, where. This is a highpass filter. The frequency response is the same as that for P.P.14.1 RC. Thus, the sketches of H and φ are shown below.

Transcription

1 hapter 4, Slutn. H ( H(, where H π H ( φ H ( tan - ( Th a hghpa lter. The requency repne the ame a that r P.P.4. except that. Thu, the ketche H and φ are hwn belw. H.77 / φ 9 45 /

2 hapter 4, Slutn. H(, where H H ( φ H ( - tan - ( The requency repne dentcal t the repne n Example 4. except that. Hence the repne hwn belw. H.77 / φ / hapter 4, Slutn. (a The Thevenn mpedance acr the ecnd capactr where taken Th Th Th Th

3 Th Th ( ( Th H( ( ( Th ( ( ( H( -6 - (b (4 ( 8. 8 There are n zer and the ple are at hapter 4, Slutn 4. (a H ( ( (b H( H ( H( - ( ( -

4 hapter 4, Slutn 5. (a H ( H( (b H ( ( ( ( H( hapter 4, Slutn 6. (a Ung current dvn, I H ( I H ((.5 ((.5 ((.5 ( 5 H( 5.5 (b We apply ndal analy t the crcut belw. x I /.5 x I

5 I x x.5x But.5x I x ( I I x.5 I I ( ( I I ( I H I ( H ( (.5 ( ( H(.5 hapter 4, Slutn 7. (a (b (c.5 lg H -.5 lg H H lgh. lg H - -. H lg H.5 lg H 5 H

6 hapter 4, Slutn 8. (a H. 5 HdB lg. 5-6., φ (b H 5 HdB lg5 4.94, φ j (c H ( j HdB lg , φ (d H (.9 j j j H hapter 4, Slutn 9. db lg , φ -.55 H ( ( ( H db - lg lg - - φ - tan ( tan ( / / The magntude and phae plt are hwn belw. H db φ lg / lg arg / arg

7 hapter 4, Slutn. H ( 5 (5 5 H db 4 lg lg lg 5 φ arg / 5 arg -8 hapter 4, Slutn. H ( 5( ( H db lg 5 lg lg lg - φ -9 tan tan -

8 The magntude and phae plt are hwn belw. H db φ

9 hapter 4, Slutn..( T ( w, lg. ( / The plt are hwn belw. T (db arg T 9. -9

10 hapter 4, Slutn. ( ( G ( ( ( ( ( j G db - lg 4lg lg - - φ -8 tan tan The magntude and phae plt are hwn belw. G db φ

11 hapter 4, Slutn 4. H ( H db lg lg lg lg 5 (j 5 φ 9 tan tan The magntude and phae plt are hwn belw. H db φ

12 hapter 4, Slutn 5. H ( 4( ( ( ( ( ( H db lg lg lg lg - - φ tan tan tan - The magntude and phae plt are hwn belw. H db φ hapter 4, Slutn 6. G( (

13 G db - lg. 4lg -4-6 lg(/ 9 φ arg arg( arg hapter 4, Slutn 7. G ( ( 4 ( ( G db -lg 4 lg lg 4lg - φ -9 - tan tan - The magntude and phae plt are hwn belw. G db

14 φ hapter 4, Slutn 8. 4( G ( 5 ( 5( G db lg 4 5 4lg lg lg 5 lg where lg φ -9 tan tan 5 tan - The magntude and phae plt are hwn belw. G db φ

15 hapter 4, Slutn 9. H ( ( H lg lg lg db - φ 9 tan The magntude and phae plt are hwn belw. H db φ

16 hapter 4, Slutn. N ( ( ( ( N db lg lg lg - - φ tan tan tan - The magntude and phae plt are hwn belw. N db φ hapter 4, Slutn. ( T ( ( ( TdB lg lg lg

17 lg lg φ 9 tan tan tan The magntude and phae plt are hwn belw. T db φ hapter 4, Slutn. lg k k A zer lpe db / dec at A ple lpe - db / dec at

18 A ple lpe - db / dec at Hence, ( H ( ( ( H( 4 ( ( ( hapter 4, Slutn. A zer lpe db / dec at the rgn j A ple lpe - db / dec at A ple lpe - 4 db/ dec at ( Hence, H ( ( ( H( ( ( hapter 4, Slutn 4. The phae plt decmped a hwn belw. φ 9 45 arg ( / arg ( arg /

