summary.typ (18699B)
1 #import "@preview/zap:0.2.1" 2 #import "@preview/cetz-plot:0.1.2": plot, chart 3 4 #set columns(gutter: 5pt) 5 #set rect(outset: 0pt) 6 #set figure(supplement: "", numbering: none) 7 // #set block(spacing: 5pt) 8 #let section(..args) = block(width: 100%, fill: silver, spacing: 5pt, below: 5pt, breakable: false, ..args) 9 #set page( 10 // columns: 2, 11 numbering: "1", 12 margin: 1cm, 13 header: rect(width: 100%, stroke: (bottom: 1pt), inset: (left: 0pt, right: 0pt))[ 14 #smallcaps[Elektronische Schaltungen] 15 #h(1fr) 16 Gero Beckmann 17 ] 18 ) 19 20 #let out(name, pos) = { 21 import zap.cetz.draw: * 22 on-layer(1, { 23 circle(pos, name: name, radius: .1, fill: white) 24 }) 25 } 26 27 #let arrow(a,b,..args) = { 28 import zap.draw: * 29 line((a,.2,b), (b, .2, a), name: "line", mark: (end: (symbol: ">", fill: black))) 30 content("line", anchor: "east", padding: .2, ..args) 31 } 32 33 34 35 #columns(2, [ 36 37 #section[ 38 == E 24 Reihe 39 #{range(24) 40 .map(n => calc.pow(calc.root(10,24),n)) 41 .map(e => str(calc.round(e, digits: 1) + calc.pow(10,-10)).slice(0,3)) 42 .join(" | ") 43 } 44 45 #let units = ( 46 ([Giga], $10^9$), 47 ([Mega], $10^6$), 48 ([Kilo], $10^3$), 49 ([Milli], $10^(-3)$), 50 ([Mikro $mu$], $10^(-6)$), 51 ([Nano], $10^(-9)$), 52 ([Piko], $10^(-12)$), 53 ([Femto], $10^(-15)$), 54 ) 55 56 #text(size: 8pt)[#table(columns: units.len() * (1fr,), inset: 3pt, table.header(..units.map(array.first)), ..units.map(array.last)) 57 ] 58 59 #grid(columns: 2 * (1fr,), align: (right, left), gutter: 10pt, 60 [Knotenregel, $sum I = 0$], [Maschenregel $sum U = 0$], 61 [Parallelwiderstände], $R_1 || R_2 = 1 / (1 / R_1 + 1 / R_2) = (R_1 dot R_2) / (R_1 + R_2)$, 62 [Spannungsteiler], $U_2 = U dot R_2 / (R_1 + R_2)$, 63 [Stromteiler], $I_1 = I dot R_2 / (R_1 + R_2)$, [3 dB-Grenzfrequenz], $f_"3dB" = 64 1 / (2 pi dot C dot R)$ 65 ) 66 Übertragungsfunktion normiert: $1/(1+j omega K)$ bzw $(j omega K)/(1 + j omega K)$ \ 67 $omega_"3dB" = 1 / K => f_"3dB" = 1 / (2 pi K)$ 68 $Z_L = j omega L, Z_C = 1 / (j omega C)$ \ 69 $abs(H(omega)) = abs(a+b j) = sqrt(a^2 + b ^2)$ 70 71 ] 72 #colbreak() 73 74 #section[ 75 == Diode #box(zap.canvas({zap.diode("d", (0,0),(1,0))})) 76 77 #v(-.5cm) 78 #grid(columns: 2 * (1fr,), align: (right, left), gutter: 10pt, 79 [], $" mit " U_T = (k_B dot T)/mono(e) approx 26"mv"$, 80 [Diodenstrom], $I_D &= I_s dot (e^(U_D/U_T) -1)$, 81 [Diodenspannung], $U_D &= U_T dot ln(I_D/I_S)$ , 82 [Kleinsignal], $r_D &= U_T / I_D$ 83 ) 84 85 #zap.canvas({ 86 import zap: * 