Download Chapter 14-Electrical Circuit Analysis-Problem Solutions and more Exercises Electrical Circuit Analysis in PDF only on Docsity! Chapter 14, Problem 1. Find the transfer function V o /V i of the RC circuit in Fig. 14.68. Express it using oω = 1/RC. Figure 14.68 For Prob. 14.1. Chapter 14, Solution 1. RCj1 RCj Cj1R R )( i o ω+ ω = ω+ ==ω V V H =ω)(H 0 0 j1 j ωω+ ωω , where RC 1 0 =ω 2 0 0 )(1 )(H ωω+ ωω =ω= H ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ω ω − π =ω∠=φ 0 1-tan 2 )(H This is a highpass filter. The frequency response is the same as that for P.P.14.1 except that RC10 =ω . Thus, the sketches of H and φ are shown below. 0 90° 45° ω0 = 1/RC ω φ 0 1 0.7071 ω0 = 1/RC ω H docsity.com Chapter 14, Problem 2. Obtain the transfer function V o (s)/V i of the circuit in Fig. 14.69. Figure 14.69 For Prob. 14.2. Chapter 14, Solution 2. 6667.0s 4s 6 1 s/812 s/82 8/s 12010 8/s 12 V V )s(H i o + + = + + = ++ + == docsity.com Chapter 14, Problem 5. For each of the circuits shown in Fig. 14.72, find H(s) = V o (s)/V s (s). Figure 14.72 For Prob. 14.5. Chapter 14, Solution 5. (a) Let // sRLZ R sL R sL = = + o s s ZV V Z R = + ( ) ( ) o s s s s s sRL V Z sRLR sLH s sRLV Z R RR s R R LR R sL += = = = + + ++ + (b) Let 1 1// 1 1 Rx RsCZ R sC sRCR sC = = = ++ o s ZV V Z sL = + RsLLRCs R sRC1 RsL sRC1 R sLZ Z V V )s(H 2i o ++ = + + += + == docsity.com Chapter 14, Problem 6. For the circuit shown in Fig. 14.73, find H(s) = I o (s)/I s (s). Figure 14.73 For Prob. 14.6. Chapter 14, Solution 6. 1H j L sL sω⎯⎯→ = = Let //1 1 sZ s s = = + We convert the current source to a voltage source as shown below. 2 2 1( 1) 1 ( 1) 3 11 1 s s o s s s sI sIZ sV I x IsZ s s s s ss s += = = = + + + + + ++ + + 21 3 1 o s o V sII s s = = + + 2( ) 3 1 o s I sH s I s s = = + + + _ Vo Is ⋅ 1 Z 1 S + _ docsity.com Chapter 14, Problem 7. Calculate )(ωH if H dB equals (a) 0.05dB (b) -6.2 dB (c) 104.7 dB Chapter 14, Solution 7. (a) Hlog2005.0 10= Hlog105.2 10-3 =× == × -3105.210H 005773.1 (b) Hlog206.2- 10= Hlog0.31- 10= == -0.3110H 4898.0 (c) Hlog207.104 10= Hlog235.5 10= == 235.510H 510718.1 × Chapter 14, Problem 8. Determine the magnitude (in dB) and the phase (in degrees) of H(ω ) = at ω = 1 if H ( )ω equals (a) 0.05 dB (b) 125 (c) ω ω j j +2 10 (d) ωj+1 3 + ωj+2 6 Chapter 14, Solution 8. (a) 05.0H = == 05.0log20H 10dB 26.02- , =φ °0 (b) 125H = == 125log20H 10dB 41.94 , =φ °0 (c) °∠= + = 43.63472.4 j2 10j )1(H == 472.4log20H 10dB 01.13 , =φ °43.63 (d) °∠=−= + + + = 34.7-743.47.2j9.3 j2 6 j1 3)1(H = , =φ –34.7˚ docsity.com ω ) = )2( 10 ωω ω jj j + + Chapter 14, Solution 11. )2j1(j )10j1(5 )( ω+ω ω+ =ωH 2j1log20jlog2010j1log205log20H 10101010dB ω+−ω−ω++= 2tan10tan90- -1-1 ω−ω+°=φ The magnitude and phase plots are shown below. φ -45° 45° ω1001 10 0.1 -90° 90° HdB -20 20 ω1001 10 0.1 -40 40 34 14 docsity.com )10( 1 + + ss s Sketch the magnitude and phase Bode plots. docsity.com Chapter 14, Solution 12. 201.0log20, )10/1( )1(1.0)( −= + + = ωω ω jj jwT The plots are shown below. |T| (db) 20 0 ω 0.1 1 10 100 -20 -40 arg T 90o 0 ω 0.1 1 10 100 -90o docsity.com