19 G ( k ( ( k (( ( where k a cntant nce arg k. Hence, G( k (, where k k ( cntant hapter 4, Slutn (4 ( kω ( 5 krad / ( 4 j ( 4 j (5 ( ( 4 j(5 4 5 ( 4 j.75 kω ( j (5 - ( j (4-6 (5 ( ( 4 j( 5 ( j. kω ( j

20 - ( j ((5 (4-6 ((5 ( ( j. kω (4 j ( 4 j (4(5 (4-6 (4(5 ( ( 4 j.75 kω hapter 4, Slutn 6. (a π π 5x 9 xx.5khz (b B x krad/ 6 x (c Q x hapter 4, Slutn 7. At renance, Ω, B and Q B Hence, Q ((8 6 H 5

21 Therere, 5 µ F (5 (6 B 6 Ω,.65 rad / 6 H, 5 µ F, B.65 rad / hapter 4, Slutn 8. et Ω..5 H B µ F ( (.5 Q B 5 Therere, Ω then.5 H, µ F, Q 5 hapter 4, Slutn 9. /

22 j Snce v (t and (t are n phae, Im( 4 -± rad /.68 hapter 4, Slutn. Select Ω. Q (( ((.5.5 H 5 mh. F B ((..5 rad / Therere, Ω then 5 mh,. F, B.5 rad / hapter 4, Slutn. X X B X 6 πxx x5.6x 4x x rad/

23 hapter 4, Slutn. Snce Q >, B, B B Q krad / rad / rad / hapter 4, Slutn. Q 8 Q π 6 πx5.6x x4x pf Q πq 4x 6 πx5.6x x8 4. µ H hapter 4, Slutn 4. (a 6 8x x6x.44 krad/ (b B 6 5x x6x. rad/ 6 (c Q.44x x5x x6x 4. 9

24 hapter 4, Slutn 5. At renance, Y Y 5-4 Ω Q 8 µ F ( (4 Q -6.5 µ H (4 ( B Q 8.5 krad / B krad / B. 5.5 krad / hapter 4, Slutn 6. 5 rad / Y( ( kω 4 Y ( 4 j.5 j8.75 ks 4 ( 4.5 j j5. Ω Y ( j.5 j7.5 ks

25 j.75.5 ( Ω 74 j j7.5 ks.5 j ( Y ( Ω 74 j j8.75 ks j (4 Y 4 ( Ω j5..4 hapter 4, Slutn 7. ( j( j j j j ( j j //( j ( ( Im( Thu, hapter 4, Slutn 8. j j j j Y At renance,,.e. Im( Y

26 (4 - ( rad / hapter 4, Slutn 9. (a B π( π(9 86x π 8 krad / ( π(88x 76π B B 8πx xx 9.89nF (b 64.4H 9 (76π x9.89x (c 76π 55.9krad / (d B 8π 5.krad / 76π (e Q B 8π hapter 4, Slutn 4. (a 5 5 mh 5x 6 xx.857 k rad/ec

27 Q.857x x5x xx 9.8 B rad 6 5x x (b T ncreae B by % mean that B 4. 6 B 5x x4 µf Snce µ F and µf, we then btan µf. Therere, t ncreae the bandwdth, we merely add anther µf n ere wth the rt ne. hapter 4, Slutn 4. (a Th a ere crcut. 6 8 Ω, H,.4 F.58 rad /.4 Q B 8 rad / (b Th a parallel crcut. ((6 µ F and 6 µ F µ F 6 µ F, kω, mh

28 ( ( 5 krad / -6 - (5 ( Q - ( ( 5 krad / B -6 hapter 4, Slutn 4. (a ( ( n n n ( ( ( At renance, Im(,.e. n ( (b ( n n ( ( ( n (- [( ( ] At renance, Im(,.e. n (

29 ( (c ( n n n ( ( ( ( [( ] ( At renance, Im(,.e. n ( hapter 4, Slutn 4. nder the crcut belw. / n (a ( n ( n

30 n j n ( ( ( n - ( n (- [ ( ] ( ( At renance, Im(,.e. n ( ( ( (.(9.57 krad / -6 (. (9-6 (b At.57 krad /, - j(.57 ( j47.4 j j. j j47.4 j(.57 (9 6 n ( ( (

31 n ( (.9996 j.(. j47.4 (.9996 j. (. j47.4 n ( Ω hapter 4, Slutn 44. We nd the nput mpedance the crcut hwn belw. (/ / /, j j -j.5 j -j.5 j v (t and (t are n phae when purely real,.e. -.5 ( r F Ω I ( ( v (t n(t,.e.