87 import zap.cetz.draw: * 88 89 scale(.6) 90 content((-5,-.3), [Kleinsignalersatzschaltbild]) 91 out("A", (0,0)) 92 out("K", (3,0)) 93 resistor("rd", "A", "K", label: (content: $r_D$, anchor: "south", distance: 0pt)) 94 95 translate((0.8,-1.5)) 96 content((-4.2,0), [Erweitertes Kleinsignalersatzschaltbild]) 97 translate((2.4,.4)) 98 scale(.6) 99 out("A", (0,0)) 100 out("K", (5,0)) 101 resistor("RB", "A", (3,0), label: (content: $R_B$, anchor: "south", distance: 0pt)) 102 resistor("rd", (2,0), "K", label: (content: $r_D$, anchor: "south", distance: 0pt)) 103 capacitor("CD", 104 (rel: (0.5, 1), to: "rd.in"), 105 (rel: (-.5, 1), to: "K"), 106 label: (content: $C_D$, anchor: "north", distance: 1pt)) 107 wire("CD.in", (rel: (0,-1))) 108 wire("CD.out", (rel: (0,-1))) 109 }) 110 #stack(dir: ltr,[ 111 #zap.cetz.canvas({ 112 import zap.draw: * 113 plot.plot(axis-style: "school-book", name: "plot", size: (2,2), x-label: $U(V)$, y-label: 114 $I(A)$, x-tick-step: none, y-tick-step: none, { 115 plot.add(domain: (-23,15), u => if (u > 0) {(u, calc.exp(u - 2))} 116 else {(u,-calc.exp(-u - 10))}) 117 plot.add-anchor("brk", (-8,0)) 118 plot.add-anchor("UBR", (-18,0)) 119 plot.add-anchor("UF", (14,0)) 120 }) 121 content("plot.brk", text(fill: black, weight: "extrabold")[\/\/]) 122 line((rel: (0,.2), to: "plot.UBR"), (rel: (0,-.4))) 123 content("plot.UBR", anchor: "south", padding: 8pt, $U_"Br" "/" U_Z$) 124 line((rel: (0,.2), to: "plot.UF"), (rel: (0,-.4))) 125 content("plot.UF", anchor: "north", padding: 8pt, $U_"F"$) 126 }) 127 ],[ 128 $ 129 U_F & "Flussspannung" \ 130 U_"Br" "/" U_Z & "Durchbruchspannung /" \ 131 & "Zenerspannung " 132 $ 133 ]) 134 ] 135 ]) 136 137 #section[ 138 139 #stack(dir: ltr, spacing: 1fr, [ 140 == Bipolartransistor #box[#zap.canvas({ 141 import zap: * 142 import zap.draw: * 143 scale(.5) 144 pnp("Q", (0,0)) 145 content("Q.b", "B", anchor: "east", padding: (right: 5pt)) 146 content("Q.c", "C", anchor: "west", padding: (left: 5pt)) 147 content("Q.e", "E", anchor: "west", padding: (left: 5pt)) 148 })] 149 #grid(columns: 2, align: (right, left), gutter: 10pt, 150 [Steilheit], $S = I_(C,A) / U_T$, 151 [Kleinsignal-Eingangs-\ Widerstand], $r_"BE" = beta / S$, 152 [Stromverstärkung], $beta = I_C / I_B$, 153 [Ausgangswiderstand], $r_"CE" = (abs(U_A) + U_"CE") / I_C$, 154 ) 155 ],[ 156 #figure(zap.canvas({ 157 import zap: * 158 import zap.cetz.draw: * 159 scale(.7) 160 out("UBEE", (0,0)) 161 out("UBEA", (0,-2)) 162 out("UCEE", (5,0)) 163 out("UCEA", (5,-2)) 164 165 node("B", (1,0)) 166 