + #image("../images/digitaltechnik/cmosPower.jpg", height: 6cm) + + $t_p ~ C_L / (V_"DD" - V_"Tn")$ + + $P_"stat" ~ e^(-V_T)$ + + $P_"dyn"~ V_"DD"^2$ + + + *Dynamisch:* Bei Schlaten \ + 1. Kapazitiv Verlustleistung $I_C$ \ + 2. Querstrom Verlustleistung $I_Q$ \ + + #zap.circuit({ import zap : * import cetz.draw : content import "../lib/circuit.typ" : * @@ -390,309 +671,120 @@ node("outNode", (0,0.5)) node("inNode", (-0.6,0.5)) wire((-1, 0.5), "inNode") - wire((0.2, 0.5), "outNode") + wire((0.5, 0.5), "outNode") + wire((0, -0.5), (0, -1)) - node("N2", (0,-0.5)) + node("N2", (0,-1)) node("N2", (0,1.5)) - wire((-1, -0.5), (0.5, -0.5)) + wire((-1, -1), (0.5, -1)) 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((0.8, 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") + content((-0.9, -1), scale($"GND"$, 60%), anchor: "east") }), - [ - *Inverter* - - $overline(X)$ - ], + - Quer/Kurzschluss Strom $i_q$ \ + $P_"short" = a_01 f beta_n tau (V_"DD" - 2 V_"Tn")^3$ \ + $tau$: Kurzschluss/Schaltzeit + - Lade Strome des $C_L$ $i_c$ + $P_"cap" = alpha_01 f C_L V_"DD"^2$ + *Statisch:* Konstant + - Leckstom (weil Diode) + - Gatestrom + ] - zap.circuit({ - import zap : * - import cetz.draw : content - import "../lib/circuit.typ" : * + // CMOS + #bgBlock(fill: colorRealsierung)[ + #subHeading(fill: colorRealsierung)[CMOS Verzögerung] - set-style(wire: (stroke: (thickness: 0.025))) + *Inverter*\ + $t_("p"/"nLH") ~ (C_"L" t_"ox" L_"p/n")/(W_"p/n" mu_"p/n" epsilon(V_"DD" - abs(V_"Tpn"))) $ - 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); + #grid( + columns: (1fr, 1fr), + [ + *Steigend mit* + - Last $C_L$ + - Oxyddicke $T_"ox"$ + - Kandlalänge $L_"p/n"$ + - Schwellspannung $V_"Tp/n"$ + ], + [ + *Sinkend mit* + - Kanalweite + - Landsträger Veweglichkeit $mu_"p/n"$ + ], - 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] - - *Inverter*\ - $t_("p"/"nLH") ~ (C_"L" t_"ox" L_"p/n")/(W_"p/n" mu_"p/n" epsilon(V_"DD" - abs(V_"Tpn"))) $ - - #grid( - columns: (1fr, 1fr), - [ - *Steigend mit* - - Last $C_L$ - - Oxyddicke $T_"ox"$ - - Kandlalänge $L_"p/n"$ - - Schwellspannung $V_"Tp/n"$ - ], - [ - *Sinkend mit* - - Kanalweite - - Landsträger Veweglichkeit $mu_"p/n"$ - ], - - ) - - $t_p ~ C_L/(beta(V_"DD" - abs(V_"T")))$ - - $t_p ~ C_L/(W(V_"DD" - abs(V_"T")))$ - ] - - #bgBlock(fill: colorState)[ - #subHeading(fill: colorState)[Latches, Flipflops und Register] - ] - - #bgBlock(fill: colorState)[ - #subHeading(fill: colorState)[Timing] - - *Register Bedinungen* - - #cetz.canvas(length: 0.5mm, { - import cetz.draw: * - - - let cycle_time = 38 - let cycle_start = cycle_time*0.8 - let cycle_end = cycle_time*4 - let signal_hight = 10 - let switch_offset = cycle_time/13 - let signal_storke = (paint: rgb("#2e2e2e"), thickness: 0.3mm) - - let t_c2q = 0.6 - let t_setup = 0.6 - let t_hold = 0.4 - - // clk1 - line((1*cycle_time + switch_offset/2, signal_hight + 1), (1*cycle_time + switch_offset/2, -40), stroke: (paint: rgb("#0004ff"), thickness: 0.4mm, dash: "densely-dashed")) - - // q change - line((cycle_time*(t_c2q + 1) + switch_offset/2, -15 + signal_hight + 1), (cycle_time*(t_c2q + 1) + switch_offset/2, -40), stroke: (paint: rgb("#0004ff"), thickness: 0.4mm, dash: "densely-dashed")) - - // d change - line((cycle_time*(t_setup + 2) + switch_offset/2, -30 + signal_hight + 1), (cycle_time*(t_setup + 2) + switch_offset/2, -40), stroke: (paint: rgb("#0004ff"), thickness: 0.4mm, dash: "densely-dashed")) - - // clk - line((cycle_time*3 + switch_offset/2, signal_hight + 1), (cycle_time*3 + switch_offset/2, -40), stroke: (paint: rgb("#0004ff"), thickness: 0.4mm, dash: "densely-dashed")) - - // hold time - line((cycle_time*(3+t_hold) + switch_offset/2, -30 + signal_hight + 1), (cycle_time*(3+t_hold) + switch_offset/2, -40), stroke: (paint: rgb("#0004ff"), thickness: 0.4mm, dash: "densely-dashed")) - - - content(( cycle_start -7, 5), "clk") - - line((cycle_start,0), (cycle_time,0), (cycle_time + switch_offset,signal_hight), (cycle_time*2, signal_hight), (cycle_time*2 + switch_offset, 0), (cycle_time*3, 0), (cycle_time*3 + switch_offset, 10), (cycle_end, signal_hight), stroke: signal_storke) - - translate((0, -15)) - content((cycle_start -7, 5), "Q") - - line( - (cycle_start,0), (cycle_time*(t_c2q + 1), 0), - (cycle_time*(t_c2q + 1) + switch_offset, signal_hight), - (cycle_time*(t_c2q + 3),signal_hight), (cycle_time*(t_c2q + 3) + switch_offset, 0), - (cycle_end + switch_offset, 0), - stroke: signal_storke - ) - line( - (cycle_start,signal_hight), (cycle_time*(t_c2q + 1), signal_hight), - (cycle_time*(t_c2q + 1) + switch_offset, 0), - (cycle_time*(t_c2q + 3),0), (cycle_time*(t_c2q + 3) + switch_offset, signal_hight), - (cycle_end + switch_offset, signal_hight), - stroke: signal_storke ) - translate((0, -15)) - content((cycle_start -7, 5), "D") + $t_p ~ C_L/(beta(V_"DD" - abs(V_"T")))$ - line( - (cycle_start,0), (cycle_time*(t_setup + 2), 0), - (cycle_time*(t_setup + 2) + switch_offset, signal_hight), (cycle_end + switch_offset, signal_hight), stroke: signal_storke - + $t_p ~ C_L/(W(V_"DD" - abs(V_"T")))$ + ] + + #linebreak() + + #bgBlock(fill: colorRealsierung)[ + #subHeading(fill: colorRealsierung)[Verlustleistung] + + $"#Schaltvorgänge"$ : Ganzer High-Low Cycles eines Signals + + #linebreak() + + $"Energie pro Schaltvorgang:" \ "Lade Verlust" + "Geladene Energie" \ + = E_"stored" + E_"heat" = C_L V_"DD"^2$ (unabhängig von $R_"on"$) + + #linebreak() + + $alpha = "#Schaltvorgänge"/"#Takte (#Clk Flanken)"$ + + $P_"cap" = alpha dot f_"clk" dot C dot U_"DD"^2$ + + ] + + #colbreak() + + #SIPrefixesTable + + #colbreak() + #bgBlock(fill: colorBoolscheLogic)[ + #subHeading(fill: colorBoolscheLogic)[Logik Gatter] + + #grid(columns: (auto, 1fr), + row-gutter: 2mm, + align(center, box(image("../images/digitaltechnik/logicGates.jpg", height: 6cm, fit: "cover"), clip: true, height: 6cm/4)), + align(center+horizon, [*AND* \ $and$]), + + align(center, box(inset: (top: -6cm/4), image("../images/digitaltechnik/logicGates.jpg", height: 6cm, fit: "cover"), clip: true, height: 6cm/4)), + align(center+horizon, [*OR* \ $or$]), + + align(center, box(inset: (top: -6cm/4 * 2), image("../images/digitaltechnik/logicGates.jpg", height: 6cm, fit: "cover"), clip: true, height: 6cm/4)), + align(center+horizon, [*XOR* \ $xor$]), + + align(center, box(inset: (top: -6cm/4 *3), image("../images/digitaltechnik/logicGates.jpg", height: 6cm, fit: "cover"), clip: true, height: 6cm/4)), + align(center+horizon, [*NOT* \ $not$]) ) - line( - (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 + + #truth-table( + outputs: ( + ("AND", (0, 0, 0, 1)), + ("OR", (0, 1, 1, 1)), + ("XOR", (0, 1, 1, 0)), + ), + inputs: ("A", "B") ) - }) + + #truth-table( + outputs: ( + ("NAND", (1, 1, 1, 0)), + ("NOR", (1, 0, 0, 0)), + ("XNOR", (1, 0, 0, 1)), + ), + inputs: ("A", "B") + ) + ] ] - - - - #bgBlock(fill: colorState)[ - #subHeading(fill: colorState)[Pipeline/Parallele Verarbeitungseinheiten] - ] - - #bgBlock(fill: colorState)[ - #subHeading(fill: colorState)[Zustandsautomaten] - ] - - #colbreak() - #bgBlock(fill: colorRealsierung)[ - #subHeading(fill: colorRealsierung)[Verlustleistung/Verzögerung] - - $t_p ~ C_L / (V_"DD" - V_"Tn")$ - - $P_"stat" ~ e^(-V_T)$ - - $P_"dyn"~ V_"DD"^2$ - - - *Dynamisch:* Bei Schlaten \ - 1. Kapazitiv Verlustleistung $I_C$ \ - 2. Querstrom Verlustleistung $I_Q$ \ - - #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((0.5, 0.5), "outNode") - wire((0, -0.5), (0, -1)) - - node("N2", (0,-1)) - node("N2", (0,1.5)) - - wire((-1, -1), (0.5, -1)) - wire((-1, 1.5), (0.5, 1.5)) - - content((-1, 0.5), scale($"X"$, 60%), anchor: "east") - content((0.8, 0.5), scale($overline("X")$, 60%), anchor: "east") - content((-0.9, 1.5), scale($"U"_"DD"$, 60%), anchor: "east") - content((-0.9, -1), scale($"GND"$, 60%), anchor: "east") - }), - - - Quer/Kurzschluss Strom $i_q$ \ - $P_"short" = a_01 f beta_n tau (V_"DD" - 2 V_"Tn")^3$ \ - $tau$: 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