Chapter 6 ( )( ) 8 ( ) 1.145 0.7 ( )( ) Exercise Solutions. Microelectronics: Circuit Analysis and Design, 4 th edition Chapter 6. EX6.

Micelectnic: icuit Analyi and Dein, 4 th editin hapte 6 y D. A. Neaen xecie Slutin xecie Slutin X6. (a ( n 0.85 0.7 80 ( 0 ( 0.000833 0. 0 Q 3.3 0. 5. β A 0. (b 3. 846 A/ 0.06 β ( 0( 0.06 0. 8 3. k Ω hapte 6 0.833 μ A 3. (c A υ ( 3.846( 5 8. 5 + 3. + 80 X6. (a ( n.05 0.7 0.0035 A 00 ( 50 ( 0.0035 0. 4875 β A β 0.4875 8.75 A/ 0.06 ( 50( 0.06 0.4875 8 k Ω A 50 308 k Ω 0.4875 8 (b A υ ( 8.75( 308 6 8. 7 + 8 + 00 X6.3 (a n.45 0.7 50 0.0089 A hen β 90 0.0089 0.80 A Nw

Micelectnic: icuit Analyi and Dein, 4 th editin hapte 6 y D. A. Neaen xecie Slutin 0.80 30.8 A/ 0.06 ( 90( 0.06 β.9 kω 0.80 A 0 50 kω 0.80 (b We have ( and A υ + + (.9 ( 30.8 ( 50.5.9 + 50 which yield A υ 4. 8 X6.4 Uin Fiue 6.3 4 4 0. A, 7.8 < hie < 5 kω, 60 < hfe < 5, 6. 0 < h 50 0, (a F e < 5 < h < 3 μh e 4 4 5 A, 0.7 < hie <. kω, 40 < hfe < 0,.05 0 < h.6 0, (b F e < < he < 35 μh X6.5 H 50 75 57.7 k Ω 75 H ( 5 + 75 + 50 H.54 H n H + + + 3.48 μ A β ( 0( 3.38 μa 0.48 A (a Nw 048. 6. 08A/ 006. β ( 0( 0. 06 746. kω 0. 48 We have.54 0.7 ( β 57.7 ( 0.6

Micelectnic: icuit Analyi and Dein, 4 th editin hapte 6 y D. A. Neaen xecie Slutin We find + + β 7.46 + 0.6 ib ib 80. kω Al 50 75 57.7 k Ω ib 57.7 80. 33.54 k Ω We find ib 33.54 ib S + + 33.54 0.5 0.985 Nw + β + + 0.6 7.46 ( 0.093 ( 0.093( 0.985 S Av ( 6.08( 0.093( 0.985( 5.6 A v 8.7 X6.6 (a 4.4 0. 73 k Ω H 0 H + 0 + 4.4 0 0.3 + 0.7 +.73 + 0. 0. 6 6 0.060 A β.60 A; ( + β. 6 A Q (.6( 4 (.6( 0.3 5..60 (b 6. 54 A/ 0.06 β A ( 00( 0.06.60 (.65 k Ω ( 00( 4 0 β L (c Aυ 8.95 + ( + β.65 + ( 0( 0.3

Micelectnic: icuit Analyi and Dein, 4 th editin hapte 6 y D. A. Neaen xecie Slutin X6.7 (a i S + + ( + β + 0 [ 00 + ( 4 ] 0. 007363 + 0.7 5 0.7 β 0.8836 A β 0.8836 33.98 A/ 0.06 ( 0( 0.06 0.8836 0.5 + 00 3.53 3.9 k Ω i 3.53 k Ω A 80 (b 90. 5 k Ω 0.8836 00 3.53 υ υ ( 0. 87 υ S 00 3.53 0.5 + + Aυ ( ( 33.98( 4 90.5( 0.87 4 υ X6.8 (a (b A A υ A υ 0.5 0.06 9.65 A/ 00 400 k Ω 0.5 c ( ( 9.65( 400 00 769 ( ( 9.65( 400 00 00 c L 47 A υ X6.9 5 0.7 0.0067 A 0 + ( 6( 5 0.84 A, Q 0.847 A Q 3.83 dc lad line + ( ( + 0 7.3 Q 0 ( 0.84(.3 ( 0.847( 5 A

