# MICROELECTRONIC CIRCUIT DESIGN Third Edition

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1 MICROELECTRONIC CIRCUIT DESIGN Third Edition Richard C. Jaeger and Travis N. Blalock Answers to Selected Problems Updated 1/25/08 Chapter years, 5.06 years years, 6.46 years MW, 511 ka mv, 5.12 V, V mv/bit, A, cos (1000t) A 1.19 v DS = [5 + 2 sin (2500t) + 4 sin (1000t)] V V, 2.31 V, 70.0 µa, 210 µa µa, 125 µa, 10.3 V Ω, v s kω, 1.33 x 10-3 v s MΩ, 2.50 x 10 8 i s / 45, 100 / sin 750πt mv, 11.0 sin 750πt µa R 2 /R V, V 1.41 Band-pass amplifier sin (2000πt) cos (8000 πt) V V 1.47 [2970Ω, 3030Ω], [2850Ω, 3150Ω], [2700Ω, 3300Ω] Ω, 800 ppm/ o C , 0.995, 6.16; 3.295, , 6.155

2 Chapter For Ge: 35.9/cm3, /cm 3, /cm x10 6 cm s, x10 5 cm s, 2.80x10 4 A cm 2, 1.00x10 10 A cm K ΜΑ/cm x 10 7 A/cm 2, 4.00 A K 2.19 Donor, acceptor V/cm x 10 3 atoms x /cm 3, 2.50 x 10 5 /cm x /cm 3, 16.7/cm 3, 5 x 10 9 /cm 3, 8.80 x /cm x /cm 3, 333/cm /cm 3, /cm 3, 375 cm 2 /s, 100 cm 2 /s, p-type, 62.4 mω-cm /cm 3, 10 4 /cm 3, 800 cm 2 /s, 1230 cm 2 /s, n-type, Ω-cm x /cm Yes add equal amounts of donor and acceptor impurities. Then n = n i = p, but the mobilities are reduced. See Prob /Ω-cm, 3.1 x /cm 3, K: 6.64 mv, 150K: 12.9 mv, 300K: 25.8 mv, 400K: 34.5 mv x10 5 exp (-5000 x/cm) A/cm 2 ; 12.0 ma 2.48 The width in the figure should be 2 µm: For x = 0, -535 A/cm µm 2

3 Chapter µm, µm, 3.39 x 10-3 µm, V, 5.24 x 10 5 V/cm /cm 3, 10 2 /cm 3, /cm 3, 10 2 /cm 3, V, µm V, 1.05 µm A/cm x /cm K K , 3.17 pa V; V; 0 A; 9.43 x A, x A V; 1.38 V V; V V; V mv/k V, µm, 3.89 µm, 12.0 µm V V, 0 Ω nf/cm 2 ; 188 pf ff, 10 fc; 100 pf, 0.5 pc MHz; 15.7 MHz V, V V, V 3.56 (a) Load line: (450 µa, V); SPICE: (443 µa, V) (b) Load line: (-667 µa, -4 V); (c) Load line: (0 µa, -3 V); 3.59 (0.600 ma, -4 V), (0.950 ma, 0.5 V), (-2.00 ma, -4 V) 3.65 Load line: (50 µa, 0.5 V); Mathematical model: (49.9 µa, V); Ideal diode model: (100 µa, 0 V); CVD model: (40.0µA, 0.6 V) 3.69 (a) ma, 3 V; ma, -5 V; 0 A, -5 V; 0 A, 7 V 3.71 (a) (409 µa, 0 V), (270 µa, 0 V); (c) (0 A V), (230 µa, 0 V) 3.73 (a) (0.990 ma, 0 V) (0 ma, V) (1.09 ma, 0) (d) (0 A, V) (0 A, V) (1.16 ma, V) 3.76 (1.50 ma, 0 V) (0 A, V) (1.00 ma, 0) 3.78 (I Z, V Z ) = (792 µa, 4.00 V) mw W, 4.50 W V V; 1.05 F; 17.8 V; 3530 A; 841 A (ΔT = ms) 3

4 V, F, 17.8 V, 3540 A, 839 A F; 8.6 V; 3.04 V; 1920 A; 9280 A V; 1.35 F; 42.4 V; A; 1650 A F, 8.6 V, 3.04 V, 962 A, 4910 A µf; 3000 V; 2120 V; 44.4 A; 314 A ma, 4.4 ma, 3.6 ma, 5.59 ns (0.969 A, V); W; 1 A, V µm, µm; far infrared, near infrared 4

5 Chapter x 10-9 F/cm µa/v 2, 86.3 µa/v 2, 173 µa/v 2, 345 µa/v (a) 4.00 ma/v 2 (b) 4.00 ma/v 2, 8.00 ma/v µa; 880 µa Ω; 35.7 Ω µa/v 2 ; 1.5 V; enhancement mode; 1.25/ A, 0 A, 1.88 ma, 7.50 ma, 3.75 ma/v (a) 460 µa, triode region; 1.56 ma, saturation region; 0 A, cutoff 4.23 saturation; cutoff; saturation; triode; triode; saturation ms, 13.0 ms ma; 2.25 ma ma, 18.1 ma, 10.8 ma 4.37 Triode region ma; 1.29 ma µa; 199 µa; 99.5 µa; 99.5 µa µa; 184 µa V µa; 72.0 µa; 4.41 µa; 32.8 µa /1; 2330/ Ω; 235 Ω A/V µa λ x 18λ; 7.9% x 10-8 F/cm 2 ; 17.3 ff 4.81 (350 µa, 1.7 V); triode region 4.84 (390 µa, 4.1 V); saturation region 4.86 (778 µa, 9.20 V) 4.94 (134 µa, 4.64 V) ; (116 µa, 5.36 V) kω, 470 kω, 12 kω, 12 kω, 5/ (124 µa, 2.36 V) (a) (33.3 µa, 1.01 V) (23.5 µa, V) (73.1 µa, 9.37 V) ma; 16.0 ma; 1.61 ma ma; 45.2 ma; 13.0 ma / (153 µa, V) ; (195 µa, V) 5

