Chapter 14, Problem 1. Find the transfer function V o. /V i. of the RC circuit in Fig Express it using ω = 1/RC. Figure For Prob - PDF

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Chapter 4, Prblem. Fnd the traner unctn V /V the C crcut n Fg Expre t ung /C. Fgure 4.68 Fr Prb. 4.. Chapter 4, Slutn. V H ( ) V H() jc jc jc j 0 j 0, where 0 C H 0 π - H ( ) φ H ( ) tan ( 0 ) 0

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Chapter 4, Prblem. Fnd the traner unctn V /V the C crcut n Fg Expre t ung /C. Fgure 4.68 Fr Prb. 4.. Chapter 4, Slutn. V H ( ) V H() jc jc jc j 0 j 0, where 0 C H 0 π - H ( ) φ H ( ) tan ( 0 ) 0 Th a hghpa lter. The requency repne the ame a that r P.P.4. except that 0 C. Thu, the ketche H and φ are hwn belw. H /C φ /C POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem. Obtan the traner unctn V ()/V the crcut n Fg Fgure 4.69 Fr Prb. 4.. Chapter 4, Slutn. V H() V / / 8 8 / 8 / POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem. Fr the crcut hwn n Fg. 4.70, nd H() V /V (). Fgure 4.70 Fr Prb Chapter 4, Slutn. 0.F 5 jc (0.) 0.F 0 (0.) The crcut becme that hwn belw. V V _ 0 5 V _ et (5 ) 5( ) 0 5 0( ) //(5 ) ( ) ( ) V V 5 V V V V 5 5/ 0( ) V ( ) 0 5 H() V 0( ) ( ) ( ) 0( ) 8 5 POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 4. Fnd the traner unctn H( ) V O /V the crcut hwn n Fg Fgure 4.7 Fr Prb Chapter 4, Slutn 4. (a) jc jc H ( ) V V jc j jc j( jc) (b) H() H ( ) H() - C j j jc( j) j jc jc( j) - C jc C jc POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 5. Fr each the crcut hwn n Fg. 4.7, nd H() V ()/V (). Fgure 4.7 Fr Prb Chapter 4, Slutn 5. (a) et // V V V H() V ( ) (b) et x // C C C C V V V H() V C C C POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 6. Fr the crcut hwn n Fg. 4.7, nd H() I ()/I (). Fgure 4.7 Fr Prb Chapter 4, Slutn 6. H j et // We cnvert the current urce t a vltage urce a hwn belw. S I _ V _ ( ) I I V I x I V I I I H() I ( ) POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 7. Calculate H ( ) H db equal (a) 0.05dB (b) -6. db (c) 04.7 db Chapter 4, Slutn 7. (a).05 0lg 0 0 H lg0 H.5 H (b) (c) lg H 0. lg H H lg0 H 5.5 lg0 H H 5 Chapter 4, Prblem 8. Determne the magntude (n db) and the phae (n degree) H( ) at H ( ) equal 0 j (a) 0.05 db (b) 5 (c) j Chapter 4, Slutn 8. (a) H HdB 0lg , φ 0 (b) H 5 HdB 0lg , φ 0 j0 (c) H () j 0lg , φ 6.4 HdB (d) H ().9 j j j HdB 0lg , φ 4.7 (d) j 6 j POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 9. A ladder netwrk ha a vltage gan H( ) ( 0 j )(0 j) Sketch the Bde plt r the gan. Chapter 4, Slutn 9. H ( ) ( j)( j 0) H db -0 lg0 j 0lg0 j/0 - φ - tan ( ) tan ( - /0) The magntude and phae plt are hwn belw. H db lg0-0 j/ lg0 j φ arg j/0 arg j -80 POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 0. Sketch the Bde magntude and phae plt : 50 H(j ) j (5 j) Chapter 4, Slutn 0. H (j) 50 j(5 j) 0 j j 5 H db lg lg j 00 0lg j 5 φ arg j / 5 arg j -80 POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem. Sketch the Bde plt r 0 j H( ) j( j) Chapter 4, Slutn. 