Obtain the z parameters for the network in Fig. 19.65.

1 Chapter 19, Problem 1. Obtain the z parameters for the network in Fig. Figure For Prob. and 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 19, Solution 1. To get z 11 and z 21 , consider the circuit in Fig. (a). 1 4 I2 = 0. + Io +. I1 V1 V2.. (a). V1. z 11 = = 1 + 6 || (4 + 2) = 4 . I1. 1. Io = I , V2 = 2 I o = I 1.

2 2 1. V2. z 21 = = 1 . I1. To get z 22 and z 12 , consider the circuit in Fig. (b). I1 = 0 1 4 . Io '. + +. V1 V2.. (b). V2. z 22 = = 2 || (4 + 6) = . I2. 2 1. Io' = I2 = I2 , V1 = 6 I o ' = I 2. 2 + 10 6. V1. z 12 = = 1 . I2. 4 1 . Hence, [z ] = . 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 19, Problem 2.

3 * Find the impedance parameter equivalent of the network in Fig. Figure For Prob. * An asterisk indicates a challenging problem. Chapter 19, Solution 2. Consider the circuit in Fig. (a) to get z 11 and z 21 . 1 Io ' 1 1 1 I2 = 0. + Io +. I1 V1 V2.. 1 1 1 1 . (a). 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 V1. z 11 = = 2 + 1 || [ 2 + 1 || (2 + 1) ]. I1. 3 (1)(11 4) 11. z 11 = 2 + 1 || 2 + = 2+ = 2 + = 4 1 + 11 4 15. 1 1. Io = Io' = Io'. 1+ 3 4. 1 4. Io' = I1 = I1. 1 + 11 4 15. 1 4 1. I o = I1 = I1. 4 15 15. 1. V2 = I o = I. 15 1. V2 1. z 21 = = = z 12 = I 1 15. To get z 22 , consider the circuit in Fig. (b). I1 = 0 1 1 1 1 . + +. V1 V2.. 1 1 1 1 . (b). V2. z 22 = = 2 + 1 || (2 + 1 || 3) = z 11 = I2. Thus, . [z ] = .. 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 19, Problem 3. Find the z parameters of the circuit in Fig. Figure For Prob. Chapter 19, Solution 3. z12 = j 6 = z21. z11 z12 = 4 . z11 = z12 + 4 = 4 + j 6 . z22 z12 = j10 . z22 = z12 j10 = j 4 . 4 + j6 j6 4 + j6 j6 . [ z] = = . j6.. j 4 j6 j4 . 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.

6 Chapter 19, Problem 4. Calculate the z parameters for the circuit in Fig. Figure For Prob. Chapter 19, Solution 4. Transform the network to a T network . Z1 Z3. (12)( j10) j120. Z1 = =. 12 + j10 j5 12 + j5. - j60. Z2 =. 12 + j5. 50. Z3 =. 12 + j5. The z parameters are (-j60)(12 - j5). z 12 = z 21 = Z 2 = = - 144 + 25. ( j120)(12 j5). z 11 = Z1 + z 12 = + z 12 = + 169. (50)(12 j5). z 22 = Z 3 + z 21 = + z 21 = 169. Thus, + - . [z ] = . - . 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 19, Problem 5. Obtain the z parameters for the network in Fig. as functions of s. Figure For Prob. Chapter 19, Solution 5. Consider the circuit in Fig. (a). 1 s I2 = 0. + Io +. I1 V1 1/s V2.. (a). 1 1 1 . 1 + s + . 1 1 s 1 s + 1 s . z 11 = 1 || || 1 + s + = || 1 + s + =. s s 1 s 1 1. 1+ +1+ s +. s s + 1 s s + s +1. 2. z 11 = 3. s + 2s 2 + 3s + 1. 1 1 s 1 ||. s s +1 s +1. Io = I = I = I1. 1 1 1 1 1 1 s 1 || + 1 + s + +1+ s + + s + s +1. 2. s s s +1 s s +1. s Io = 3 I1. s + 2s + 3s + 1. 2. 1 I1. V2 = I o = 3. s s + 2s 2 + 3s + 1. V2 1. z 21 = = 3. I 1 s + 2s + 3s + 1. 2. PROPRIETARY MATERIAL. 2007 The McGraw-Hill Companies, Inc.

8 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. Consider the circuit in Fig. (b). I1 = 0 1 s + +. V1 1/s V2.. (b). V2 1 1 1 1 . z 22 = = || 1 + s + 1 || = || 1 + s + . I2 s s s s + 1 . 1 1 1. 1 + s + 1 + s +. s s + 1 s +1. z 22 = =. 1 1 s +1+ s + 1+ s + s2 +. s s +1 s +1. s 2 + 2s + 2. z 22 =. s 3 + 2s 2 + 3s + 1. z 12 = z 21. Hence, s2 + s + 1 1 . s 3 + 2s 2 + 3s + 1 s 3 + 2s 2 + 3s + 1.

9 [z ] = . 1 s 2 + 2s + 2 . s 3 + 2s 2 + 3s + 1 s 3 + 2s 2 + 3s + 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 19, Problem 6. Compute the z parameters of the circuit in Fig. Figure For Prob. and Chapter 19, Solution 6. To find z11 and z21 , consider the circuit below. I1 5 10 4I1 I2=0. Vo +.

10 +. V1 + 20 . V2. _.. 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. V1 (20 + 5) I1. z11 = = = 25 . I1 I1. 20. Vo = V1 = 20 I1. 25. V o 4 I 2 + V2 = 0 . V2 = Vo + 4 I1 = 20 I1 + 4 I1 = 24 I1. V2. z21 = = 24 . I1. To find z12 and z22, consider the circuit below. I1=0 5 10 4I1 I2. +. +. +. V1 20 _. V2.. V2 = (10 + 20) I 2 = 30 I 2.