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

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1 Micelectnic: icuit Analyi and Dein, 4 th editin hapte 6 y D. A. Neaen xecie Slutin xecie Slutin X6. (a ( n ( 0 ( Q β A 0. (b A/ 0.06 β ( 0( k Ω hapte μ A 3. (c A υ ( 3.846( X6. (a ( n A 00 ( 50 ( β A β A/ 0.06 ( 50( k Ω A k Ω (b A υ ( 8.75( X6.3 (a n A hen β A Nw

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

3 Micelectnic: icuit Analyi and Dein, 4 th editin hapte 6 y D. A. Neaen xecie Slutin We find + + β ib ib 80. kω Al k Ω ib k Ω We find ib ib S Nw + β ( ( 0.093( S Av ( 6.08( 0.093( 0.985( 5.6 A v 8.7 X6.6 (a k Ω H 0 H A β.60 A; ( + β. 6 A Q (.6( 4 (.6( (b A/ 0.06 β A ( 00( (.65 k Ω ( 00( 4 0 β L (c Aυ ( + β.65 + ( 0( 0.3

4 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 ] β A β A/ 0.06 ( 0( k Ω i 3.53 k Ω A 80 (b k Ω υ υ ( υ S Aυ ( ( 33.98( ( υ X6.8 (a (b A A υ A υ A/ k Ω 0.5 c ( ( 9.65( ( ( 9.65( c L 47 A υ X A 0 + ( 6( A, Q A Q 3.83 dc lad line + ( ( Q 0 ( 0.84(.3 ( 0.847( 5 A

5 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 X β 5 (b A; β A; A Q ( ( 4 ( ( (c Δ Δ ( Δ ( 90.5 Δ ( 3.83 F Δ 4.4 hen Δ 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, A 0 hen 0.7 (.( which yield 5.4 kω Since H. k Ω, we find 58.7 kω Al Q

6 Micelectnic: icuit Analyi and Dein, 4 th editin hapte 6 y D. A. Neaen xecie Slutin (b ac lad line Δυ i ( Δ ic A Want Al Δ vec Δυ ec 3.49 Nw. 37 k Ω L Δi.5 c S k Ω which yield L ec c L L 5.56 kω X6. (a k Ω H 4. H A ( 8( β 0. A, β A 0 ( 0.0( Q Q (b A/ Ω, 379. Ω ( + β ( Aυ + + β ( 8( ( ( 8( (c + ( + β ( ( 8( ib ib.6 k Ω X 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 H H 48. kω

7 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 ( ( 5 ( β H H + + We can wite O ( which yield 65.8 kω Since 48. k Ω, we btain 78.8 kω (b β ( 00( kω.5 A 5 00 kω.5 We ay nte that Al Nw b β b ib ib whee + ( β ( L ( 0( kω ( β + + L b + ib We can then wite A ( + β + + We have kω A L ib ( b

8 Micelectnic: icuit Analyi and Dein, 4 th editin hapte 6 y D. A. Neaen xecie Slutin A 9.9 (c + β Ω X6.5 (a kω H 6 H ( 0 5 ( H 4.05 We find ( 5.9 μ A and β ( 5(.9 μa A Q ( + β A At the cllect f Q, ( 5 + ( + β ( ( 6(.5 which yield.99 al Q 5 ( 0.368( hen Q 99. ( We find 07. ( 5 Q 486. A 5. and β 5 Q ( A + β 6 We find and Q

9 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 A/ 0.06 ( 5( 0.06 β kω A/ 0.06 ib + + β We find O ib 34. kω and ib + ( + β ( L ( 6( 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 ( 6(.5 0

10 Micelectnic: icuit Analyi and Dein, 4 th editin hapte 6 y D. A. Neaen xecie Slutin (c k Ω i ib β 6 and Ω et Yu Undetandin Slutin YU6. i i i b b υ + υ υ in ωt ib in ωt ( μ A. + i in ωt ( μ A b 3. υbe υ ( 0.065inωt inωt ( υ n + υ inω ( be t υ ( 8.5( 0.065inωt ωt υ Aυ in ( υ ce + υ in ωt ( Q ce YU6. (a + ( n β 0.0 A ( 0.( (b A/ 0.06 β A ( 0( k Ω k Ω μ A (c A ( ( 7.69( (d υ + i k Ω k Ω

11 Micelectnic: icuit Analyi and Dein, 4 th editin hapte 6 y D. A. Neaen xecie Slutin YU6.3 H k Ω Nw n + + β H + H H ( ( 0.5 β A β We find H ( 0( A/ k Ω A [ ( + β ] 0 [ ( 0.5 ] hen β.67 ( 0( 4 A ( υ + + β 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. ( which yield + 5 kω We have kω and 454. kω We have A β 00 and 0. + β H Al H ( 459. ( 5 H H kω H k Ω

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

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

14 Micelectnic: icuit Analyi and Dein, 4 th editin hapte 6 y D. A. Neaen xecie Slutin YU6.9 F, S Q Q Δ Δ Δ Q Δ ( 8 Q ( 4 ( 0.( ( 0.( Q hen ( 0.( ( ( ( Q Q hen peak-t-peak value ae Δ 67 ( Δ A YU6.0 We can wite ( μ A ( μ A 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 kω find the vltae ain: ib Al ( + h fe hie + ( + h fe whee L ib h e S k Ω hen Av 0.89 find the cuent ain ( 0.896( 35( ( 35( 4.7 A

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

16 Micelectnic: icuit Analyi and Dein, 4 th editin hapte 6 y D. A. Neaen xecie Slutin β Ω YU6. (a + ( n + ( + β A 00 + ( A; A Q Q ( 0.643( ( + β ( L i + + β L i + S (b Aυ We find A/ 0.06 ( 0( k Ω 0.69 Nw + + β ib L hen i ib A υ k Ω ( 5 + ( 5 Al Ai β + A i 3. (c We fund ib 3.7 k Ω Nw k Ω ( + ib L + S β 7 Ω YU6.3 (a dc analyi: ( n Q 0.93 A 0 β 00 Q ( A + β 0

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

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

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

20 Micelectnic: icuit Analyi and Dein, 4 th editin hapte 6 y D. A. Neaen xecie Slutin + β ( β + ( + β Nw + ( + β A v + ( + β ( 38.( 0 ( 4 65 A v.63 + ( 0 65 A v 77.0 (d + + β i i 53 kω YU6.7 9 (a k Ω k Ω ( ( k Ω 90 hen 5 k Ω S k Ω ( 00( 0.06 (b A/;.6 k Ω (c A ( ( υ L + β 0 k Ω

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

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

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