6 V, 10.8 ma, 43.2 ma ma; 27.1 ma; 10.4 ma (59.8 µa, V), 130 kω (55.3 µa, V), 164 kω kω (138 µa, -5 V) One possible design: 220 kω, 200 kω, 5.1 kω, 4.7 kω (260 µa, V) (36.1 µa, 80.6 mv); (32.4 µa, V); (28.8 µa, V) ff, 17.3 ff GHz, 2.55 GHz; 637 GHz, 255 GHz µa, 86.3 µa A, A 6

7 Chapter , 0.667, 3.00, 0.909, 49.0, , , fa; 1.01 fa, V µa, µa, +150 µa, V fa ma; 5.34 ma µa, -100 µa, +75 µa, 65.7, 1/3, 0, V µa, µa, +35 µa, V µa , 0.333, 2.02 fa, 6.00 fa , 87.5, mv/dec, 49.5 mv/dec, 59.4 mv/dec, 69.3 mv/dec V, 50 V, 6 V ma; 388 µa; V 5.40 Cutoff 5.42 saturation, forward-active region, reverse-active region, cutoff aa, fa, 0.25 fa 5.47 I C = 16.3 pa, I E = 17.1 pa, I B = pa, forward-active region; although I C, I E, I B are all very small, the Transport model still yields I C β F I B , 6.81 fa , 1.73 fa µa, µa, 54.6 µa MHz , 24.2 aa µa, 26.5 µa, µa mv, mv A, 10.1 A V, V, 27.5 mv µa ff; 0.4 pf; 40 pf MHz, 3.75 MHz µm , 43.1 V , 37.6 V µa, 4.52 µa, 95.5 µa, V, (c) 38.7 ms pf at 1 ma 7

8 5.82 (80.9 µa, 3.80 V) ; (405 µa, 3.80 V) 5.86 (42.2 µa, 4.39 V) 5.92 (7.5 ma, 4.3 V) 5.94 (5.0 ma, 1.3 V) kω, 620 kω; 24.2 µa, V V Ω µa, 867 µa, 3.90 V, 5.83 V percent; 70 percent The minimum I C case, (109 µa, 7.36 V). For the maximum I C case, the transistor is saturated. 8

9 Chapter µw/gate, 4 µa/gate V, 0 V, 0 W, 62.5 µw; 3.3 V, 0 V, 0 V, 109 µw 6.5 V OL = 0 V, V OH = 3.3 V, V REF = 1.1 V; Z = A V, 0 V, 2 V, 1 V, V, 0 V, 2 V, 5 V, 3 V, 2 V V, 0 V, 3.0 V, 0.25 V, 1.8 V, 1.5 V, 1.2 V, 1.25 V V, 1.35 V ns µw/gate, 0.40 µa/gate, 1 fj RC; 2.20 RC V, 1.36 V, 1 ns, 1 ns, 9.5 ns, 9.5 ns, 4 ns, 4 ns, 4 ns 6.24 Z = Z = ; A pf µw/gate, µa/gate kω, 1/ (b) 2.5 V, V, 30.8 µw 6.40 (a) V, 1.49 V kω; 1.52/1; 1.49 V, V Ω; 1000 Ω; a resistive channel exists connecting the source and drain; 20/ V V, 0.06 V /1, 6.67/ V 6.61 ratioed logic so V H = 1.55 V, V L = 0.20 V; P = 0.24 mw V /1, 1.36/ /1, 1/ /1, V, V 6.77 (a) 88.8 µa, V (b) V, V /1, 1/1.80, V, V /1, 1.81/ /1, 1.11/1, V, 6.43/1, 6.74/1, 7.09/1 9

10 6.90 Y = ( A + B)(C + D)(E + F), 6.66/1, 1.81/ Y = ACE + ACDF + BF + BDE, 3.33/1, 26.6/1, 17.8/ /1.80, 3.33/ Y = (C + E)[ A(B + D) + G] + F ; 3.62/1, 13.3/1, 4.44/1, 6.67/ /1, 6.43/1, 7.09/1, 6.74/ /1, 6.43/1, 6.74/ /1, 26.6/1, 8.88/1, 13.3/ (a) 5.43/1, 9.99/1, 20.0/ I DS = 2I DS, P D = 2P D mw, 139 mw ns ns, a potentially stable state exists with no oscillation ns, 4.39 ns, 5.86 ns ns, 5.94 ns, 15.3 ns ns, 10.2 ns, 9.00 ns /1, 27.8/1, 12.8 ns, ns (a) 1/1.68 (d) 1/5.89 (f) 1/ V, V /3.30, 1.75/ V, 1.07 V Y = A + B 10