5( j 0) H ( ) j( j ) H db 0lg0 5 0lg0 j 0 0lg0 j 0lg0 j - φ -90 tan 0 tan - The magntude and phae plt are hwn belw. H db φ POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem. A traner unctn gven by T() ( 0) Sketch the magntude and phae Bde plt. POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Slutn. 0.( j) T ( w), 0lg0. 0 j( j /0) The plt are hwn belw. T (db) arg T POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem. Cntruct the Bde plt r G(), j ( 0) Chapter 4, Slutn. j ( 0)( j) G ( ) (j) (0 j) (j) ( j 0) G db -0 0lg0 j 40lg0 j 0lg0 - - φ -80 tan tan 0 j 0 The magntude and phae plt are hwn belw. G db φ POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 4. Draw the Bde plt r 50( j ) H( ) j( 0 j 5) Chapter 4, Slutn H ( ) 5 j j j0 j 5 5 H db lg 0lg j 0lg j 0lg 0 j 5 (j 5) φ -90 tan tan 5 The magntude and phae plt are hwn belw. H db φ POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 5. Cntruct the Bde magntude and phae plt r 40( ) H(), j ( )( 0) Chapter 4, Slutn 5. H ( ) 40( j) ( j)(0 j) ( j) ( j )( j 0) H db 0lg0 0lg0 j 0lg0 j 0lg0 j φ tan tan tan - The magntude and phae plt are hwn belw. 0 H db φ POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 6. Sketch Bde magntude and phae plt r H() ( 0, j 6) Chapter 4, Slutn 6. 0 / H ( ) j j j j j j 4 4 j HdB 0lg lg j 0lg j 4 (0lg0, ) The magntude and phae plt are hwn belw. H 0 0 lg (j) lg j j φ tan - 6 POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 7. Sketch the Bde plt r G(), j ( ) ( ) Chapter 4, Slutn 7. G ( ) ( 4) j ( j)( j ) G db -0lg0 4 0lg0 j 0lg0 j 40lg0 j - φ tan tan - The magntude and phae plt are hwn belw. G db φ POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 8. A lnear netwrk ha th traner unctn H() ( 7 4, j 8 4 5) Ue MATAB r equvalent t plt the magntude and phae (n degree) the traner unctn. Take 0. 0 rad/. Chapter 4, Slutn 8. The MATAB cde hwn belw. wlgpace(-,,00); *w; h(7*.^4)./(.^8*.^4*5); Phaeunwrap(angle(h))*57.; emlgx(w,phae) grd n H(jw) Phae w POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Nw r the magntude, we need t add the llwng t the abve, Hab(h); HdB0*lg0(H); emlgx(w,hdb); grd n HdB w POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 9. Sketch the aympttc Bde plt the magntude and phae r 00 H(), j ( 0)( 0)( 40) Chapter 4, Slutn j j / 80 H ( ) ( j 0)( j 0)( j 40) j j j ( )( )( ) j j j HdB 0lg(/ 80) 0lg j / 0lg 0lg 0lg (0lg(/80) -8.06) The magntude and phae plt are hwn belw. H 0 lg j lg j 0 lg φ POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 0. Sketch the magntude Bde plt r the traner unctn 0 j H( ) ( j )( j 5) ( j 40) Chapter 4, Slutn 0. 0 j j /00 H ( ) (5)(40)( j )( j / 5) ( j / 40) ( j )( j / 5) ( j / 40) 0lg(/00) -40 The magntude plt hwn belw lg j 0 lg j lg lg j lg j 5 POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem. Sketch the magntude Bde plt r ( 0) H(), j ( )( 60) (400) Chapter 4, Slutn. j( j 0) 0 j( j/ 0) H ( ) ( j )( 60 j 400) j 400( j )( 60 j/ 400 ) j( j/ 0) H ( ) 6j j ( j) 40 0 j HdB 0 lg(0.05) 0lg j 0 lg 0 The magntude plt a ketched belw. H&B 40 0lg j 0 0 lg j 0 lg 0 lg j/0 j6 j lg lg j lg j6 j 40 0 POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem. Fnd the traner unctn H( ) wth the Bde magntude plt hwn n Fg Fgure 4.74 Fr Prb. 4.. Chapter 4, Slutn. 