32 hapter 4, Slutn 45. (a, Tranrm the current urce gve the crcut belw. I I H( I ( (b H ( ( j H(. 5 ( hapter 4, Slutn 46. (a Th an ere crcut. (πx5x xx.6nf (b, I / / 6 A πx5x xx (c Q 5π 47.

33 hapter 4, Slutn 47. j j ( H ( H and ( H hwng that th crcut a lwpa lter. At the crner requency, ( H c,.e. c c r c Hence, c c π π π - c khz 796 hapter 4, Slutn 48. j j j ( H j j j j j ( H H( j ( H and hwng that ( H th crcut a lwpa lter.

34 hapter 4, Slutn At dc, H (. Hence, H ( H( 4 4 c 4 8 c c. H( 4 j j H (.99 In db, lg H( arg H( -tan hapter 4, Slutn 5. H ( H ( and H ( hwng that th crcut a hghpa lter. H ( c c c r c π c c π π. 8. Hz

35 hapter 4, Slutn 5. H ( (rm Eq. 4.5 Th ha a unty paband gan,.e. H (. 5 c H ^ j ( H ( 5 H( j 5 hapter 4, Prblem 5. Degn an lwpa lter that ue a 4-mH cl and ha a cut- requency 5 khz. hapter 4, Slutn 5. π c c - c 5 π (π( (4 5. kω hapter 4, Slutn 54. π π π π B π π

36 Q B π.5 π (π ( H B B (π ( kω hapter 4, Slutn 55. c π c π c πxx xx 65.kΩ hapter 4, Slutn (5 B - Q 5. 4 (.4.4 krad / krad / 9.8 B. 9.8 krad / r.56 khz π. B.. krad / r.6 khz π Therere,.56 khz < <.6 khz

37 hapter 4, Slutn 57. (a Frm Eq 4.54, H ( Snce B and, B H( B (b Frm Eq. 4.56, H ( H( B hapter 4, Slutn 58. (a nder the crcut belw. I I / / (

38 ( ( ( ( I ( I I ( I ( H ( H Thu, r rad / B rad / (b Smlarly, ( ( ( ( I, ( I I I

39 H ( Thu, rad / B rad / hapter 4, Slutn 59. (a - (.(4 6.5 rad / (b B. 4.5 B Q A a hgh Q crcut, B 4 (5 49 krad / B 4 (5 5 krad / (c A een n part (b, Q 5

40 hapter 4, Slutn 6. nder the crcut belw. / ( ( ( ( H ( n ( n n n ( ( ( ( Im( n mple that - [ ] (

41 5.8 krad / - -6 ( (4 H ( H max H( r H max H( lm j ( At and, H H mzx ( ( ( ( ( ( ( ( (96 ( -6 4 ( (96 ( -6 4 ( ( 4 ( (96 ( 4 ( ( (96 ( 4-8 ( 96 (

42 Hence, 4.65 krad / 7.6 krad / B krad / hapter 4, Slutn 6. (a, Snce, H( (b, Snce, H(

43 hapter 4, Slutn 6. Th a hghpa lter. H ( j H (, c π ( c H ( j c j (a H ( Hz j5 m j5.5 m (b H ( khz j.5 m j.5 7. m (c H ( khz j. m j. 9.4 m hapter 4, Slutn 6. Fr an actve hghpa lter, H( (

44 But / H( ( mparng ( and ( lead t: Ω M Ω k.. hapter 4, Slutn 64. j j j j j Hence, - ( H j ( j ( j - Th a bandpa lter. ( H mlar t the prduct the traner unctn a lwpa lter and a hghpa lter. hapter 4, Slutn 65. j j j Snce,

