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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

70 75 80 85 90 95 100 200 300 400 500 600 700 800 900

Cash Accounts Receivable Supplies Equipment Accounts Payable Notes Payable Capital Drawing Fees Income

CHAP. 1]

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

4.2485 4.3175 4.3820 4.4427 4.4998 4.5539 4.6052 5.2983 5.7038 5.9915 6.2146 6.3069 6.5511 6.6846 6.8024

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

x 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 ex 1.0000 1.0513 1.1052 1.1618 1.2214 1.2840 1.3499 1.4191 1.4918 1.5683 1.6487 1.7333 1.8221 1.9155 2.0138 2.1170 2.2255 2.3396 2.4596 2.5857 2.7183 3.0042 3.3201 3.6693 4.0552 4.4817 4.9530 5.4739 6.0496 6.6859 e x 1.0000 0.9521 0.9048 0.8607 0.8187 0.7788 0.7408 0.7047 0.6703 0.6376 0.6065 0.5769 0.5488 0.5220 0.4966 0.4724 0.4493 0.4274 0.4066 0.3867 0.3679 0.3329 0.3012 0.2725 0.2466 0.2231 0.2019 0.1827 0.1653 0.1496

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

$9,000 11,000 32,000 4,000 26,000

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

x 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 6 7 8 9

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

ex 12.182 13.464 14.880 16.445 18.174 20.086 22.198 24.533 27.113 29.964 33.115 36.598 40.447 44.701 49.402 54.598 60.340 66.686 73.700 81.451 90.017 99.484 109.95 121.51 134.29 148.41 403.43 1096.6 2981.0 8103.1

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