0 0lg0 k k 0 A zer lpe A ple lpe A ple lpe 0 db/ dec at j - 0 db/ dec at - 0 db/ dec at 0 00 j 0 j 00 Hence, H ( ) H() 0( j ) ( j 0)( j 00) 0 4 ( j) (0 j)(00 j) POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem. The Bde magntude plt H( ) hwn n Fg Fnd H( ). Fgure 4.75 Fr Prb. 4.. Chapter 4, Slutn. A zer lpe 0 db/ dec at the rgn j A ple lpe - 0 db/ dec at j A ple lpe - 40 db/ dec at 0 ( j 0) Hence, H ( ) j ( j)( j 0) 00 j H() ( j)(0 j) POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 4. The magntude plt n Fg repreent the traner unctn a preampler. Fnd H(). Fgure 4.76 Fr Prb Chapter 4, Slutn lg0 K K 00 There a ple at 50 gvng /(j/50) There a zer at 500 gvng ( j/500). There anther ple at gvng /( j/). Thu, r 40 x ( 500) 40( j / 500) H ( ) 500 ( j/ 50)( j/ ) x ( 50)( ) ( 500) H() ( 50)( ) POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 5. A ere C netwrk ha k Ω, 40 mh, and C µ F. Calculate the mpedance at renance and at ne-urth, ne-hal, twce, and ur tme the renant requency. POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Slutn 5. - C (40 0 )( ( 0 ) ( 0 kω 0 4) j 4 ) 4 C 0 5 krad / ( 0 4) 000 j (5 0 )( 0 ) ( 0 4) 000 j( ) ( 0 4) ( 0 j0.75 kω 0 ) j C 0 (5 0 ) - ( 0 ) 000 j (40 0 ) -6 (5 0 )( 0 ) ( 0 /) 00j(00-000/5) ( 0 ) j0. kω ( 0 ) j 0 C 0 - ( 0 ) 000 j ()(5 0 )(40 0 ) -6 ()(5 0 )( 0 ) ( 0 ) j0. kω (4 0 ) j C 0 - ( 4 0 ) 000 j (4)(5 0 )(40 0 ) -6 (4)(5 0 )( 0 ) ( 4 0 ) j0.75 kω POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 6. A cl wth retance Ω and nductance 00 mh cnnected n ere wth a capactr 50 pf, a retr 6 Ω and a gnal generatr that gve 0 V rm at all requence. Calculate, Q, and B at renance the reultant ere C crcut. Chapter 4, Slutn 6. Cnder the crcut a hwn belw. Th a ere C renant crcut. 6 Ω 50 µf Ω _ 00 mh 6 9 Ω 447. krad/ C 00x0 x50x0 447.x0 x00x0 Q x0 B 90 rad/ Q 4969 POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 7. Degn a ere C renant crcut wth 40 rad/ and B 0 rad/. Chapter 4, Slutn C C 40 B 0 0 I we elect Ω, then /0 0. H and C 6.5 mf x0. Chapter 4, Prblem 8. Degn a ere C crcut wth B 0 rad/ and,000 rad/. Fnd the crcut Q. et 0 Ω. Chapter 4, Slutn 8. et 0 Ω H B 0 µ F (000) (0.5) C 0 0 Q B Therere, 0 Ω then 0.5 H, C µ F, Q 50 POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 9. et v 0 c(at) V n the crcut Fg Fnd, Q, and B, a een by the capactr. Fgure 4.77 Fr Prb Chapter 4, Slutn 9. We cnvert the vltage urce t a current urce a hwn belw. k 45 k µf 60 mh 0 c t, //45 x45/ kω 4.08 krad/ 6 C 60x0 xx0 B rad/ C x 0 x Q B POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 0. A crcut cntng a cl wth nductance 0 mh and retance 0 Ω cnnected n ere wth a capactr and a generatr wth an rm vltage 0 V. Fnd: (a) the value the capactance that wll caue the crcut t be n renance at 5 khz (b) the current thrugh the cl at renance (c) the Q the crcut Chapter 4, Slutn 0. Select 0 Ω H 50 mh 0Q (0)(0) C 