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Suppose the bridge circuit in Fig. 1-24 is balanced by letting R1 R2 R3 R4 R. Find the elements of the Norton equivalent circuit. Ans: IN 0; YN 1=R Use SPICE methods to determine voltage vab for the circuit of Fig. 1-24 if Vb 20 V, RL 10 , R1 1 , R2 2 , R3 3 , and R4 4 . (Netlist code available at author download site.) Ans: vab V 2; 3 1:538 V
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For the circuit of Fig. 1-25, (a) determine the Thevenin equivalent of the circuit to the left of terminals a; b, and (b) use the Thevenin equivalent to nd the load current iL . Ans: a VTh 120 V; ZTh 20 ; b iL 4 A
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+ 30 V _ _ 0 b 0.25Lab 10 W RL = 10 W
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Fig. 1-25
Apply SPICE methods to determine load current iL for the circuit of Fig. 1-25 if (a) the element values are as shown and (b) the VCCS has a value of 0.5vab with all else unchanged. (Netlist code available at author download site.) Ans: a iL 4 A; b iL 6 A
In the circuit of Fig. 1-26, let R1 R2 RC 1  and nd the Thevenin equivalent for the circuit to the right of terminals a; b (a) if vC 0:5i1 and (b) if vC 0:5i2 . Ans: a VTh 0; ZTh RTh 1:75 ; b VTh 0; ZTh RTh 1:667 
RC + R2
Fig. 1-26
Find the Thevenin equivalent for the network to the left of terminals a; b in Fig. 1-15 (b) if k 0:1. Use the Thevenin equivalent to verify the results of Problem 1.4. Ans: a VTh 200 V; ZTh RTh 100 ; b VTh 250 V; ZTh RTh 125 
(a) if k 0, and
Find the Thevenin equivalent for the circuit to the left of terminals a; b in Fig. 1-16, and use it to verify the results of Problem 1.6. Ans: VTh 1 1 vs ; ZTh RTh 1 3  2 2 An alternative solution for Problem 1.3 involves nding a Thevenin equivalent circuit which, when connected across the nonlinear R2 0:25i, allows a quadratic equation in current i to be written via KVL. Find the elements of the Thevenin circuit and the resulting current. Ans: VTh 25 V; ZTh RTh 5 ; i 4:142 A Use (1.10) to (1.15) to nd expressions for the z parameters in terms of the h parameters. Ans: z11 h11 h12 h21 =h22 ; z12 h12 =h22 ; z21 h21 =h22 ; z22 1=h22
CHAP. 1]
CIRCUIT ANALYSIS: PORT POINT OF VIEW
For the two-port network of Fig. 1-20, (a) nd the voltage-gain ratio V2 =V1 in terms of the z parameters, and then (b) evaluate the ratio, using the h-parameter values given in Problem 1.15 and the results of Problem 1.36. Ans: a z21 RL = z11 RL z11 z22 z12 z21 ; b 200
Find the current-gain ratio I2 =I1 for the two-port network of Fig. 1-20 in terms of the h parameters. Ans: h21 = 1 h22 RL
Find the current-gain ratio I2 =I1 for the two-port network of Fig. 1-20 in terms of the z parameters. Ans: z21 = z22 RL
Determine the Thevenin equivalent voltage and impedance, in terms of the z parameters, looking right into port 1 of the two-port network of Fig. 1-20 if RL is replaced with an independent dc voltage source Vd , connected such that V2 Vd . Ans: VTh z12 Vd =z22 ; ZTh z11 z22 z12 z21 =z22
Find the Thevenin equivalent voltage and impedance, in terms of the h parameters, looking right into port 1 of the network of Fig. 1-20 if RL is replaced with a voltage-controlled current source such that I2 V1 , where > 0 and the h parameters are understood to be positive. Ans: VTh 0; ZTh h11 h22 h12 h21 = h22 h12
Determine the driving-point impedance (the input impedance with all independent sources deactivated) of the two-port network of Fig. 1-20. Ans: z11 RL z11 z22 z12 z21 = z22 RL
Evaluate the z parameters of the network of Fig. 1-16. Ans: z11 2 ; z12 1 ; z21 1 ; z22 2 
Find the current i1 in Fig. 1-3 if 2; R1 R2 R3 1 ; Vb 10 V, and vs 10 sin !t V. Ans: 2 A
For a one-port network with passive sign convention (see Problem 1.22), v Vm cos !t V and i I1 I2 cos !t  A. Find (a) the instantaneous power owing to the network and (b) the average power to the network. Ans: a Vm I1 cos !t 1 Vm I2 cos 2!t  cos  ; b 1 Vm I2 cos  2 2
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