content("B", anchor: "south", padding: 5pt, [Basis]) 167 node("K", (3.5,0)) 168 content("K", anchor: "south", padding: 5pt, [Kollektor]) 169 node("E", (2.5,-2)) 170 content("E", anchor: "north", padding: 5pt, [Emitter]) 171 172 wire("UBEE", "B", i: "hi") 173 wire("UCEE", "K") 174 wire("UBEA", "UCEA") 175 176 resistor("RBE", "B", ((), "|-", "E"), label: (content: $r_"BE"$, anchor: "south", distance: 0pt)) 177 isource("SUBE", "K", ((), "|-", "E"), label: (content: $S dot u_"BE"$, distance: 1pt)) 178 set-style(zap: (wires: (stroke: red))) 179 wire("B", (2.5,0), stroke: red) 180 capacitor("CBE", ("E"), (rel: (0,2)), stroke: red, label: (content: text(fill:red, $C_"BE"$), anchor: "west", distance: 5pt)) 181 capacitor("", ("K"), (rel: (-1,0)), stroke: red) 182 content((rel: (-1.5,0), to: "K"), text(fill: red, $C_"BC"$)) 183 }), 184 caption: [#text(fill:red)[vollständiges] \ Kleinsignalersatzschaltbild]) 185 ], [ 186 #figure(zap.canvas({ 187 import zap: * 188 import zap.cetz.draw: * 189 scale(.7) 190 out("UBEE", (0,0)) 191 out("UBEA", (0,-2)) 192 out("UCEE", (5,0)) 193 out("UCEA", (5,-2)) 194 195 node("B", (1.5,0)) 196 content("B", anchor: "south", padding: 5pt, [Basis]) 197 node("K", (3.5,0)) 198 content("K", anchor: "south", padding: 5pt, [Kollektor]) 199 node("E", (2.5,-2)) 200 content("E", anchor: "north", padding: 5pt, [Emitter]) 201 202 wire("UBEE", "B", i: "hi") 203 wire("UCEE", "K") 204 wire("UBEA", "UCEA") 205 206 diode("RBE", "B", ((), "|-", "E")) 207 isource("SUBE", "K", ((), "|-", "E"), label: (content: $S dot u_"BE"$, distance: 1pt)) 208 }),caption: [Großsignalersatzschaltbild]) 209 ]) 210 #align(right + horizon, stack(dir: ltr, [ 211 #figure(zap.canvas({ 212 import zap: * 213 import zap.cetz.draw: * 214 scale(.7) 215 out("U1E", (0,0)) 216 out("U1A", (0,-2)) 217 out("U2E", (5,0)) 218 out("U2A", (5,-2)) 219 set-style(zap: (wires: (stroke: green))) 220 resistor("Z1", (1.5,0), (1.5,-2), stroke: green, label: (content: text(fill: green, $Z/(1-A)$), distance: 1pt)) 221 resistor("Z2", (5-1.5,0), (5-1.5,-2), stroke: green, label: (content: text(fill: green, $(A Z)/(A-1)$), distance: 1pt)) 222 wire("U1E", "Z1.in") 223 wire("U2E", "Z2.in") 224 wire("U1A", "U2A") 225 set-style(zap: (wires: (stroke: red))) 226 resistor("Z","Z1.in", "Z2.in", stroke: red, label: (content: text(fill: red, $Z$), distance: 1pt)) 227 228 arrow("U1E", "U1A", $u_1$, anchor: "west") 229 arrow("U2E", "U2A", $u_2$, anchor: "west") 230 }),caption: [ 231 ]) 232 ], [ 233 Miller-Theorem: $A = u_2/u_1$\ 234 #text(fill: red)[verbundene Impedanz $Z$] wird \ 235 zu #text(fill: green)[zwei getrennte Impedanzen] 236 ])) 237 238 #table(columns: 3 * (1fr,), align: center, 239 table.header([Ermitterschaltung], [Basisschaltung], [Kollektorschaltung]),[ 240 #set text(size: 9pt) 241 #zap.canvas({ 242 import zap: * 243 import zap.cetz.draw: * 244 245 246 scale(.8) 247 out("e", (0,0)) 248 out("a", (2.5,1)) 249 out("eg", (0,-1)) 250 out("ag", (2.5,-1)) 251 252 pnp("n1", (1.5,0)) 253 wire("e", "n1.b") 254 wire("n1.c", ((), "|-", "a"), "a") 255 wire("n1.e", ((), "|-", "ag"), "ag") 256 wire("n1.e", ((), "|-", "eg"), "eg") 257 258 scale(.3) 259 resistor("", "n1.e", (rel: (0,-2)), stroke: red, label: (content: text(fill: red, size:8pt,$R_E$), distance: 1pt)) 260 261 line(("e",.2,"eg"), ("eg", .2, "e"), name: "line", mark: (end: (symbol: ">", fill: black))) 262 content("line", anchor: "east", padding: .2, $U_e$) 263 264 line(("a",.2,"ag"), ("ag", .2, "a"), name: "line", mark: (end: (symbol: ">", fill: black))) 265 content("line", anchor: "east", padding: .2, $U_a$) 266 }) 267 ], 268 [ #zap.canvas({ 269 import zap: * 270 import zap.cetz.draw: * 271 scale(.8) 272 out("e", (-1.25,0)) 273 out("a", (1.5,1)) 274 out("eg", (-1.25,-1)) 275 out("ag", (1.5,-1)) 276 277 rotate(x:180deg) 278 rotate(z:-90deg) 279 pnp("n1", (0,0)) 280 set-transform(none) 281 282 wire("e", "n1.e") 283 wire("n1.c", ((), "|-", "a"), "a") 284 wire("n1.b", ((), "|-", "ag"), "ag") 285 wire("n1.b", ((), "|-", "eg"), "eg") 286 287 line(("e",.2,"eg"), ("eg", .2, "e"), name: "line", mark: (end: (symbol: ">", fill: black))) 288 content("line", anchor: "east", padding: .2, $U_e$) 289 290 line(("a",.2,"ag"), ("ag", .2, "a"), name: "line", mark: (end: (symbol: ">", fill: black))) 291 content("line", anchor: "east", padding: .2, $U_a$) 292 }) 293 ],[ 294 295 #zap.canvas({ 296 import zap: * 297 import zap.cetz.draw: * 298 scale(.8) 299 out("e", (0,0)) 300 out("a", (2.5,1)) 301 out("eg", (0,-1)) 302 out("ag", (2.5,-1)) 303 304 rotate(x: 180deg) 305 pnp("n1", (1.5,0)) 306 wire("e", "n1.b") 307 wire("n1.e", ((), "|-", "a"), "a") 308 wire("n1.c", ((), "|-", "ag"), "ag") 309 wire("n1.c", ((), "|-", "eg"), "eg") 310 311 line(("e",.2,"eg"), ("eg", .2, "e"), name: "line", mark: (end: (symbol: ">", fill: black))) 312 content("line", anchor: "east", padding: .2, $U_e$) 313 314 line(("a",.2,"ag"), ("ag", .2, "a"), name: "line", mark: (end: (symbol: ">", fill: black))) 315 content("line", anchor: "east", padding: .2, $U_a$) 316 }) 317 ] 318 ,[ 319 #text(size: 8pt)[ 320 #grid(columns: 2 * (1fr,), [ 321 $ 322 