0. F 0 (00)(0.05) B 0.5 rad / C (0)(0.) Therere, 0 Ω then 50 mh, C 0. F, B 0.5 rad / Chapter 4, Prblem. Degn a parallel renant C crcut wth 0rad/ and Q 0. Calculate the bandwdth the crcut. et 0Ω. Chapter 4, Slutn. X X B X 6 πx0x0 x5.6x0 40x x0 rad/ POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem. A parallel C crcut ha the llwng value: 60 Ω, mh, and C 50 µ F. Fnd the qualty actr, the renant requency, and the bandwdth the C crcut. Chapter 4, Slutn krad/ 6 C 0 x50x0 B. rad/ C 6 60 x 50 x Q.4 B. Chapter 4, Prblem. A parallel renant crcut wth qualty actr 0 ha a renant requency rad/. Calculate the bandwdth and hal-pwer requence. Chapter 4, Slutn. Q 80 Q C C π 6 πx5.6x0 x40x0 pf 40x0 Q 4. µh Q 6 π πx5.6x0 x80 Chapter 4, Prblem 4. A parallel C crcut renant at 5.6 MHz, ha a Q 80, and ha a retve branch 40 k Ω. Determne the value and C n the ther tw branche. Chapter 4, Slutn 4. (a) C 6 8x0 x60x0.44 krad/ (b) B C 5x0 x60x0 6. rad/ 6 (c) Q C.44x0 x5x0 x60x POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 5. A parallel C crcut ha 5k Ω, 8 mh, and C µ F. Determne: (a) the renant requency (b) the bandwdth (c) the qualty actr Chapter 4, Slutn 5. At renance, Y 40 Ω Y Q 80 Q 0C C 0 µ F 0 (00 0 )(40) µ C C (4 0 )(0 0 ) 0 H B.5 krad / Q 80 B krad/ B krad/ POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 6. It expected that a parallel C renant crcut ha a mdband admttance 5 0 S, qualty actr 80, and a renant requency 00 krad/. Calculate the value,, and C. Fnd the bandwdth and the hal-pwer requence. Chapter 4, Slutn 6. 0 C 5000 rad / Y( 0 ) ( 0 ) kω Y ( ) j C 0.5 j8.75 ms 4 0 ( 0 4).4 j5. Ω j Y ( 0 0 ) j C 0.5 j7.5 ms 0 ( 0 ) 8.85 j. 74 Ω j Y (0 ) j j7.5 ms 0C ( 0 ) 8.85 j. 74 Ω Y (40 ) j j8.75 ms 4 0C ( 4 0 ).4 j5. Ω POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 7. ewrk Prb. 4.5 the element are cnnected n parallel. Chapter 4, Slutn 7. ) C ( ) C j( j C j C j ) C j ( j ) C j //( j ) C (C 0 ) C ( C C Im() Thu, C C Chapter 4, Prblem 8. Fnd the renant requency the crcut n Fg Fgure 4.78 Fr Prb Chapter 4, Slutn 8. Y jc j j jc At renance, Im( Y ) 0,.e C 0 C 0 0 C 484 rad / 0 ( )( ) POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 9. Fr the tank crcut n Fg. 4.79, nd the renant requency. Fgure 4.79 Fr Prb. 4.9 and 4.9. Chapter 4, Slutn 9. (a) B π( ) π(90 86)x0 π 8 krad / ( ) π(88)x0 76πX0 B C C B 8πx0 xx0 9.89nF (b) µh C 9 C (76πX0 ) x9.89x0 (c ) 76π 55.9krad / (d) B 8π 5.krad / 76π (e) Q B 8π POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 40. A parallel renance crcut ha a retance k Ω and hal-pwer requence 86 khz and 90 khz. Determne: (a) the capactance (b) the nductance (c) the renant requency (d) the bandwdth (e) the qualty actr Chapter 4, Slutn 40. (a) mh 0 C 5x0 6 x0x0.857 k rad/ec Q 0C.857x0 x5x0 x0x0 9.8 B rad/ C 6 5x0 0x0 6 (b) T ncreae B by 00% mean that B 4. C B 5x0 x4 0 µf Snce C C C 0µ F and C 0 µf, we then btan C 0 µf. C C Therere, t ncreae the bandwdth, we merely add anther 0 µf n ere wth the rt ne. POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 4. Fr the crcut hwn n Fg. 4.80, next page: (a) Calculate the renant requency, the qualty actr Q, and the bandwdth B. (b) What value capactance mut be cnnected n ere wth the 0- µ F capactr n rder t duble the bandwdth? Fgure 4.80 Fr Prb Chapter 4, Slutn 4. (a) Th a ere C crcut. 