11 Chapter µa/v 2 ; 6.1 µa/v pa; 450 pa; 450 pa V, 0 V 7.8 cutoff, triode, triode, cutoff, saturation, saturation V, 42.3 µa; V, 25.4 µa V, 16.0 µa; V, 96.2 µa 7.15 (b) 2.5 V, V V, 2.77 ma V, V ns, 2.36 ns, ns ns, 4.74 ns, 2.77 ns /1, 5.26/ /1, 15.0/ ns, 2.3 ns, 1.1 ns, 0.9 ns, C = 138 ff µw/gate, 45.9 ff, 80.0 ff W; 1.74 W µa; 25.0 µa pj, 283 MHz, 616 µw 7.44 αδt, α 2 P, α 3 PDP /1, 20/1; 6/1, 60/ / ns, 3.95 ns, 11.8 ns 7.60 (a) 5 transistors (b) The CMOS design requires 47% less area Y = ( A + B)(C + D)E = ACE + ADE + BDE + BCE, 18/1, 30/1, 15/ Y = A + B ( )( C + D) ( E + F) = AB + CD + EF, 4/1, 15/ /1, 4/1, 6/1, 20/ (a) Path through NMOS A-D-E (d) Paths through PMOS A-C and B-E /1, 6/1, 10/ /1, 24/1, 40/ ns, 2.21 ns ns, 23.7 ns ns, 3.7 ns 7.91 V DD 2 3 V DD 1 2 V DD; R 7.97 N = 8, A = 22.6 A o 2V IH V DD V IH = 2V IH NM H, C C 2 11

12 Ω, 658 Ω /1, 96.2/ V, 2.5 V Latchup does not occur. 12

13 Chapter ,435,456 bits, 1,073,741,824 bits; 2048 blocks pa/cell, 233 fa/cell V, µv V, 0 V, 3.59 V level is discharged by junction leakage current V, 1.43 V mv; 2.48 V V, 1.90; Junction leakage will destroy the 1 level V, 1.60 V; 1.83 V mw µa, 1.36 W 8.23 For C BL = 500 ff, V V, (The sense amplifier provides a gain of 10.5.) V, 1.43 V, 3.00 V , V DD 2 3 V DD 1 2 V DD; R 8.37 W 1 = , W 3 = /1 2V IH V DD V IH = 2V IH NM H ; C C 2 13

14 Chapter V, V V, V, 0 V V, 0.4 V; 3.39 kω; Saturation, cutoff; Cutoff, saturation V, 1.70 V, 1.20 V, 1.00 V V, 1.50 V, 1.10 V, 2.67 kω; V, V, V Ω, V, V, V kω, 16.0 kω, 93.6 kω, 336 kω V, V, V, V, V, 1.10 mw V V µa, V 9.24 Standard values: 11 kω, 150 kω, 136 kω V, V, 336 Ω ma ma Ω, 60.0 ma 9.40 (c) 0 V, -0.7 V, 3.93 ma (d) 3.7 V, ma (e) 2920 Ω 9.43 Y = A + B ns V; 3.59 pj V, V, 5.67 mw; Y = A + B + C, 5 vs kω, 5.40 kω, 31.6 kω, 113 kω kω, 1 kω, 1.30 mw kω, 4.84 kω, 60.1 kω pa, 74.5 fa ; 0.976; 5; V V, V mv, mv V, 0.15 V, 0.66 V, 0.80 V, mv, 2.47 ma kω, 22.4 kω V, 0.15 V, 0, 1.06 ma, 31; 1.06 ma vs ma, 0 ma vs. 0.2 ma ma, 34.9 ma 14

15 9.88 (I B, I C ): (a) (135 µa, 169µA); (515µA, 0); (169 µa, 506 µa); (0, 0) (b) all 0 except I B1 = I E1 = 203 µa V, 0.15 V; 62.5 µa, 650 µa; Y = ABC ; 1.9 V; 0.15 V; 0, 408 µa V, 0.25 V; 0, 1.00 ma; V, 191 µa, 59 µa, 1.18 ma ma, 0, 4.28 ma, 0, 129 µa, 1.00 ma; 0, 0, 0, 0, 1.23 ma, Y = A + B + C; 0 V, 1.0 V; 0.90 V Y = A + B + C; 0 V, 0.80 V; 0.40 V ma, 26.9 µa fj; 10 fj ns; 0.5 mw 15