Micelectnic: icuit Analyi and Dein, 4 th editin hapte 6 y D. A. Neaen xecie Slutin ac lad line (nelectin υ i i ce c (.3 5 i (.58 L c c X6.0 0.7 + + β 5 (b 0 + 0.007363 A; β 0. 884 A; 0. 8909 A Q ( 0.8836( 4 ( 0.8909( 4. 90 0 (c Δ Δ ( Δ ( 90.5 Δ ( 3.83 F.9 0.5. 4 Δ 4.4 hen Δ 0. 66 A; Δυ ce 4. 8, peak-t-peak 3.83 X6. H H + (a H ( 0.( + β ( 0.( H. kω, H (.( We can wite + β + n + + H H We have.6.6 A, 0.033 A 0 hen 0.7 (.( 0.033.+ which yield 5.4 kω Since H. k Ω, we find 58.7 kω Al.6 4.6 3.99 Q

Micelectnic: icuit Analyi and Dein, 4 th editin hapte 6 y D. A. Neaen xecie Slutin (b ac lad line Δυ i ( Δ ic 0..6 0..5 A Want Al Δ vec 3.99 0.5 3.49 Δυ ec 3.49 Nw. 37 k Ω L Δi.5 c S 4. 37 k Ω which yield L ec c L L 5.56 kω X6. (a.3 4. 0. 997 k Ω H 4. H 9. 636 +.3 + 4. 9.636 0.7.473 A 0.997 + ( 8( 0.03 + β 0. A, β 0. 978 A 0 ( 0.0( 30 6. 0 Q Q 0.978 (b 7. 608 A/ 0.06 0.5 Ω, 379. Ω ( + β ( Aυ + + β ( 8( 379. 30 ( 0.5 + ( 8( 379. 30 (c + ( + β ( 0.5 + ( 8( 379. 30 ib 0.9953 ib.6 k Ω X6.3 0.5 30 379. 0. Ω + β 8 9 X6.4.5 A and β 00, we find (a Q.6 A and 0.05 A F Q 0 Q Nw O 4 0 (.6 which yield 4.76 kω hen 0. + β 0. 0 4.76 H H 48. kω

Micelectnic: icuit Analyi and Dein, 4 th editin hapte 6 y D. A. Neaen xecie Slutin We have ( 0 5 H ( 0 5 H + H ( 48 5 0.7 ( 5 ( β H H + + We can wite O ( 48 5 0.7 + 5 0.05 48.+ 0 4.76 which yield 65.8 kω Since 48. k Ω, we btain 78.8 kω (b β ( 00( 0.06.08 kω.5 A 5 00 kω.5 We ay nte that Al Nw b β b ib ib whee + ( β ( L ( 0( 4.76 00 +.08 + 84.9 kω ( β + + L b + ib We can then wite A ( + β + + We have 4.76 00 4.54 kω A L ib 4.54 48. ( 0 4.54 + 48.+ 84.9 b

Micelectnic: icuit Analyi and Dein, 4 th editin hapte 6 y D. A. Neaen xecie Slutin A 9.9 (c + β.08 4.76 00 0 0.5 Ω X6.5 (a 70 6 5.53 kω H 6 H ( 0 5 ( 0 5 + 70 + 6 H 4.05 We find 4.05 0.7 ( 5.9 μ A 5.53 + 6 0. and β ( 5(.9 μa 0.364 A Q ( + β 0.368 A At the cllect f Q, 5 0.7 ( 5 + ( + β 5 0.7 ( 5 0.364 + 5 ( 6(.5 which yield.99 al Q 5 ( 0.368( 0. 5 4. 93 hen Q 99. ( 493. 79. We find 07. ( 5 Q 486. A 5. and β 5 Q ( 486. 48. A + β 6 We find 07. 99. 07. 9. and 5 5. 9. 7 Q

Micelectnic: icuit Analyi and Dein, 4 th editin hapte 6 y D. A. Neaen xecie Slutin (b he all-inal tanit paaete ae: ( 5( 0.06 β 8.93 kω 0.364 0.364 4.0 A/ 0.06 ( 5( 0.06 β 0.674 kω 4.8 4.8 85 A/ 0.06 ib + + β 8. 93+ 6 0. We find O ib 34. kω and ib + ( + β ( L ( 6(.5 0 65 0.674 + k Ω he all-inal equivalent cicuit i: We can wite + β whee ( b L ( b + ib ib hen Aυ β A υ A 7. 7 v i ( + ( + L ib ib 5 5 5 + 65 34. ( 6(.5 0

