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chapter 17 - Chapter 17 Two-Port and Three Port Networks...

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Chapter 17- Two-Port and Three Port Networks Exercises Ex. 17.4-1 1 25(100) 10 250 a c a b c R R R R R R = = = + + 2 (125)(125) 12.5 250 b c a b c R R R R R R = = = + + 3 100(125) 50 250 a b a b c R R R R R R = = = + + Ex. 17.5-1 12 21 1 21 Y Y = − = ( ) ( ) 11 12 11 22 21 22 1 1 1 21 42 42 42 1 1 10.5 1/ 7 21 10.5 Y Y Y Y Y Y + = = − − = + = = − − = 3 1 1 41 21 1 1 21 7 = Y 2 1 1 1 11 0 1 2 22 0 2 1 12 21 0 2 42 (21 10.5) 18 42 31.5 10.5(63) 9 73.5 6 I I I V Z I V Z I V Z Z I = = = + = = = + = = = = = = 2 1 2 2 18 6 10.5 42(10.5) Since , then 6 Z = 73.5 73.5 6 9 I I V I I = = = 17-1
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Ex. 17.6-1 1 11 1 2 21 1 1 6 1 .167 6 I Y V I Y V = = = = − = − 1 12 2 2 22 2 0.0567 0.944 I Y V I Y V = = = = Ex. 17.7-1 2 2 1 6 , (9 1) 10 , 1 I i V i i V i = = + = = 2 22 2 1 12 2 6 0.6 S 10 0.1 10 I i h V i V i h V i = = = = = = 1 1 1 1 2 1 10 9 9 44 5 9 9 V i V I i i V I i i = = + = = = Therefore ( ) ( ) ( ) 1 11 1 2 21 1 0.9 10 9 44 9 4.4 10 9 V i h I i i I h I i = = = = = = 17-2
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Ex. 17.8-1 2 1 2 1 12 6 4 1 1 15 5 5 5 and S 30 1 2 75 50 30 1 2 3 4 10 5 10 15 = = = = Y Y Z = Ex. 17.8-2 ( ) ( ) ( ) ( ) 2/5 1 1/10 1/10 4 10 1/30 2/15 1/3 4/3 1/10 1/10 = = T Ex. 17.9-1 a b c 1 12 1 0 1 3 = , = and = 0 1 1/6 1 0 1 T T T 1 12 1 0 3 12 1 3 3 21 0 1 1/ 6 1 1/ 6 1 0 1 1/ 6 3/ 2 a b c c     = = =         T T T T Problems Section 17-4: T-to-T1 Transformations P17.4-1 17-3
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P17.4-2 P17.4-3 21 1 2 21 2 i 22 L 1 22 L (forward current gain) z I I z I A z R I z R = = = + + ( ) 12 i 1 1 11 1 12 2 12 21 in 11 11 1 1 1 22 L (input resistance) z A I V z I z I z z R z z I I I z R + = = = = + i L 2 2 2 L i L 1 1 in 1 v 1 in and (forward voltage gain) A R V V I R A R I V R I A V R = − = = = = L 2 p i v i in R A A A A R = = 17-4
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P17.4-4 First, simplify the circuit using a -Y transformation: eq 1 || 5|| 20 4 3 R R R = = = Mesh equations: 2 2 30 18 10 50 10 20 I I I I = = Solving for the required current: 30 10 50 20 100 0.385 A 18( 20) ( 10)10 260 I = = = P17.4-5 17-5
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Section 17-5: Equations of Two-Port Networks P17-5-1 12 11 12 11 22 21 22 6 12 18 3 9 Z Z Z Z Z Z Z = = = = = 2 1 1 1 11 1 0 1 2 12 21 2 2 0 2 2 22 2 2 0 1 S 14 6 1 S (6 12) 21 / 7 1 S 7 V V V I Y V I I Y V V I V Y V V = = = = = = = = − = + = = = Υ 1 1 14 21 = 1 1 21 7 Υ P17.5-2 2 4 4 4 2 j j j j = + Z 17-6
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P17.5-3 2 2 1 2 11 21 1 1 0 0 and V V I I Y Y V V = = = = 1 2 1 2 2 1 1 1 1 2 and I I I I I V b G G G V + + = + = 1 so 1 1 2 1 1 2 2 1 ( ( 1) ) 1 and ( 1) 3 I G b G V V I b G V V = = − = = Finally 11 21 Y 1 S and Y 3 S = − = Next 1 2 2 2 3 2 and 2 I I I V V G G + = = 1 1 1 12 2 2 0 2 22 2 3 2 0 1 S 4 S V V I Y G V I Y G G V = = = = − = − = = + = P17.5-4 Using Fig. 17.5-2 as shown: 12 21 12 21 11 12 22 21 0.1 S or 0.1 S 0.2 0.3 S 0.05 0.15 S Y Y Y Y Y Y Y Y = − = = = − = = = = P17.5-5 12 21 11 12 11 10 S 13.33 S 23.33 S Y Y Y Y Y µ µ µ = − = + = = 22 21 22 20 S 30 Y Y Y S µ µ + = = 17-7
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P17.5-6 2 2 1 11 1 0 2 1 21 1 1 0 3 3 2 (3 ) 2 2 I I V Z j j I V j I Z j I I = = j = = + = + = = = − 1 1 1 12 2 0 2 22 2 0 2 2 I I V Z j I V Z j I = = = = − = = − P17.5-7 11 21 11 21
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