16 Chapter (a) 41.6 db, 35.6 db, 94.0 db, 100 db, db 10.3 Using MATLAB: t = linspace(0,.004); vs = sin(1000*pi*t)+0.333*sin(3000*pi*t)+0.200*sin(5000*pi*t); vo= 2*sin(1000*pi*t+pi/6)+sin(3000*pi*t+pi/6)+sin(5000*pi*t+pi/6); plot(t,vs,t,vo)par 500 Hz: 1 0, 1500 Hz: , 2500 Hz: ; 2 30, 1 30, , 3 30, 5 30 yes db, 111 db, 73.2 db db, 93.0 db, 59.0 db; Vo = 17.9 V, recommend ± 20-V supplies (20 db), 0.1 V; 0, 0 V v O = [8 4 sin (1000t)] volts; there are only two components; dc: 8 V, 159 Hz: 4 V db, 11.2% x10-8 S, x10-3, 1.00, 99.0 Ω ms, , -1710, 1.78 MΩ ms, 1.00, 2001, 20.0 kω db, 150 db, 102 db; 11.7 mv; 31.3 mw mv, 1.00 W ,, 125 mw, db, 26.5 khz kω, µf db, 181 Hz db, 10 khz, 10 Hz, 9.99 khz, band-pass amplifier db,, 100 Hz,, high-pass amplifier db, 100 khz, 28.3 Hz, 100 khz sin (2πt ) V, 1.34 sin (100πt ) V, 3.00 sin (10 4 πt ) V sin (3.18x10 5 πt ) V, 5.00 sin (10 5 πt ) V, 5.00 sin (4x10 5 πt 179 )V x10 8 π s π - 2x108 π s π db, 16.1 khz, -40 db/decade db, 12.8 khz, -60 db/decade sin (1000πt + 10 ) sin (3000πt + 30 ) sin (5000πt + 50 ) V; Using MATLAB: t = linspace(0,.004); A=10^(10/20); vs = sin(1000*pi*t)+0.333*sin(3000*pi*t)+0.200*sin(5000*pi*t); vo = A*sin(1000*pi*t+pi/18)+3.33*sin(3000*pi*t+3*pi/18)+2.00*sin(5000*pi*t+5*pi/18); plot(t, A*vs, t, vo) 16

17 Chapter db, 120 db, 89.9 db; 5.05 mv 11.3 R id 4.95 MΩ mv, 140 db 11.7 (a) 46.8, 4.7 kω, 0, 33.4 db (d) ( sin 2500πt) V kω, 1.00 MΩ kω,, A v = -20.1, R in = 30.1 kω ,, 0, 83.9 db (d) ( sin 3250πt) V kω, 1.05 kω, A v = (0.510 sin 3770t 1.02 sin 10000t) V, sin 4000πt V; sin 4000πt V; 0 to V in mV steps /1, 50/ , 110 kω, 10 kω,, ( cos 8300πt) V, ( cos 8300πt) V V, 3.1 V, 2.82 V, 2.82 V, V; 3.80 µa; 3.80 µa, 2.80 µa , ( sin 4000πt) V (a) 10 kω, 100 kω, 79.6 pf (b) 10 kω, 100 kω, 82 pf, 19.4 khz T(s) = -src , 20.0 kω, 0; +9.00, 75.0 kω, 0; 0, 160 kω, , 10 kω, A, 2.83 V, > 10 W (choose 15 W) A; V; V; 7.03 W (choose 10 W), 7.27 W v 1 v 2 R, ; If the voltage gain were finite with value A, R out = R( 1 + A) V, 3.99 V, 1.99 V, 1.99 V, 3.99 V, 200 µa; 5 MΩ! kω, kω resistors, 1024: V, V, V, V V V X V µv, , ns A and B taken together, B and C taken together ,, , 3.9 kω, kω, 8.62 kω , 47 kω, 0, V, 0V, V, 0 V, V, 0 V, V, 0V (ground node) , 2434, 3094, 1 MΩ, 1.02 MΩ, 980 kω 17

18 11.73 (b) µf, µf, 1.13 kω V O V S = K s 2 R 1 R 2 C 1 C 2 + s R 1 C 1 1 K pf, 270 pf, 23.2 kω (a) 51.2 khz, 7.07, 7.23 khz (a) 1 rad/s, 4.65, rad/s khz, 4.09, 1.34 khz kω, 100 kω, 20 kω, µf V Hz [ ( ) + C 2 ( R 1 + R 2 )] +1 S K Q = K 3 K V O = -V 1 V 2 /10 4 I S V, 2.38 V, 0.24 V V, V, V khz f = 0. V O = 0 is a stable state. The circuit does not oscillate , V, 69.0 mv kω, 30 kω, 51 kω, 150 pf 18

19 Chapter (a) 13.49, 9.11x10-3, % 12.3 (a) , 2.76x10-3, % db µa, 100 µa, pa (a) 13.5, 371 MΩ, 169 mω (a) -8.39, 5.60 kω, 37.5 mω MΩ, 785 MΩ, 3.75 mω If the gain specification is met, the input and output specifications cannot be met % V, 1.00 V, 13.1% db db V, 4.99 V, 5.01 V, V, V, V, V, µa, -375 µa, +175 µa V, -26 mv, 90.9 kω , mv The nearest 5% values are 1 MΩ and 10 kω V, 0 V; V, V V, 0 V; 15 V, V Ω and 22 kω represent the smallest acceptable resistor pair Ω , 24.0 kω, 6.00 mω , 3.57 GΩ, 14.0 mω A v ( s) = V O = 1+ R 2 V S R 1 SC( R 1 R 2 ) +1 SCR , -40.3, -27.0; 4.83 khz, 3.65 khz, 10.7 khz stages, 270 pf, 15.0 kω, 1.5 kω Z out = R o 1+ A o β ( ) s ω B s ω B 1+ A o β ( ) R o 1+ A o β ( ) 1+ s ω B 1+ s βω T 19