A &= -S R_C \ 323 r_e &= r_"BE" \ 324 r_a &= r_"CE" || R_C 325 $ 326 ],text(fill: red)[ 327 Stromgegen-\kopplung $ 328 A &= -R_C / R_E \ 329 r_e &= r_"BE" \ 330 r_a &= r_"CE" || R_C 331 $ 332 ]) 333 ] 334 ], [ 335 336 #text(size: 9pt, $ 337 A &= S R_C \ 338 r_e &= 1 / S \ 339 r_a &= r_"CE" || R_C 340 $) 341 ], [ 342 #text(size: 9pt, $ 343 A &= 1 \ 344 r_e &= r_"BE" + beta R_E \ 345 r_a &= 1 / S 346 $) 347 ]) 348 349 ] 350 351 == Übergangsfunktion und 3dB-Grenzfrequenz 352 353 #grid(columns: 3*(1fr,), [ 354 #scale(80%, reflow: true)[ 355 #zap.canvas({ 356 import zap: * 357 // acvsource("UE", (0,0), (1,0)) 358 vsource("UE", (0,0), (0,-2), u: (label:$u_e$, position: bottom)) 359 resistor("R1", (0,0), (3,0), label: (content: $R 1 = 250 Omega$)) 360 wire((3,0), (5,0)) 361 resistor("RL", (3,0), (3,-2), label: (content: $R_L = 500 Omega$, anchor: "south"), distance: 0pt) 362 inductor("L", (5,0), (5,-2), u: (label: $u_L$, position: bottom), i: $i_L$, label: (content: $L = 850 "pH"$)) 363 wire((0,-2), (5,-2)) 364 }) 365 ] 366 $ 367 H(omega) =& u_l / u_e = (j omega L || R_2) / (R_1 + (j omega L || R_2)) \ 368 =& (j omega L dot R_2) / (R_1 dot R_2 + j omega L dot (R_1 + R_2)) \ 369 =& R_2 / (R_1 + R_2) (j omega K) / (1+j omega K) 370 $ 371 ], [ 372 #v(.3cm) 373 $ 374 " mit " K &= L dot (R_1 + R_2) / (R_1 dot R_2) = 5,1 "ps" \ 375 abs(H(omega)) =& R_2 / (R_1 + R_2) (omega K) / sqrt(1 + (omega K)^2) \ 376 &=> f_"3dB" = omega_"3dB" / (2 pi) = 1 / ( 2 pi K) \ 377 & = 1 / ( 2 pi * 5,1 "ps") = 31,2 "GHz" \ 378 H(omega -> oo) &= R_2 / (R_1 + R_2) = 2 / 3 | 20 log(x) \ 379 &= -3,51 "dB" 380 $ 381 ], [ 382 #zap.canvas({ 383 import zap.draw: * 384 plot.plot( 385 x-tick-step: none, y-tick-step: none, 386 size: (4,3), 387 x-label: $f " in Hz"$, 388 y-label: $abs(H) " in dB"$, 389 legend: (-1,-1), 390 x-min: 100, 391 x-max: 150000, 392 y-min: -40, 393 x-mode: "log", 394 x-base: 10, 395 y-max: 0, 396 x-ticks: ((100,$100 M$), (1000,$1 G$), (10000,$10 G$), (100000,$100 G$)), 397 y-ticks: (-40, -20, 0), { 398 plot.add-hline((-3.52), label: $H(omega -> oo) = -3,51 "dB"$) 399 plot.add-vline((31200), label: $f_"3dB" = 31,2 "GHz"$) 400 plot.add(((500, -40), (31200, -3.52), (150000,-3.52))) 401 plot.annotate({ 402 line((1500,-30),(6000,-30),(6000,-18)) 403 content((14000,-24), $20 "dB"/"Dek"$) 404 }) 405 }) 406 }) 407 ]) 408 409 #section[ 410 #grid(columns: (2fr, 3fr), [ 411 == Feldeffekttransistor (FET) #box[#zap.canvas({ 412 import zap: * 413 import zap.draw: * 414 scale(.5) 415 pmos("Q", (0,0)) 416 content("Q.gl", "G", anchor: "east", padding: (right: 5pt)) 417 content("Q.d", "D", anchor: "west", padding: (left: 5pt)) 418 content("Q.s", "S", anchor: "west", padding: (left: 5pt)) 419 })] 420 421 $ 422 r_"DS" = (partial U_"DS") / (partial I_D) = (abs(U_A) + U_"DS") / I_D \ 423 S = (partial I_D) / (partial U_"DS") = beta (U_"GS" - U_"th") \ 424 beta = mu dot C'_"ox" dot omega / l 425 $ 426 ], [ 427 #grid(columns: 2 * (1fr,), align: center, [ 428 #scale(60%, reflow: true)[#table(columns: (auto, 1fr, 1fr), [], [n-Kanal], [p-Kanal], 429 rotate(-90deg, reflow: true)[normal\ leitend], 430 zap.canvas({ zap.nmos("", (), mode: "depletion") }), 431 zap.canvas({ zap.pmos("", (), mode: "depletion") }), 432 rotate(-90deg, reflow: true)[normal\ sperrend], 433 zap.canvas({ zap.nmos("", ()) }), 434 zap.canvas({ zap.pmos("", ()) }), 435 )] 436 ], [ 437 #figure(scale(65%, reflow: true)[ 438 #zap.canvas({ 439 import zap: * 440 import zap.cetz.draw: * 441 scale(.9) 442 out("G", (0,0)) 443 content("G", "G", anchor: "east", padding: 5pt) 444 out("S", (0,-2)) 445 content("S", "S", anchor: "east", padding: 5pt) 446 out("D", (6,0)) 447 content("D", "D", anchor: "west", padding: 5pt) 448 out("DA", (6,-2)) 449 node("", (4,0)) 450 node("", (2,-2)) 451 node("", (4,-2)) 452 isource("Su", (2,0), (2,-2), i: (label: [#h(.6cm)$S dot u_"GS"$], position: end + top )) 453 resistor("", (4,0), (4,-2), label: (content: $r_"DS"$, anchor: "south", distance: 3pt)) 454 wire((2,0), "D") 455 wire("S", "DA") 456 line(("G",.2,"S"), ("S", .2, "G"), name: "line", mark: (end: (symbol: ">", fill: black))) 457 content("line", anchor: "east", padding: .2, $u_"GS"$) 458 line(("D",.2,"DA"), ("DA", .2, "D"), name: "line", mark: (end: (symbol: ">", fill: black))) 459 content("line", anchor: "east", padding: .2, $u_"DS"$) 460 }) 461 ], caption: [ Kleinsignalersatzschaltbild ]) 462 ]) 463 464 $ 465 I_D &= cases( 466 0 & U_"GS" <= U_"th", 467 beta dot ((U_"GS" - U_"th") - U_"th"^2 / 2) dot (1 + U_"DS" / U_A) & "linearer Bereich", 468 beta / 2 dot (U_"GS" - U_"th")^2 dot (1 + U_"DS" / U_A) & "Sättigungsbereich" 469 ) 470 $ 471 ]) 472 473 474 #table(columns: 3 * (1fr,), align: center, 475 table.header([Source-Schaltung], [Gate-Schaltung], [Drain-Schaltung]) ,[ 476 #zap.canvas({ 477 import zap: * 478 import zap.cetz.draw: * 479 480 scale(.8) 481 out("e", (0,0)) 482 out("a", (2.5,1)) 483 out("eg", (0,-1)) 484 out("ag", (2.5,-1)) 485 486 scale(.5) 487 nmos("n1", (3,0.5)) 488 wire("e", "n1.g") 489 wire("n1.d", ((), "|-", "a"), "a") 490 wire("n1.s", ((), "|-", "ag"), "ag") 491 