Micelectnic: icuit Analyi and Dein, 4 th editin hapte 6 y D. A. Neaen xecie Slutin (c 70 6 34. 4.76 k Ω i ib + 0676. + 5 5. + β 6 and 43. 7 Ω et Yu Undetandin Slutin YU6. i i i b b υ + υ υ 80 + 3.. 0.065 in ωt ib 0.308 in ωt ( μ A. + i 0.833 + 0.308in ωt ( μ A b 3. υbe υ ( 0.065inωt 0.00960inωt ( + 3. + 80 υ n + υ 0.7 + 0.00969inω ( be t υ ( 8.5( 0.065inωt 0.554 ωt υ Aυ in ( υ ce + υ.8 0.554in ωt ( Q ce YU6. (a + ( n β 0.0 A ( 0.( 7. 9 3.3 0. (b 7. 69 A/ 0.06 β A ( 0( 0.06 0.0 80 0.0 400 3.3 0.7.455 80 4.3 k Ω k Ω 4.3 4.3 + 80.85 μ A (c A ( ( 7.69( 7 400 8. 0 (d υ + i + 80 + 4.3 94.3 k Ω 7 400 6.88 k Ω

Micelectnic: icuit Analyi and Dein, 4 th editin hapte 6 y D. A. Neaen xecie Slutin YU6.3 H 00 5 0 k Ω Nw n + + β H + H H 5 00 + 5 ( 5. 0.0 0.7 0 + ( 0.5 β 0.764 A β We find H 0.764 0.06 7.55 ( 0( 0.06 0.764 A/ 4.355 k Ω 0.00597 A [ ( + β ] 0 [ 4.355+ ( 0.5 ] 0 34.605. 67 + hen β.67 ( 0( 4 A ( 0.9807 υ + + β.67 + 0.5 4.355 + 0.5 A υ 3.6 YU6.4 Av A a fit appxiatin, eultin ain i alway alle than thi value. he effect f S i vey all. 0 Set 5 ( + + Q Nw 5 ( 05. ( + + 5. which yield + 5 kω We have 0 0. 454 kω and 454. kω We have 05. 0005. A β 00 and 0. + β 0. 0 0. 454 H Al H ( 459. ( 5 H H + 459. kω H k Ω

Micelectnic: icuit Analyi and Dein, 4 th editin hapte 6 y D. A. Neaen xecie Slutin Al ( + n + +β 3 H H ( 0005. ( 459. 07. ( 0( 0005. ( 0454. + + that which yield 4. kω Since 4. 59 k Ω, then 567. kω YU6.5 A a fit appxiatin Av Set 9 Nw + + ( 7.5 0.6 9 + + 3.75 which yield 0.65 kω and 5.6 kω We have 0. + β 0. 0 0.65 H Al 6.3 7.5 H H We have 0.6 0.006 A β 00 and + β + n + + H H H 6.3 kω 7.5 ( 0( 0.006( 0.65 + 0.7 + ( 0.006( 6.3 + ( 6.3( 7.5 which yield 7.4 kω Since H 6. 3 k Ω, then 4. 5 k Ω YU6.6 We have β Av ( 0.95 + ( + β A v ( 0.95 4.75 0.4 Aue, f xaple 6.5 that,. k Ω

Micelectnic: icuit Analyi and Dein, 4 th editin hapte 6 y D. A. Neaen xecie Slutin hen β ( β. + + 0.4 4.75 β 76 YU6.7 Dc analyi: by yety, 0 H H 0 0 0 k Ω We can wite 0 0.7 ( 5 0.0067 A 0 + 6 5 β 5 0.0067 0.84 A Sall-inal tanit paaete: β ( 5( 0.06 3.87 kω 0.84 0.84 3.3 A/ 0.06 A 00 38 kω 0.84 (a We can wite ( L and A υ L 3.3 38.3 5 A υ 50. 5 (b 38.3.8 k Ω YU6.8 We find 0.48 A, Q 5 ( 0.48( 5.6 ( 0.48( 0.6 0 Q.4 S Δ v (.4 0.5, Δ v 3.8