20 s R Z in = R 1 + R 2 id ω B ( 1+ A o ) s R 1+ id + R 2 ω B ( 1+ A o ) R R id A o (a) A v ( s) = V s O s V S ( ) ( ) = 1 src ( ) ω T (b) A v ( s) = RC s 2 + s ω B + ω T ω B s + ω T RC RC , 143 khz; -8000, 72.9 khz Two stages ω T RC ( ) s + 1 A o RC (a) In a simulation of 5000 cases, 33.5% of the amplifiers failed to meet one of the specifications. (b) 1.5% tolerance , 7.53, 6.35; 145 khz, 157 khz, 133 khz V/µs V/µs Ω, 7.96 pf, 4x10 6, R o not specified , 47.0 kω, 40.0 mω, 79.9 khz; 50.0 mv, 5.00 µv, -500 mv, µv, V, V, V, V, V, 0 V , 3070, 2460; 1 MΩ, 1.02 MΩ, 980 kω; 21.0 mω, 21.8 mω, 20.2 kω; 357 khz, 371 khz, 344 khz , 613 MΩ, 98.0 mω, 29.6 khz; 0 V, 10.0 mv, 49.0 mv, 389 µv, V, V, V, V, V, 0 V 20

21 Chapter sin 2000πt V; sin 2000πt V; sin 2000πt V; 2.82 ma 13.3 (a) C 1 is a coupling capacitor that couples the ac component of v I into the amplifier. C 2 is a coupling capacitor that couples the ac component of the signal at the collector to the output v O. C 3 is a bypass capacitor. (b) The signal voltage at the top of resistor R 4 will be zero (a) C 1 is a coupling capacitor that couples the ac component of v I into the amplifier. C 2 is a bypass capacitor. C 3 is a coupling capacitor that couples the ac component of the signal at the collector to output v O. (b) The signal voltage at the emitter will be ve = (a) C 1 is a coupling capacitor that couples the ac component of v I into the amplifier. C 2 is a coupling capacitor that couples the ac component of the signal at the drain to output v O (a) C 1 is a coupling capacitor that couples the ac component of v I into the amplifier. C 2 is a bypass capacitor. C 3 is a coupling capacitor that couples the ac component of the signal at the drain to the output v O. (b) The signal voltage at the top of R 4 will be zero (22.5 µa, 6.71 V) (1.78 ma, 6.08 V) (98.4 µa, 4.96 V) (82.2 µa, 6.04 V) (307 µa, 3.88 V) (338 µa, 5.41 V) (1.25 ma, 10.6 V) Thévenin equivalent source resistance, gate-bias voltage divider, gate-bias voltage divider, sourcebias resistor sets source current, drain-bias resistor sets drain-source voltage, load resistor Ω, 2.5 TΩ, V Ω for T = 200K Errors: +10.7%, -9.37%; +23.0%, % (c) 1.25 µa (188 µa, V CE 0.7 V ), 7.50 ms, 533 kω (b) +16.7%, -13.6% , 120; 95, [ 95.0, 94.1] Yes, using I C R C = (V CC + V CE )/ ma; 30.7 V V No, there will be significant distortion (b)

22 /1, V A %, 20% (156 µa, 9 V) Virtually any desired Q-point = 133,000i P + v PK ; (1.4 ma, 215 V); 1.6 ms, 55.6 kω, 89.0; BJT FET µa, , 200, 8.00 ms, ms db V (125 µa, 7.5 V) V, 28 V kω, 94.4 kω kω, 1.46 MΩ kω, 40.1 kω MΩ, 45.8 kω, independent of K n MΩ, 3.53 kω v i, 3.62 kω v i, 508 kω (b) 1 MΩ, 0, 7.45 MΩ, 3.53 MΩ , 1.42 kω, 982 Ω , 142 kω, 98.2 kω µw, mw, mw, mw, 2.43 mw mw, mw, mw, 16.4 µw, 44.3 µw, 1.29 mw V CC / V, 13.6 V (V CC ) 2 /8R L, (V CC ) 2 /2R L, 25% V V V V V, 8.5 V 22

23 Chapter (a) C-C or emitter-follower (b) not useful, signal is being injected into the drain (c) C-E (h) C-B (k) C-G (o) C-D or source-follower , 2 MΩ, 26.5 kω, -3770; 8.03, 2 MΩ, 10.0 kω, , 9.58 kω, 596 kω, -27.1; 17.0, 11.6 kω, 1060 kω, (a) 6.91 (e) kω, 33 kω , -7.10, 19.0 kω, 39 kω, 5.13 mv , -4.23, 3.86 kω, 8.20 kω, 6.30 mv, , 10.1, 368 kω, 75 kω, 160 mv, , -952, 10 MΩ, 1,80 kω, 1.00 V , -6.41, 1.55 kω, 95.1 kω, 5.81 mv , 29.8 kω, 104 Ω, , 2 MΩ, 100 Ω, 20, , 7.94 MΩ, 247 Ω, , 45.2 kω, 27.8 Ω, V , 1 MΩ, 507 Ω, 6.19 V , 12.6 MΩ, 1.34 kω, V v i ( V RE ) V , 25.0 V , 1.94 kω, 4.92 MΩ, 0.990; 23.6, 1.94 kω, 10.1 MΩ, , 1.20 kω,, 0.600; 5.81, 1.43 kω,, , 185 Ω, 39.0 kω, 18.5 mv , 1.32 kω, 20 kω, 354 mv , 3.02 kω, 24 kω, 352 mv Ω Ω ( β o +1)r o =154 MΩ Low R in, high gain: Either a common-base amplifier operating at a current of 71.4 µa or a common-emitter amplifier operating at a current of approximately 7.14 ma can meet the specifications with V CC 14 V Large R in, moderate gain: Common-source amplifier Low R in, high gain: Common-emitter amplifier with 5-Ω input "swamping" resistor Common-drain amplifier Cannot be achieved with what we know at this stage in the text Ω