6 8 Ω, H, C 0.4 F 0.58 rad / C 0.4 Q B 8 rad / (b) Th a parallel C crcut. ()(6) µ F and 6 µ F µ F 6 C µ F, kω, 0 mh C ( 0 )(0 0 5 krad / ) (5 0 )(0 0 Q ) B rad/ C ( 0 )( 0 ) POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 4. Fr the crcut n Fg. 4.8, nd the renant requency, the qualty actr Q, and the bandwdth B. Fgure 4.8 Fr Prb POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Slutn 4. (a) ( jc) ( j) n n n j jc j C jc j jc ( j)( C jc) ( C) C At renance, Im( n ) 0,.e. 0 0( 0C) 0 C 0 C C C 0 C C (b) (j jc) n n n (j jc) ( C) j jc ( C) jc ( C)[( C) jc] ( C) C At renance, Im( n ) 0,.e. 0 ( C) C C 0 0 C POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 4. Calculate the renant requency each the crcut n Fg Fgure 4.8 Fr Prb Chapter 4, Slutn 4. Cnder the crcut belw. /jc n j (a) j) ( jc) n ( n n n n n j j jc j j jc j jc j ( (- j ( j C) j)( j C) C - C j C C j( C j )[ C C j( C)] ( C C ( C) ) C) POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part At renance, Im( n ) 0,.e. 0 C( C) ( C C ) 0 C C 0 C ( C C ) C C C (0.0)( krad / -6 ) (0.) (9 0-6 ) (b) At 0.57 krad /, - j j(.57 0 )(0 0 ) j47.4 j47.4 j j0.0 j j47.4 jc j(.57 0 )(9 0 ) 6 n ( 0 ) ( j) ( jc) ( j0.0)(0. j47.4) n ( 0 ) ( j0.0) (0. j47.4) n ( 0 ) Ω POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 44. * Fr the crcut n Fg. 4.8, nd: (a) the renant requency (b) n ( ) Fgure 4.8 Fr Prb * An aterk ndcate a challengng prblem. Chapter 4, Slutn 44. We nd the nput mpedance the crcut hwn belw. j(/) /j /jc j j jc, jc C jc -j.5 j -j0.5 jc C v (t) and (t) are n phae when purely real,.e. C (C ) r C F C C Ω C V I ( )(0) 0 v (t) 0n(t) V,.e. V 0 V POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 45. Fr the crcut hwn n Fg. 4.84, nd, B, and Q, a een by the vltage acr the nductr. Fgure 4.84 Fr Prb Chapter 4, Slutn 45. Cnvert the vltage urce t a current urce a hwn belw. I 0 kω 50 µf 0 mh 50 kω 0//50 0x50/ kω Th a parallel renant crcut rad/ 6 C 0x0 x50x0 B.067 rad/ C x 0 x 50 x Q 49. B.067 POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 46. Fr the netwrk llutrated n Fg. 4.85, nd (a) the traner unctn H( ) V ( )/I( ), (b) the magntude H at rad/. Fgure 4.85 Fr Prb. 4.46, 4.78, and 4.9. Chapter 4, Slutn 46. (a) Th an C ere crcut. C (πx5x0 ) C x0x0.6nf (b), I V/ 0/0 6 A πx5x0 x0x0 (c ) Q 5π POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 47. Shw that a ere crcut a lwpa lter the utput taken acr the retr. Calculate the crner requency c mh and 0 k Ω. Chapter 4, Slutn 47. H ( ) V V j j Hence, H (0) and H ( ) 0 hwng that th crcut a lwpa lter. At the crner requency, H( c ),.e. c r c c π c c c π π khz POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 48. Fnd the traner unctn V /V the crcut n Fg Shw that the crcut a lwpa lter. Fgure 4.86 Fr Prb Chapter 4, Slutn 48. H ( ) H ( ) H() jc j jc