wire("n1.s", ((), "|-", "eg"), "eg") 492 493 line(("e",.2,"eg"), ("eg", .2, "e"), name: "line", mark: (end: (symbol: ">", fill: black))) 494 content("line", anchor: "east", padding: .2, $U_e$) 495 496 line(("a",.2,"ag"), ("ag", .2, "a"), name: "line", mark: (end: (symbol: ">", fill: black))) 497 content("line", anchor: "east", padding: .2, $U_a$) 498 }) 499 ], 500 [ 501 #zap.canvas({ 502 import zap: * 503 import zap.cetz.draw: * 504 scale(.8) 505 out("e", (-1.25,0)) 506 out("a", (1.5,1)) 507 out("eg", (-1.25,-1)) 508 out("ag", (1.5,-1)) 509 510 rotate(x:180deg) 511 rotate(z:-90deg) 512 scale(.5) 513 nmos("n1", (0,0)) 514 set-transform(none) 515 516 wire("e", "n1.s") 517 wire("n1.d", ((), "|-", "a"), "a") 518 wire("n1.g", ((), "|-", "ag"), "ag") 519 wire("n1.g", ((), "|-", "eg"), "eg") 520 521 line(("e",.2,"eg"), ("eg", .2, "e"), name: "line", mark: (end: (symbol: ">", fill: black))) 522 content("line", anchor: "east", padding: .2, $U_e$) 523 524 line(("a",.2,"ag"), ("ag", .2, "a"), name: "line", mark: (end: (symbol: ">", fill: black))) 525 content("line", anchor: "east", padding: .2, $U_a$) 526 }) 527 ], [ 528 #zap.canvas({ 529 import zap: * 530 import zap.cetz.draw: * 531 scale(.8) 532 out("e", (0,0)) 533 out("a", (2.5,1)) 534 out("eg", (0,-1)) 535 out("ag", (2.5,-1)) 536 537 rotate(x: 180deg) 538 scale(.5) 539 nmos("n1", (3,.5)) 540 wire("e", "n1.g") 541 wire("n1.s", ((), "|-", "a"), "a") 542 wire("n1.d", ((), "|-", "ag"), "ag") 543 wire("n1.d", ((), "|-", "eg"), "eg") 544 545 line(("e",.2,"eg"), ("eg", .2, "e"), name: "line", mark: (end: (symbol: ">", fill: black))) 546 content("line", anchor: "east", padding: .2, $U_e$) 547 548 line(("a",.2,"ag"), ("ag", .2, "a"), name: "line", mark: (end: (symbol: ">", fill: black))) 549 content("line", anchor: "east", padding: .2, $U_a$) 550 }) 551 ], 552 [ 553 #text(size: 9pt, $ 554 r_e &= oo \ 555 r_a &= R_D || r_"DS" \ 556 A &= -S dot (R_D || r_"DS") 557 $) 558 559 ] ,[ 560 #text(size: 9pt, $ 561 r_e &= 1/S \ 562 r_a &= R_D || r_"DS" \ 563 A &= S dot (R_D || r_"DS") 564 $) 565 ], [ 566 #text(size: 9pt, 567 $ 568 r_e &= oo \ 569 r_a &= 1 / S || R_S \ 570 A &= (S dot R_S) / (1 + S dot R_S) 571 $ 572 ) 573 ]) 574 ] 575 576 == Arbeitspunkt und Lastgerade 577 578 #grid(columns: 3*(1fr,),[ 579 #scale(80%, reflow: true, [ 580 #zap.canvas({ 581 import zap: * 582 import zap.draw: * 583 584 out("UEE", (0,0)) 585 arrow((0,0), (0,-2), $u_e$) 586 ground("UEA", (0,-2)) 587 out("", (0,-2)) 588 capacitor("", (0,0), (2,0)) 589 resistor("RG2", (2,0), (2,-2), label: (content: $R_"G2"$, anchor: "south")) 590 ground("", (2,-2)) 591 resistor("RG1", (2,3),(2,0), i: (label: $i_a$, position: bottom), label: (content: $R_"G1"$, anchor: "south")) 592 wire((2,0), (3,0)) 593 nmos("Q", (4,0.5)) 594 wire("Q.s", (rel: (0,-2))) 595 ground("", (4,-2)) 596 resistor("RD", (4,3), (4,1), i: $i_D$, label: (content: $R_D$)) 597 wire((2,3), (6,3)) 598 out("Ub", (6,3)) 599 content((6,3), anchor: "west", padding: 5pt, $U_b = 2 V$) 600 capacitor("", (4,1), (6,1)) 601 out("UAE", (6,1)) 602 arrow((6,1),(6,-2), $U_a$) 603 ground("", (6,-2)) 604 out("UAA", (6,-2)) 605 }) 606 ]) 607 ],[ 608 $ 609 U_b = U_"DS1" + R_D dot I_D \ 610 <=> I_D = (U_b - U_"DS1") / R_D 611 $ 612 $ 613 P 1: I_D (U_"DS1" = 0) = U_D / R_D = 16"mA" \ 614 P 2: I_D (U_"DS1" = U_b = 2 V) = 0 615 $ 616 617 ],[ 618 #v(-1cm) 619 #zap.canvas({ 620 import zap.draw: * 621 plot.plot(name: "plot", size: (5,5), 622 x-label: $U_"DS1" "in V"$, 623 y-label: $I_D "in mA"$, 624 y-tick-step: 4, 625 x-tick-step: .5, 626 y-min: 0, y-max: 16, 627 x-min: 0, x-max: 2.1, 628 { 629 plot.add-anchor("AP", (1,8)) 630 plot.add-anchor("P1", (2,0)) 631 plot.add(((0,16), (2,0))) 632 plot.add(domain: (0.00001,2.1), u => 2 * calc.log(u) + 2) 633 plot.add(domain: (0.00001,2.1), u => 1.5 * calc.log(u) + 5) 634 plot.add(domain: (0.00001,2.1), u => 1 * calc.log(u) + 8) 635 plot.add(domain: (0.00001,2.1), u => .5 * calc.log(u) + 11) 636 plot.add(domain: (0.00001,2.1), u => .2 * calc.log(u) + 14) 637 plot.annotate({ 638 content((2.7,3), anchor: "east", padding: 0, $U_"GS1" = 0,8 V$) 639 content((2.7,6), anchor: "east", padding: 0, $U_"GS1" = 0,9 V$) 640 content((2.7,9), anchor: "east", padding: 0, $U_"GS1" = 1,0 V$) 641 content((2.7,12), anchor: "east", padding: 0, $U_"GS1" = 1,1 V$) 642 content((2.7,15), anchor: "east", padding: 0, $U_"GS1" = 1,2 V$) 643 }) 644 plot.annotate({ 645 content((1,8), $times$) 646 content((1,8), anchor: "north", padding: 20pt, [AP]) 647 content((2,0), $times$) 648 content((2,0), anchor: "north", padding: 20pt, [P1]) 649 content((0,16), $times$) 650 content((0,16), anchor: "north", padding: 20pt, [P2]) 651 }) 652 }) 653 }) 654 ]) 655 #v(-1.3cm) 656 $ 657 "Einstellen sodass " U_"GS1" = 1 V": " & R_"G1" + R_"G2" = U_D / I_D =^! (2 V) / (8"mA") = 25 k Omega \ 658 &R_"G1" / (R_"G1" + R_"G2") =^! U_"GS1" = 1 V \ 659 &R_"G2" / (R_"G1" + R_"G2") dot U_D =^! U_D - U_"GS1" = 1 V => R_"G1" = R_"G2" = 660 &12,5 k Omega 661 $ 662 663 NOT #box(align(horizon, stack(dir:ltr, rect[1],circle(radius: 3pt)))) 664 AND #box(rect[&]) 665 OR #box(rect[$>=1$]) 666