24 v i 1 khz 2 khz 3 khz THD 5 mv 5.8 mv mv (5.7%) mv (0.74% 5.9% 10 mv 12.4 mv 1.54 mv (12.5%) mv (2.1%) 12.8% 15 mv 20.6 mv 4.32 mv (21%) 1.18 mv (5.4%) 22% v i, 384 kω v i, 297 Ω , , , , 0.993, V SPICE: (116 µa, 7.53 V), 150, 19.6 kω, 37.0 kω SPICE: (115 µa, 6.30 V), -20.5, 368 kω, 65.1 kω SPICE: (12.7 µa, 5.68 V), 0.986, 10.7 MΩ, 2.00 kω SPICE: (66.7 µa, 4.47 V), 16.8, 1.10 MΩ, 81.0 kω SPICE: (5.59 ma, V), -3.27, 10.0 MΩ, 1.52 kω SPICE: (6.20 ma, 12.0 V), 0.953, 2.00 MΩ, 388 Ω µf, 270 µf, 0.15 µf; 2.7 µf µf, 270 µf; 100 µf, 0.15 µf µf, µf pf, 820 pf; µf, 1800 pf, µf ma R 1 = 120 kω, R 2 = 110 kω The second MOSFET A v Only slightly beyond the limits in the Monte Carlo results Voltage is not sufficient - transistor will be saturated , 1.00 MΩ, 64.3 Ω , 1.00 MΩ, 64.3 Ω , 73.6 kω, 18.8 kω , 107 kω, 20.0 kω , 10.0 kω, 18.8 kω , 94.7 Ω, 113 Ω Use C 3 = 2.2 µf, 19.2 Hz, 18.0 Hz Hz, 1.22 Hz Hz, 5.72 Hz Hz, Hz Use 1 µf for all capacitors; 1.42 khz, 1.68 khz 24

25 Chapter (20.7 µa, 5.87 V); 273, 243 kω, 660 kω; 0.604, 47.1 db, 27.3 MΩ 15.2 (5.25 µa, 1.68 V); 21.0, , 24.4 db, 572 kω, 4.72 MΩ, 200 kω, 50.0 kω 15.4 (182 µa, 0.92 V); 728, -1.05, 50.8 db, 27.4 kω, 4.75 MΩ, 200 kω, 50.0 kω 15.7 R EE = 1.1 MΩ, R C = 1.0 MΩ 15.8 (a) (198 µa, 4.98 V); differential output: 309, 0, (b) single-ended output: 155, , 64.1 db; 25.2 kω, 20.2 MΩ, 78.0 kω, 19.5 kω V, V, V, 3.94 V V O = V, v o = 0; V O = V; v O = 1.36 V, V O = V, v o = V; 5.48 mv (47.4 µa, 6.22 V); Differential output: 380, 0, ; single-ended output: 190, 0.661, 49.2 db; 158 kω, 22.7 MΩ V, V, V (4.94 µa, 1.77 V); differential output: 77.2, 0, ; single-ended output: 38.6, 0.661, 25.4 db; 808 kω, 405 MΩ, 1.60 V , , 95.2 db , , 95.6 db (107 µa, 10.1 V); differential output: 18.2, 0, ; single-ended output: 9.1, 0.487, 25.4 db;, kω, 5.6 kω (20 µa, 4.32 V); differential output: 38.0, 0, ; single-ended output: 19.0, 0.120, 44.0 db;, (20 µa, 5.71 V); differential output: 38.1, 0, ; single-ended output: 19.0, 0.120, 44.0 db;, µa, 27 kω , , 13.8,, V, 2.64 V, 48.3 mv , , 751 kω (99.0 µa, 10.8 V); 30.1, 0.165, 554 kω (49.5 µa, 3.29 V), (49.5 µa, 8.70 V); 149, , 101 kω (100 µa, 1.63 V), (100 µa, 3.16 V); 13.4, 0, (24.8 µa, 12.0 V), (500 µa, 12.0 V), 893, 202 kω, 20.6 kω, 147 MΩ, v [-10.6 V, 11.3 V] (24.8 µa, 11.3 V), (4.95 µa, 11.3 V), (495 µa, 12.0 V), 9180, 202 kω, 19.2 kω, 145 MΩ, v (98.8 µa, 14.3 V), (300 µa, 14.3 V); 551, 40.5 kω; 34.6 MΩ; v [-13.6 V, 13.6 V] (98.8 µa, 14.3 V), (300 µa, 14.3 V); 27800, 40.5 kω; 2.51 MΩ (250 µa, 15.6 V), (500 µa, 15.0 V); 4300, ; 165 kω

