CHAPTER 11. Solutions for Exercises. (b) An inverting amplifier has negative gain. Thus L

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1 CHPTE Slutn fr Exerce E. (a nnnertng amplfer ha pte gan. Thu ( t ( t 50 ( t 5.0 n(000πt (b n nertng amplfer ha negate gan. Thu ( t ( t 50 ( t 5.0 n(000πt E. V V c 75 V V I I 75 G.75 0 c 00 E. ecall that t maxmze the pwer elere t a la frm a urce wth fxe nternal retance, we make the la retance equal t the nternal (r Théenn retance. Thu we make 5 Ω. epeatng the calculatn f Exerce. wth the new alue f, we hae V 5 c V I I 5 G 5 0 4

2 E.4 By npectn, 000 Ω an 0 Ω. V c c c c V + + V c V E.5 Swtchng the rer f the amplfer f Exerce.4 t --, we hae 000 Ω an 00 Ω V c c c c V + + V c V E. P ( 5 V (.5.5 W P P + P P W P η 00 %.% P E.7 The nput retance an utput retance are the ame fr all f the amplfer mel. Only the crcut cnfguratn an the gan parameter are fferent. Thu we hae kω an 0 Ω an we nee t fn the pen-crcut ltage gan. The current amplfer wth an pen-crcut la :

3 c c c c 4 E.8 Fr a trancnuctance-amplfer mel, we nee t fn the hrtcrcut trancnuctance gan. The current-amplfer mel wth a hrtcrcut la : G c c c mc 0. S The mpeance are the ame fr all f the amplfer mel, we hae 500 Ω an 50 Ω. E.9 Fr a tranretance-amplfer mel, we nee t fn the pen-crcut tranretance gan. The trancnuctance-amplfer mel wth an pen-crcut la : mc c Gm c Gmc kω / The mpeance are the ame fr all f the amplfer mel, we hae MΩ an 0 Ω. E.0 The amplfer ha kω an kω. (a We hae < 0 Ω whch much le than, an we al hae > 00 kω whch much larger than. Therefre fr th urce an la, the amplfer apprxmately an eal ltage amplfer.

4 (b We hae > 00 kω whch much greater than, an we al hae < 0 Ω whch much maller than. Therefre fr th urce an la, the amplfer apprxmately an eal current amplfer. (c We hae < 0 Ω whch much le than, an we al hae < 0 Ω whch much maller than. Therefre fr th urce an la, the amplfer apprxmately an eal trancnuctance amplfer. ( We hae > 00 kω whch much larger than, an we al hae > 00 kω whch much larger than. Therefre fr th urce an la, the amplfer apprxmately an eal tranretance amplfer. (e Becaue we hae, the amplfer e nt apprxmate any type f eal amplfer. E. We want the amplfer t repn t the hrt-crcut current f the urce. Therefre, we nee t hae <<. Becaue the amplfer hul eler a ltage t the la that nepenent f the la retance, the utput retance hul be ery mall cmpare t the mallet la retance. Thee fact ( ery mall an ery mall ncate that we nee a nearly eal tranretance amplfer. E. The gan magntue hul be cntant fr all cmpnent f the nput gnal, an the phae hul by prprtnal t the frequency f each cmpnent. The nput gnal ha cmpnent wth frequence f 500 Hz, 000 Hz an 500 Hz, repectely. The gan 5 0 at a frequency f 000 Hz. Therefre the gan hul be 5 5 at 500 Hz, an 5 45 at 500 Hz. E. We hae n( t Vm c( ωt ( t 0 n( t 0.0 0V c[ ω( t 0.0] 0V c( ωt 0.0ω m The crrepnng phar are V n V m 0 an V 0V m 0.0ω. Thu the cmplex gan V 0V m 0.0ω 0 0.0ω V V 0 n m m 4

