Ch07s - Chapter 7 Problem Solutions 7.1 a. T (s) = T (s) =...

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Chapter 7 Problem Solutions 7.1 a. () 01 11 1/ 1 1 i Vs s C Ts s CR sR C == + ⎡⎤ ⎣⎦ = + b. ± T ± 1 f H ± 159 Hz f ( ) 36 159 Hz 2 21 0 HH ff RC π = c. () () 0 1 1 i Vs Vs sRC =⋅ + For a step function 1 i s = 12 0 1 2 1 1 2 1 1 1 0 / 0 1 1 1 and 1 1 1 1 1 tRC KK s sR C s sR C Ks R C K s ss R C K R CK R C R C K R C s s vt e = + ++ = + = + =− = =+ + + 7.2 a. 0 2 22 1 i R Rs C sR C sR C + = + b.
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± T ± 1 f L ± 1.59 Hz () ( ) 46 22 11 1.59 Hz 2 21 0 1 01 0 LL ff RC π == = × c. () () 0 0 / 0 1 1 1 1 1 i i tRC sR C Vs Vs sR C Vs s sR C s vt e =⋅ + = + + = 7.3 a. 0 1 1 1 1 1 P P i PS P PP P P P P R sC Ts RR s Cs C R sC R R sC sR C R sC ⎛⎞ ++ ⎜⎟ ⎝⎠ + + & & & Then 1 1 1 1 1/ 1 P P P S P S P P SS P P PSS SP S R s R C sC R s R R C C sR R C C RRCs RRCRR = + = + + ⎡⎤ + + + ⎢⎥ + + ⎣⎦ b.
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() 11 31 1 6 46 8 8 10 10 10 1 1/ 1 5 10 10 10 10 20 10 21 0 1 0 11 1 2 15 1 0 0.02 2 1 1 0 0.02 Ts s s s s sj Tj j ω ⎛⎞ ⎜⎟ + + + × + ×⋅ ⎝⎠ ≅⋅ ++ × = =⋅ ⎡⎤ ⎢⎥ ⎣⎦ ( ) ( ) 8 For 50 0 2 1 0 5 1 0 50 0.02 2 2 L SR S RRC j j == = + × ≈⋅ For ( ) ( ) 7 1 78 7 0 51 0 2 1 12 1 0 5 1 0 0 0 . 0 2 2 2 1 In each case, 2 H SP P P PS j j R RR ωω = × × ×− × + + & c. ( ) 37 47 4 3 10 k , 0.1 F 1 1 1/ 1 5 10 10 22 1 0 2 1 0 2 0 CC s s j μ Ω +⋅+ + × × = × × ( ) 4 3 1 For 500 0 2 1 1.5 500 5 10 500 2 10 0.298 2 1.5 0.75 j j × × =
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() ( ) ( ) ( ) 3 37 34 33 1 For 2 10 51 0 1 0 11 1/ 1.5 2 10 5 10 2 21 0 21 0 0.298 2 1.5 0.75 1 In each case, 2 P PS Tj j j R RR ω == × × ⎧⎫ ⎛⎞ ⎡⎤ ⎪⎪ ⎜⎟ ⎢⎥ =⋅ + × × ⎨⎬ ×× ⎣⎦ ⎝⎠ ⎩⎭ = + <⋅ + 7.4 Circuit (a): 0 22 2 2 1 1 1 1 1 2 1 1 1 2 1 2 1 2 1/ 1 or 1 1 i o i V T Rs C V R R C sC R C s R C V R R R CR V RR s C R sR C = + + + ++ = + + + + Low frequency: 2 12 20 2 10 20 3 o i V R VR R === High frequency: ( ) 46 1 1 1 36 1 2 2 2 2 1 1 10 10 10 0.10 1.59 2 1 10 20 10 10 10 0.0667 2.39 2 o i V V RC f Hz RR C f H z τ πτ ττ = × = × × × = ± T ± 1.0 0.67 1.59 2.39 f Circuit (b): 2 2 2 2 1 2 2 12 2 1 1 1 1 1 1 o i R R sC V sR C T R V R sR C sC R sRRC + = + + + = + + Low frequency: 2 20 2 20 10 3 10 20 10 10 10 0.0667 1 2.39 2 o i V R R RRC fH z × × × =
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± T ± 0.67 2.39 f 7.5 a. () [ ] 36 31 2 30 10 10 10 10 0.40 s 30 10 10 50 10 0.375 s Si P S S Pi P P P rR R C r R C r μ =+ =+×× × = == ⎡⎤ ×× × = ⎣⎦ b. 6 11 0.398 Hz 22 0 . 4 424 kHz 2 2 0.375 10 LL S HH P ff r r ππ π = = × At midband. S C short, P C open 30 10 7.5 oi i P i P VIR R Ts RR Ts k = c. ± T ± 7.5 k ± f L f H 7.6 (a) ( ) ( ) 2 2 max 2 10 1 12 1 1 At 1 20log 6 2 Phase 2tan 2 1 2 45 Phase 90 dB dB TT jf f f T fT d B f πτ −− = ++ + = = + ⎛⎞ = ≅− ⎜⎟ ⎝⎠ = ° =− ° (b) Slope 2 6 / 12 / 40 / Phase 2 90 Phase 180 dB oct dB oct dB decade ° ° 7.7 (a)
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() 3 4 4 22 10 20 1 2000 1 20 2000 51 0 2.5 10 11 2000 20 2000 2.5 10 20 2000 j Tj jj j j T ω ωω = ⎛⎞ ++ ⎜⎟ ⎝⎠ −× × == × = +⋅ + ± T ± 5 ± 10 ² 3 2.5 ± 10 ² 4 1 20 2000 ³ (b) 2 2 10 10 1 10 1000 1 1000 0.10 1 10 1 1000 j j T + = + + = + 10 0.10 10 1000 ± T ± ³ 7.8 (a) ( ) ( ) 105 10 5 55 5 10 5 500 10 500 10 500 10 10 500 10 500 Ts j =⋅
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± T ± 0.02 10 500 ± (rod/s) (b) Midband gain = 0.02 (c) 500 rad/s ω = (d) 10 rad/s = 7.9 (a) () 4 35 4 4 21 0 10
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This homework help was uploaded on 02/10/2008 for the course ECE 138 taught by Professor N/a during the Spring '08 term at CSU Fresno.

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Ch07s - Chapter 7 Problem Solutions 7.1 a. T (s) = T (s) =...

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