Micelectnic: icuit Analyi and Dein, 4 th editin hapte 6 y D. A. Neaen xecie Slutin YU6.9 F, S Q Q 0 4 + 4 0 Δ Δ Δ Q Δ ( 8 Q 0. 0.7 ( 4 ( 0.( 4 0. 7 ( 0.( 4 + 0. 7 Q hen ( 0.( 4 + 0.7 0 ( 8 0. 8083 0 ( 0.8083( 8 3. 533 Q Q hen peak-t-peak value ae 3.533 0.7 5. Δ 67 ( 0.8083 0.. 4 Δ A YU6.0 We can wite 0 0.7 ( 0 6.60 μ A 00 + 3 0 ( μ A 30 6.60 0.857 A Aue ninal all-inal paaete f: h 4 kω, h 34 ie fe he 0, he μs 83.3 kω he We find ib hie + ( + hfe L he 4 + 35 0 0 83.3 64 kω find the vltae ain: ib 00 64 + 00 64+ 0 0. 896 Al ( + h fe hie + ( + h fe whee L ib h e S 0 0 83.3 4.7 k Ω hen Av 0.89 find the cuent ain ( 0.896( 35( 4.7 4 + ( 35( 4.7 A

Micelectnic: icuit Analyi and Dein, 4 th editin hapte 6 y D. A. Neaen xecie Slutin h e Ai i + L he 0 83.3 0 83.3 + 0 A i 8.59 find the utput eitance: hie + S h + h e fe + h fe + ib 00 00 + 64 ( 35 4 + 0 00 0 83.3 96. 0 Ω 35 YU6. H 50 50 5 k Ω Nw H + and ( β n + + H H ( 5. 5 5 0.7.5 0.00793 A 5 + 0 00 0.00793 0.793 A Sall-inal tanit paaete: 0.793 30.5 A/ 0.06 ( 00( 0.06 β 3.8 kω 0.793 A 5 58 kω 0.793 (a Define 0.5 58 0.40 kω L ( + β ( β ( 0.4 0 Av + + 3.8 + 0 0.4 A υ 0. 95 (b + + β 3.8 + 0 0.4 ib ib 43.7 kω

Micelectnic: icuit Analyi and Dein, 4 th editin hapte 6 y D. A. Neaen xecie Slutin 3.8 58 + β 0 3.0 Ω YU6. (a + ( n + ( + β + 0 3.3 0.7 0.00358 A 00 + ( 5 0.643 A; 0. 69 A Q Q ( 0.643( 5 4. 4 6.6 ( + β ( L i + + β L i + S (b Aυ We find 0.69 6.65 A/ 0.06 ( 0( 0.06 9.5 k Ω 0.69 Nw + + β 9.5 + 5 3. 7 ib L hen i ib A υ 9.5 3.7 00 69.94 k Ω ( 5 + ( 5 Al Ai β + A i 3. (c We fund ib 3.7 k Ω Nw 69.94 0.89 69.94 + + k Ω 00 5 00 + 3.7 5 + ( + ib L + S 9.5 + 00 5 0.745 5 + β 7 Ω YU6.3 (a dc analyi: ( n 0 0.7 Q 0.93 A 0 β 00 Q ( 0.93 0.9 A + β 0

Micelectnic: icuit Analyi and Dein, 4 th editin hapte 6 y D. A. Neaen xecie Slutin ( Q 0 0.93 0 0.9 5 0 6. (b Sall-inal tanit paaete: β ( 00( 0.06.8 kω 0.9 0.9 35.4 A/ 0.06 Sall-inal cuent ain:, and Al i + + hen ( Ai i + + ( 35.4( 0.8 + 35.4 0.8 A 0.987 (c Sall-inal vltae ain: Av ( 35.4( 5 A v 77 YU6.4 + n + + β (a 3.3 0.7 00 + 0.0 A 0.0 7.73 A/; 0.06 0.00675 A ( 0( 0.06 5.5 k Ω ; 0.0 (b β A i + β + L + + β 0.654 A i 0 5.5 + 6 +