5 E.4 B 5.47 MHz t r E.5 Equatn. tate Percentage tlt 00πf T Slng fr f an ubttutng alue, we btan percentage tlt f 5.9 Hz πt π a the upper lmt fr the lwer half-pwer frequency. E. (a ( 00 ( t t + ( t 00 c( ω t + c ( ωt 00 c( ω t c(ωt The ere term ha an ampltue f V 00 an a ecn-harmnc trtn term wth an ampltue f V 0.5. There are n hgher rer trtn term we hae D V V r 0.5%. / + D + D % D D D (b ( t 00 ( t ( t c( ω t + 5 c ( ωt 500 c( ω t c(ωt The ere term ha an ampltue f V 500 an a ecn-harmnc trtn term wth an ampltue f V.5. There are n hgher rer trtn term we hae D V V r.5%. / D D + D + D4... D.5% E.7 Wth the nput termnal te tgether an a -V gnal apple, the fferental gnal zer an the cmmn-me gnal V. The cmmn-me gan V V 0. / 0., whch equalent t -0 cm / cm 0lg / B. Then we hae CM ( cm 0lg(500, B. E.8 (a V ( + / 0 V cm ( + / + cm cm Thu ( / +. 5

6 (b 0 V ( + / V cm ( + Thu cm. cm cm cm (c ( / + ( / cm CM 0lg 0lg cm CM 0lg 0lg 40.0 B E.9 Except fr numercal alue th Exerce the ame a Example. n the bk. Wth equal retance at the nput termnal, the ba current make n cntrbutn t the utput ltage. The extreme cntrbutn t the utput ue t the ffet ltage are n VV ff Vff + + n ( ± 0 0 ±.5 V ( The extreme cntrbutn t the utput ltage ue t the ffet current are Iff n( + V Iff n ± ( ±.5 V ( Thu, the extreme utput ltage ue t all urce are ±. 75 V. E.0 Th Exerce mlar t Example. n the bk wth 50 kω an 0. Wth unequal retance at the nput termnal, the ba current make a cntrbutn t the utput ltage gen by n VBa I B + n V

7 The extreme cntrbutn t the utput ue t the ffet ltage are n VV ff Vff n ( ± 0 0 ±. V ( The extreme cntrbutn t the utput ltage ue t the ffet current are Iff n( + V Iff n ± ( ± 0.8 V ( Thu, the extreme utput ltage ue t all urce are a mnmum f.5 V an a maxmum f 0.8 V. nwer fr Selecte Prblem P.4* G.5 0 P.5* Ω P.8*. 7 Ω. P.* P.7* n MΩ kω kω c. 0 P.9* Fe amplfer mut be cacae t attan a ltage gan n exce f

8 P.* P P P P W P.* G 0 P 9.87 W η 7.% P.* The ltage-amplfer mel : The trancnuctance-amplfer mel : P.5* c c 00 kω mc P.4* x. Ω P.44* T ene the pen-crcut ltage f a enr, we nee an amplfer wth ery hgh nput retance (cmpare t the Théenn retance f the enr. T a lang effect by the arable la retance, we nee an amplfer wth ery lw utput retance (cmpare t the mallet la retance. Thu, we nee a nearly eal ltage amplfer wth a gan f 000. P.45* The nput retance that f the eal tranretance amplfer whch zer. The utput retance f the cacae the utput retance f the eal trancnuctance amplfer whch nfnte. n amplfer 8

9 hang zer nput retance an nfnte utput retance an eal current amplfer. l, we hae G. c mc mc P.49* We nee a nearly eal trancnuctance amplfer. 98 kω 9.7 kω P.55* The cmplex gan fr the 000-Hz cmpnent 00 0 The cmplex gan fr the 000-Hz cmpnent 75 0 P.5* The gnal t be amplfe the hrt-crcut current f an electrchemcal cell (r battery. Th gnal c an therefre a ccuple amplfer neee. P.58* f 0. 4f hp B P.* The gan at 000 Hz mut be The utput gnal t c 000π t 45 + c 4000πt 90 The plt are: ( ( ( P.9* t r. µ Percentage tlt 8.8% 9

10 P.70* (a (b (c P.7* D 0. 0 D 0.0 D 4 0 D 0. 0 P.78* CM 47.9 B P.8* The extreme alue f the utput ltage are: ±5 mv 0

11 If the retr are exactly equal, then the utput ltage zer. P.8* The utput ltage can range frm -. t +. V.