26 15.63 (250 µa, 4.92 V), (6.10 µa, 4.30 V), (494 µa, 5.00 V); 4230, ; 97.5 kω (49.5 µa, 15.0 V), (360 µa, 14.3 V), (990 µa, 15.0 V); 12100, 101 kω; 1.80 kω; 66.3 MΩ; v (250 µa, 10.9 V), (2.00 ma, 9.84 V), (5.00 ma, 12.0 V); 868, ; 127 Ω (300 µa, 5.10 V), (500 µa, 2.89 V), (2.00 ma, 5.00 V), 528,, 341 Ω (300 µa, 5.55 V), (500 µa, 2.89 V), (2.00 ma, 5.00 V), 2810,, 341 Ω (99.0 µa, 4.96 V), (500 µa, 3.41V), (2.00 ma, 5.00 V), 11400, 50.5 kω, 224 Ω (49.5 µa, 13.0 V), (98.0 µa, 13.7 V), (735 µa, 18.0 V); 2700, 101 kω, 3.37 kω; [undefined, 12.3 V]; mv No, R id must be reduce or R out must be increased (24.8 µa, 17.3 V), (24.8 µa, 17.3 V), (9.62 µa, 15.9 V), (490 µa, 16.6 V), (49.0 µa, 17.3 V), µa µa µa (4.95 ma, 18.0 V), 88.5 db, 202 kω, 18.1 Ω ma, 0 ma, 10 ma, 12.5 percent percent ma, 19.6 V µa ma, 0 ma mω (a) 22.8 µa, 43.9 MΩ (a) 144 µa, 7.83 MΩ Two of many: 75 kω, 62 kω, 150 Ω; 68 kω, 12 kω, 1 kω , µa, 18.6 MΩ µa, 13.1 MΩ µa, 131 MΩ kω, 200 kω, 33 kω µa, 27.4 MΩ, 201 µa, 11.0 MΩ, 391 µa, 4.30 MΩ µa, 22.1 MΩ, 10.1 µa, 209 MΩ µa, 6.57 x Ω (4.62 µa,.62 V), (9.34µA, 9.03 V); 40.9 db, 96.5 db β o1 µ f 1 /2, For typical numbers: 20(100)(70) =140,000 or 103 db σ limits: I O = 199 µa ± 32.5 µa, R OUT = 11.8 MΩ ± 2.6 MΩ 3σ limits: I O = 201 µa ± 34.7 µa, R OUT = 21.7 MΩ ± 3.6 MΩ mv; 5.02 mv; 2% %, µa, µa, (I OS = na) 26

27 mv, 1.2%, 0.4% µa, 164 µa, 346 µa, 909 kω, 455 kω, 227 kω µa, 150 µa, 300 µa, Lsb LSB, ).613 LSB µa, 383 kω, 574 µa, 192 kω (a) 631 µa, 103 kω, 1.02 ma, 61.8 kω kω, 93.1 µa; 599 kω, 93.2 µa µa, 299 µa µa, 759 µa; 479 µa, 759 µa; 430 µa, 692 µa kω, 11.8 µa, 123 µa kω, µa, 5.10 MΩ kω kω, 17.0 kω, µa, 18.3 MΩ; 45.5 µa, 9.17 MΩ µa, 55.8 MΩ; 146 µa, 19.0 MΩ; 2770; 1.40 V µa, 80/ /g m / µa, 1.16 GΩ; 20.3 kv; 2.11 V µa, 3.89 na (b) 50 µa, 240 MΩ; 12.0 kv; 3.07 V µa, 163 MΩ, 2750 V; 2V BE = 1.40 V kω (a) 64.0 µa, 3.59 MΩ kω µa, 295 µa, 66.5 µa kω, 225 kω kω, 210 kω I C1 = 140 µa, I C2 = 47.8 µa n > 1/ µa I S C1 VCC = 2.92x10 2 I S C 2 VCC = 9.92x10 3 I (b) I D1 = 8.19 µa I D2 = 7.24 µa S D1 VDD = 7.75x10 2 I S D 2 VDD = 6.31x10 2 The currents differ considerably from the hand calculations. The currents are quite sensitive to the value of λ. The hand calculations used λ = 0. If the simulations are run with λ = 0, then the results are identical to the hand calculations µa, 6.00 µa, 3.45 µa 27

28 I C2 = 15.2 µa I C1 = 28.5 µa - Similar to hand calculations. I S C1 VCC =1.81x10 3 I S C 2 VCC µa, 308 µa µa , 6.28 x10-5, 122 db , 6.97 x10-5, 117 db , 4 x10-3, 110 db, ±2.9 V = 7.07x (100 µa, 8.70 V), (100 µa, 7.45 V), (100 µa, V), (100 µa, V), 323, (125 µa, 1.54 V), (125 µa, V), (125 µa, 2.50 V), (125 µa, 1.25 V); µa (b) 100 µa (250 µa, 5.00 V), (250 µa, 5.00 V), (250 µa, V), (250 µa, V), (500 µa, V), (135 µa, 5.00 V), (135 µa, V), (250 µa, 2.16 V), (500 µa, 3.25 V), (500 µa, 3.21 V), (500 µa, 3.58 V); 4130; , (250 µa, 7.50 V), (250 µa, 7.50 V), (250 µa, V), (1000 µa, V), (330 µa, 7.50 V), (330 µa, V), (1000 µa, 4.75 V), (250 µa, 2.16 V), (500 µa, 5.75 V), (1000 µa, 5.13 V), (b) 42.9/1 (c) , 574 Ω, 3.03 x 10 5, 60.0 kω ±1.4 V, ±2.4 V (a) 9.72 µa, 138 µa, 46.0 µa kω, 255 Ω V EE 2.8 V, V CC 1.4 V; 3.8 V, 2.4 V MΩ, 356 kω x (100 µa, 15.7 V), (100 µa, 15.7 V), (50 µa, V), (50 µa, V), (50 µa, V), (50 µa, V), (50 µa, 1.40 V), (50 µa, 1.40 V), (1.00 µa, 29.3 V), (100 µa, V), (100 µa, 13.6 V); 1.00 ms, 752 kω (50 µa, 15.7 V), (50 µa, 15.7 V), (50 µa, 12.9 V), (50 µa, 12.9 V), (50 µa, 1.40 V), (50 µa, 1.40 V), (1.00 µa, 29.3 V), (100 µa, 1.40 V), (1 µa, V), (1 µa, 13.6 V); 1.00 ms, 864 kω 28