45 H( It evdent that a, the gan and that the crner requency. hapter 4, Slutn 66. (a Pr (b When 4, H ( 4 4 (c When, - H ( hapter 4, Slutn 67. D gan 4 4 rner requency c π (5 rad / I we elect kω, then 8 kω and 5.95 nf (π(5( Therere, kω, then 8 kω and 5.95 nf

46 hapter 4, Slutn 68. Hgh requency gan 5 5 rner requency c π ( rad / I we elect kω, then kω and 9.8 nf (π(( Therere, kω, then kω and 9.8 nf hapter 4, Slutn 69. Th a hghpa lter wth c khz. c π c πc 4π 8 Hz may be regarded a hgh requency. Hence the hgh-requency gan r.5 4 I we let kω, then 4π 5 kω, and nf.

47 hapter 4, Slutn 7. (a ( H ( ( Y Y Y Y Y (Y Y 4 Y where Y G, Y G, Y, Y 4. H( G G G G (G G GG (b H(, H ( GG hwng that th crcut a lwpa lter. hapter 4, Slutn 7. 5 Ω, 4 mh, µ F K K m K K m (4-5 K K m ( K K m -6 K K m 6 K ( K m Subttutng ( nt (, 6 K 5K K. - K m 5K 5 -

48 hapter 4, Slutn 7. K K (4 ( (( - -6 K 4-8 K -4 K m K m (( m ((4-6 K K 5 m hapter 4, Slutn 7. m K ((8 K m 8-6 (4 K 9.6 MΩ µ F K K m pf (8( hapter 4, Slutn 74. ' K m x Ω ' K m x kω ' K m K ( µ H 6 ' K K m 8 nf

49 hapter 4, Slutn 75. ' K m x Ω ' K K m 5 (4 4 µ H ' K mk 5 x µ F hapter 4, Slutn 76. ' K m 5x 5x 5 Ω ' K m K µ H 6 6 x x mh ' 4 pf K K m 4x x x 6 4 mf hapter 4, Slutn 77. and are needed bere calng. B H B 5.5 µ F (6( (a K m (6( H K m µ F

50 (b mh K.5 K -4.5 nf K m (4( (c 5 8 mh K K K -4.5 (4( 5 m 7.8 pf hapter 4, Slutn 78. m K (( kω K K m 4 (. H K K. µ F ( ( 4 m The new crcut hwn belw. kω I kω. H. µf kω x

51 hapter 4, Slutn 79. (a Inert a - urce at the nput termnal. I / There a upernde. ( But ( Al, ( mbnng ( and ( (4 4 Subttutng ( and (4 nt ( gve

52 I ( 4 n I 4 n 4 (5 When 5,,., ( n 8 5 At renance, Im( n 4 r.8 rad / (.( (b Ater calng, K m 4 Ω 4 Ω 5 Ω 5 Ω K K m (. H. K K (( m -4 Frm (5, ( n rad / -4 (.(

53 hapter 4, Slutn 8. (a m K (( 4 Ω K m (( mh K 4 K K.5.5 µ F (( 4 m The new crcut hwn belw. a mh I x.5 µf 4 Ω.5 I x b (b Inert a -A urce at the termnal a-b. a I x A /(.5 I x b At nde, ( At nde, But, I x..5i x

54 .5 ( Slvng ( and (,.5 Th.5 At 4, Th Th 4 (j ( 4 j 6 j.5 j (j ( (.5.5( j (.5-6 (4 Th hm hapter 4, Slutn 8. (a G (G ( whch lead t ( G G j ( ( G G We cmpare th wth the gven mpedance: ( ( ( 5

55 mparng ( and ( hw that mf, / G G ms Thu, G 5.4.4Ω,.4 H, mf, G ms (b By requency-calng, K..4 Ω, G ms.4 '.4mH, ' µ F K K hapter 4, Slutn 8. K m K K c K - K m 6 5 K m 5 kω, thu, kω

56 hapter 4, Slutn 8. µ F ' K mk 6 5 x.pf 5 µ F '.5 pf kω ' K m x kω MΩ kω ' MΩ hapter 4, Slutn 84. The chematc hwn belw. A vltage marker nerted t meaure v. In the A weep bx, we elect Ttal Pnt 5, Start Frequency, and End Frequency. Ater avng and mulatn, we btan the magntude and phae plt n the prbe menu a hwn belw.

