Chapter 14, Problem 1. - UNLV

1 PROPRIETARY MATERIAL. 2007 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual, you are using it without permission. Chapter 14, Problem 1. Find the transfer function Vo/Vi of the RC circuit in Fig. Express it using o = 1/RC. Figure For Prob. Chapter 14, Solution 1. RCj1 RCjCj1RR)(io + = +== VVH = )(H00j1j + , where RC10= 200)(1)(H + = =H = = 01-tan2)(H This is a highpass filter.

2 The frequency response is the same as that for except that RC10= . Thus, the sketches of H and are shown below. 0 90 45 0 = 1/RC 0 1 0 = 1/RC H PROPRIETARY MATERIAL. 2007 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual, you are using it without permission.

3 Chapter 14, Problem 2. Obtain the transfer function Vo(s)/Vi of the circuit in Fig. Figure For Prob. Chapter 14, Solution 2. )s(Hio++=++=+++== PROPRIETARY MATERIAL. 2007 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual, you are using it without permission.

4 Chapter 14, Problem 3. For the circuit shown in Fig. , find H(s) = Vo/Vi(s). Figure For Prob. Chapter 14, Solution 3. ( )FjC ss == ( )Fss = The circuit becomes that shown below. Let 10510 1(5)5()10510(1)//(5)155(3)5(3)ssssssZsss ssss+++=+= = =+++ 12iZVVZ=+ 11555/112oissZVVVVsssZ=== ++++ 210(1)105(3)()10(1)12 (3) 10(1)852(3)oissssssVHsVsssssssss++== ==+++++++++ 2 + _ 5 10s Vi + _ Vo V1 5s PROPRIETARY MATERIAL. 2007 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation.

5 If you are a student using this Manual, you are using it without permission. Chapter 14, Problem 4. Find the transfer function H( ) = VO/Vi of the circuits shown in Fig. Figure For Prob. Chapter 14, Solution 4. (a) RCj1 RCj1||R += )RCj1(LjRRRCj1 RLjRCj1R)(io + += ++ +== VVH = )(HLjRRLC-R2 ++ (b) )LjR(Cj1)LjR(CjCj1 LjRLjR)( + + + = + + += H = )(HRCjLC1 RCjLC-22 + + PROPRIETARY MATERIAL. 2007 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation.

6 If you are a student using this Manual, you are using it without permission. Chapter 14, Problem 5. For each of the circuits shown in Fig. , find H(s) = Vo(s)/Vs(s). Figure For Prob. Chapter 14, Solution 5. (a) Let //sRLZRsLRsL==+ ossZVVZR=+ ()()osss sssRLVZsRLRsLHssRLVZRRRsRRLRRsL+== ==+++++ (b) Let 11//11 RxRsCZRsCsRCRsC== =++ osZVVZsL=+ RsLLRCsRsRC1 RsLsRC1 RsLZZVV)s(H2io++=+++=+== PROPRIETARY MATERIAL. 2007 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation.

7 If you are a student using this Manual, you are using it without permission. Chapter 14, Problem 6. For the circuit shown in Fig. , find H(s) = Io(s)/Is(s). Figure For Prob. Chapter 14, Solution 6. 1 HjLsLs == Let //11sZss==+ We convert the current source to a voltage source as shown below. 221(1)1(1)3111ssossssIsIZsVIxIsZsssssss+ ====+++ + + ++++ 2131osoVsIIss==++ 2()31osIsHsIss==++ + _ Vo Is 1 Z 1 S + _ PROPRIETARY MATERIAL. 2007 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation.

8 If you are a student using this Manual, you are using it without permission. Chapter 14, Problem 7. Calculate )( H if HdB equals (a) (b) dB (c) dB Chapter 14, Solution 7. (a) == (b) == (c) == Chapter 14, Problem 8. Determine the magnitude (in dB) and the phase (in degrees) of H( ) = at = 1 if H() equals (a) dB (b) 125 (c) jj+210 (d) j+13 + j+26 Chapter 14, Solution 8. (a) == , = 0 (b) 125H= == , = 0 (c) =+= )1(H == , = (d) = =+++= )1(H == , = PROPRIETARY MATERIAL. 2007 The McGraw-Hill Companies, Inc.

9 All rights reserved. No part of this Manual may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual, you are using it without permission. Chapter 14, Problem 9. A ladder network has a voltage gain of H( ) = )10)(1(10 jj++ Sketch the Bode plots for the gain. Chapter 14, Solution 9. )10j1)(j1(1)( + += H 10/j1log20j1log20-H1010dB + += )10/(tan)(tan--1-1 = The magnitude and phase plots are shown below.

10 HdB -40 100110 -20 10/j11log2010 + +j11log2010 -135 -45 100110 -180 -90 10/j11arg + +j11arg PROPRIETARY MATERIAL. 2007 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual, you are using it without permission. Chapter 14, Problem 10. Sketch the Bode magnitude and phase plots of: H(j ) = )5(50 jj+ Chapter 14, Solution 10.