Micelectnic: icuit Analyi and Dein, 4 th editin hapte 6 y D. A. Neaen xecie Slutin (c Nw A υ A υ L 6 5.5 S 5 S + β 0.5 7.73 8 0.0 6. 6 5.5 i i 7 Ω + β ( 7.73 0. k Ω YU6.5 dc analyi + n + 5 Q 5 0.7 4.3 + ( 0 + ( 0 ( 00( 4.3 + ( 0 Al 5 + + 5 Q Q 0 Q 0 + 00 ac analyi : ( L and + + hen β Av ( L + whee β F A, hen ( 00( 0.06 β.6 kω ( 00( Av 0.6 + which yield.4 kω

Micelectnic: icuit Analyi and Dein, 4 th editin hapte 6 y D. A. Neaen xecie Slutin hen f ( 00( 4.3 + ( 0.4 we find 4.3 k Ω YU6.6 (a dc analyi Q A, F Q 00 ( 0.990 A 0 Q 0.0099 A + β 0 Q 0.0099 0.000098 A + β 0 ( 00 0.000098 0.0098 A 0.000098 0 0.00098 0 0.7.4 + 0.0098 + 0.990 A ( O 5 4 Q.4.4 Q 0.7.7 (b all-inal tanit paaete: β ( 00( 0.06 65 k Ω 0.0098 0.0098 0.377 A/ 0.06 β ( 00( 0.06.63 k Ω 0.990 0.990 38.A/ 0.06 (c all-inal vltae ain ( + + + β + + β +

Micelectnic: icuit Analyi and Dein, 4 th editin hapte 6 y D. A. Neaen xecie Slutin + β + + + ( β + ( + β Nw + ( + β A v + ( + β.63 0.377 + ( 38.( 0 ( 4 65 A v.63 + ( 0 65 A v 77.0 (d + + β 65 + 0.63 i i 53 kω YU6.7 9 (a + + 3 90 k Ω 0. 0.7 0.7 k Ω 3 0.7 + 0.7.4 ( 9.4 3 4 90 + 3 0.7 +.5 + 0.7 3.9 ( 9 3.9 5 k Ω 90 hen 5 k Ω 0.7 +.5 +.5 5.7 S 9 5.7 3.3 k Ω ( 00( 0.06 (b 38. 46 A/;.6 k Ω 0.06.6 (c A ( 38.46 ( 3.3 0 94. 5 υ L + β 0 k Ω

Micelectnic: icuit Analyi and Dein, 4 th editin hapte 6 y D. A. Neaen xecie Slutin YU6.8 (a dc analyi 5 30 4. kω H 30 H + 5 + 30 H.3 Nw + n + +β H H.3 0.7 0.050 A 4. + ( 8( 0.5 80 0.05.00 A + β Q + β Q 8 + ( 0.5 80 6.99 Pwe diipated in : P.0 8.0 W Pwe diipated in L : LQ 0 PL 0 Pwe diipated in tanit: PQ Q + Q ( 0.05( 0.7 + (.0( 6.99 4.0 W (b With v 8cωt β ( 80( 0.06.04 kω.0 We can wite β vce ( L P cωt Pwe diipated in L : vce β pl ( L P L L 80 3 ( ( 0.08 0.04 0.479 W pl Pwe diipated in : Since p L kω,, we find 8.0 + 0.479 8.48 W

Micelectnic: icuit Analyi and Dein, 4 th editin hapte 6 y D. A. Neaen xecie Slutin P Q pq Q β P ( 3 80 0.08 3 3 ( 0 ( 6.99 ( 0 0 3.0 W.04 0 3 L YU6.9 (a dc analyi 53.8 0 8.43 kω Nw H 0 + 53.8 + 0 H H 0.7837 0.7837 0.7 0.00993 A 8.43 00 0.00993 0.993 A Q.5 5 0.993 which yield.5 kω (b Pwe diipated in : P P.48 W Pwe diipated in tanit: P 0.993.5 PQ Q Q.48 W ( 0.993.5 ( (c ac analyi Maxiu ac cllect cuent: i 0.993 cωt A c ( ( 5 Pwe diipated in : p ( 0.993 ( 0.993 (.5 p.4 W Nw p.4 Factin 0.5 P + P.48 +.48 Q