57 hapter 4, Slutn 85. We let I A that / I. The chematc hwn belw. The crcut mulated r < < khz.

58 hapter 4, Slutn 86. The chematc hwn belw. A current marker nerted t meaure I. We et Ttal Pnt, tart Frequency, and End Frequency khz n the A weep bx. Ater mulatn, the magntude and phae plt are btaned n the Prbe menu a hwn belw.

59

60 hapter 4, Slutn 87. The chematc hwn belw. I n the A Sweep bx, we et Ttal Pnt 5, Start Frequency, and End Frequency. Ater mulatn, we btan the magntude repne a hwn belw. It evdent rm the repne that the crcut repreent a hgh-pa lter.

61 hapter 4, Slutn 88. The chematc hwn belw. We nert a vltage marker t meaure. In the A Sweep bx, we et Ttal Pnt, Start Frequency, and End Frequency. Ater mulatn, we btan the magntude and phae plt a hwn belw.

62 hapter 4, Slutn 89. The chematc hwn belw. In the A Sweep bx, we type Ttal Pnt, Start Frequency, and End Frequency k. Ater mulatn, the magntude plt the repne btaned a hwn belw.

63 hapter 4, Slutn 9. The chematc hwn belw. In the A Sweep bx, we et Ttal Pnt, Start Frequency, and End Frequency k. Ater mulatn, we btan the magntude plt the repne a hwn belw. The repne hw that the crcut a hgh-pa lter.

64 hapter 4, Slutn 9. The chematc hwn belw. In the A Sweep bx, we et Ttal Pnt, Start Frequency, and End Frequency k. Ater mulatn, we btan the magntude plt the repne a hwn belw. The repne hw that the crcut a hgh-pa lter.

65 hapter 4, Slutn 9. The chematc hwn belw. We type Ttal Pnt, Start Frequency, and End Frequency n the A Sweep bx. Ater mulatng the crcut, the magntude plt the requency repne hwn belw.

66 hapter 4, Slutn 9. π , (4 ( 88 Snce <<

67 8 98 khz π 4π I reduced t 4 Ω, <<. The reult reman the ame. hapter 4, Slutn 94. c We make and a mall a pble. T acheve th, we cnnect.8 kω and. k Ω n parallel that.8x..64 kω.8. We place the -pf and -pf capactr n ere that (x/4 7.5 pf Hence, c 4.55x.64x x7.5x 6 rad/ hapter 4, Slutn 95. (a π When 6 pf, π -6 - When 4 pf, π (4 (4 (6-6 - (4 Therere, the requency range.54 MHz < <.64 MHz.54 MHz.64 MHz

68 (b Q π At.54 MHz, Q 6 (π(.54 ( At.64 MHz, Q 6 (π(.64 ( hapter 4, Slutn 96. (

69 where and Therere, ( ( ( where. hapter 4, Slutn 97.

70 (, j H( ( ( ( ( H( ( ( ( where. hapter 4, Slutn 98. B π ( π ( π π QB ((44 π ((44π (( 44 Hz π hapter 4, Slutn 99. X c π π X c 6 (π( (5-9 π X π

71 X π (π( 6 4π π MHz -4-9 π 4π π B 4π ( rad / hapter 4, Slutn. π c c π (π( (.5-6 c 5.9 Ω hapter 4, Slutn. π c c π (π(5( -6 c.6 kω hapter 4, Slutn. (a When and, we have a lw-pa lter. π c c π (π(4 (4 c Hz

72 (b We btan Th acr the capactr. ( Th Th π 5 (4.5 kω (π(.5 (4 c -9 Th c.59 khz hapter 4, Slutn. H (, H ( ( ( ( H( ( hapter 4, Slutn 4. The chematc hwn belw. We clck Analy/Setup/A Sweep and enter Ttal Pnt, Start Frequency, and End Frequency k. Ater mulatn, we btan the magntude plt the repne a hwn.

73