29 Chapter A mid = 50, F L ( s) = , s 2 ( ), yes, A s v( ) 50 ( ) ( s + 2) s s s, yes, 1.58 khz, 1.58 khz 10 5 s s + 30, 4.77 Hz, 4.80 Hz , s 2 (s + 1)( s + 2), s, Hz, 142 Hz; Hz, 133 Hz s (b) -16.5, 7.58 Hz (b) 14.1 (23.0 db), 11.5 Hz µf; 1.50 µf, 49.3 Hz (b) 0.33 µf; 1770 Hz A v s ( s) 2 = A mid s + ω 1 ( )( s + ω 2 ) 1 ω 1 = 1 C 1 R S + R E g m 1 ω 2 = C 2 R C + R 3 ( ) 2 zeros at ω = db, 151 Hz; -5.0 V, 7.9 V Hz; 91 Hz , 50.0 Hz, 12.0 V Hz db, 19.2 Hz , 15.5 Hz, 12.0 V µf µf Cannot reach 1 Hz; f L = 13.1 Hz for C 1 =, limited by C µf ps (a) 22.5 GHz ; ; , 98.0, 5000, 100, 2% error; 350, 42.9, 300, 50, 18% error Real roots: -100, -20, -15, , 1.96 MHz, 176 MHz , 849 khz , 2.75 MHz, 33 MHz 29

30 pf, 303 MHz /10 5 RC; 1/10 6 RC; 1/sRC db, 5.53 MHz , 1.12 MHz, 128 MHz, 531 MHz Ω, -31.9, 160 MHz , 7.41 MHz Ω, 1 kω ; 92.3; 100, , 64.4 MHz , 40.9 MHz , 10.9 MHz , 11.3 MHz, 20.6Hz , 114 MHz db, 75.4 MHz C GD + C GS /(1 + g m R L ) for ω << ω T Using a factor of 2 margin: 8 GHz, 19.9 ps ma - not a realistic design. A different FET is needed MHz khz, 640 khz khz khz KHz khz MHz db, 833 Hz, 526 khz MHz, -41.1, pf, 12.6, n = 2.81, 21.9 pf MHz; 27.5 MHz MHz, 7.98, 112 / 90 ; 4.74 MHz, 5.21, 46.1 / MHz, 3.96, 35.4; 10.9 MHz, 16.4, pf; 240, -4.41x10 4, 25.1 khz pf; 40 30

31 Chapter (b) 2000, 5.00, 0.05% /101, 99.0, db db /(1+Aβ); percent 17.9 (b) shunt-series feedback (d) series-shunt feedback x10 5, 20 S , 6.58 MΩ, 3.18 Ω , 1.51 MΩ, 3.60 Ω , 43.9 MΩ, 2.49 Ω, 98.9 µs kω; 11.1 Ω; Ω Ω; 46.2 Ω; 32.4 kω; kω, 50.2 kω, 2.45 kω , 973 Ω , 36.0 Ω /10.5 kω, 2.82 kω, -1/11, 4000; -11.0, 35.2 Ω, 3.57 MΩ , 36.5 MΩ, 14.9 MΩ β o /(β o + 1), 2/ g m, (β o + 1)r o µ f4 (1 + µ f3 ) r o2, 21.9 GΩ db (s/r 2C 2 )/[s 2 + s(1/r 2 C / (R 1 R 2 )C 1 ) + 1/R 1 R 2 C 1 C 2 ] Ω, 21.3 Ω MΩ, 2.48 Ω µ f4 r o2 (1 + µ f3 ), 1/g m db, 1 khz, 1 MHz; 101 MHz, 9.90 Hz; 251 MHz, 3.98 Hz db, 1 khz, 1 MHz; ( ± j9.98) Hz, (-6.37 ± j100) MHz; (-2.20 ± j19.9) Hz, (-6.37 ± j49.8) MHz Hz, 3.04 MHz , 9.99% o ; 5.1 o khz; A 2048; larger yes, but almost no phase margin;

32 17.75 yes, but almost no phase margin; o, yes, 50 o o phase margin is undefined; T ( jω) < 1for all ω o o MHz, 33.3 V/µs MHz, -100 o ; 8.0 MHz, -92 o MHz, 50 V/µs V/µs MHz /RC, 2R /RC, khz, 6.85 V khz, 10.7 V MHz, 20.1 MHz, 36.3 MHz, ms, 5.28 µa MHz, 4.53 MHz MHz, MHz, 8.11 MHz, MHz, 80 V p-p MHz MHz, 18.1 MHz, mh, ff; MHz, MHz MHz; MHz MHz; 9.19 MHz 32

### EE105 Fall 2015 Microelectronic Devices and Circuits

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