jc jc jc j jc j C H (0) and H ( ) 0 hwng that th crcut a lwpa lter. POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 49. Determne the cut requency the lwpa lter decrbed by 4 H( ) j0 Fnd the gan n db and phae H( ) at rad/. Chapter 4, Slutn 49. Hence, 4 At dc, H (0). H ( ) H(0) c c c 0. H() 4 j0 j0 H () In db, 0lg0 H() arg H() -tan POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 50. Determne what type lter n Fg Calculate the crner requency c. Fgure 4.87 Fr Prb Chapter 4, Slutn 50. H ( ) V V j j H (0) 0 and H ( ) hwng that th crcut a hghpa lter. H ( r c ) c π c c c c π π Hz POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 5. Degn an lwpa lter that ue a 40-mH cl and ha a cut requency 5 khz. Chapter 4, Slutn 5. The lwpa lter hwn belw. v v - - H V V j j / c π c π c πx5x0 x40x0.56kω Chapter 4, Prblem 5. In a hghpa lter wth a cut requency 00 khz, 40 mh. Fnd. Chapter 4, Slutn 5. π c c 5 - π (π)(0 )(40 0 ) 5. kω c POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 5. Degn a ere C type bandpa lter wth cut requence 0 khz and khz. Aumng C 80 pf, nd,, and Q. Chapter 4, Slutn 5. π 0π 0 π π 0 B π 0 0 π 0 0 π Q 0.5 B π 0 C 0C.87 - (π 0 ) (80 0 ) H B B (π 0 )(.87) kω Chapter 4, Prblem 54. Degn a pave bandtp lter wth 0 rad/ and Q 0. Chapter 4, Slutn 54. Th an pen-ended prblem wth everal pble lutn. We may che the bandtp lter n Fg C 0.0 C Q 0 0 I we elect H, then 0.5 Ω, and C 0.0/ 0 mf. POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 55. Determne the range requence that wll be paed by a ere C bandpa lter wth 0 Ω, 5mH, and C 0.4 µ F. Fnd the qualty actr. Chapter 4, Slutn 55. C ( B 0 Q )( krad / ) 0 krad / 9.8 B krad / r.56 khz π 0. B krad / r.6 khz π Therere,.56 khz .6 khz POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 56. (a) Shw that r a bandpa lter, B H(), jw B 0 where B bandwdth the lter and the center requency. (b) Smlarly, hw that r a bandtp lter, 0 H(), jw B 0 Chapter 4, Slutn 56. (a) Frm Eq 4.54, H () C C C C C Snce B and 0, C B H() B 0 (b) Frm Eq. 4.56, C H () C C C 0 H() B 0 POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 57. Determne the center requency and bandwdth the bandpa lter n Fg Fgure 4.88 Fr Prb POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Slutn 57. (a) Cnder the crcut belw. I I /C V /C V () C C C () C( C) C C () C( C) V I C V I I C ( C) C C C V I V C( C) C C C V H () V C C C C H () C C Thu, 0 r rad / C C 0 B C rad / POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part (b) Smlarly, ( ) () ( ) () V I, I I V ( ) V I V V H () V Thu, rad / 0 B rad / POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Chapter 4, Prblem 58. The crcut parameter r a ere C bandtp lter are k Ω, 0. H, C 40 pf. Calculate: (a) the center requency (b) the hal-pwer requence (c) the qualty actr Chapter 4, Slutn 58. (a) - C (0.)(40 0 ) rad / (b) 0 4 B Q 5 B 4 0 A a hgh Q crcut, B (50 ) 490 krad / B (50 ) 50 krad / (c) A een n part (b), Q 5 POPIETAY MATEIA. 007 The McGraw-Hll Cmpane, Inc. All rght reerved. N part Cha
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