To determine Find the voltage v o in the given interconnected cascade network. Explanation Given data: The h parameters of the first two-port circuit are h 11 = 1000 Ω , h 12 = 5 × 10 − 4 , h 21 = 40 , h 22 = 25 μ S . The value of resistance R is 72 k Ω . The value of source voltage is v g = 9 mV . Refer to Figure given in the textbook. The internal source impedance is Z g = 800 Ω . The load impedance is Z L = 72 k Ω . Formula used: Write the general relationship which relates the a parameters in terms of the h parameters. a 11 ' = − Δ h h 21 (1) a 12 ' = − h 11 h 21 (2) a 21 ' = − h 22 h 21 (3) a 22 ' = − 1 h 21 (4) Δ h = h 11 h 22 − h 12 h 21 (5) Here, h 11 is the input admittance of the network, h 12 is the reverse voltage gain, h 21 is the forward current gain, and h 22 is the output impedance of the network. Write the general expression for a parameters of the Two-port model of a network. a 11 " = V 1 V 2 | I 2 = 0 (6) a 21 " = I 1 V 2 | I 2 = 0 (7) a 12 " = − V 1 I 2 | V 2 = 0 (8) a 22 " = − I 1 I 2 | V 2 = 0 (9) Write the general expression for the a parameters of the interconnected network. a 11 = a 11 ' a 11 " + a 12 ' a 21 " (10) a 12 = a 11 ' a 12 " + a 12 ' a 22 " (11) a 21 = a 21 ' a 11 " + a 22 ' a 21 " (12) a 22 = a 21 ' a 12 " + a 22 ' a 22 " (13) Refer to Table Terminated Two-Port Equations in the textbook. Write the expression in terms of the a parameters. V 2 V g = Z L ( a 11 + a 21 Z g ) Z L + a 12 + a 22 Z g (14) Calculation: Find the a parameters of the first two port circuit. Substitute 1000 for h 11 , 5 × 10 − 4 for h 12 , 40 for h 21 , and 25 μ for h 22 in equation (11) to find Δ h . Δ h = ( 1000 ) ( 25 μ ) − ( 5 × 10 − 4 ) ( 40 ) = 5 × 10 − 3 Substitute 5 × 10 − 3 for Δ h and 40 for h 21 in equation (1) to find a 11 ' . a 11 ' = − 5 × 10 − 3 40 = − 1.25 × 10 − 4 Substitute 1000 for h 11 and 40 for h 21 in equation (2) to find a 12 ' . a 12 ' = − 1000 40 = − 25 Ω Substitute 25 μ for h 22 and 40 for h 21 in equation (3) to find a 21 ' . a 21 ' = − 25 μ 40 = − 25 × 10 − 6 40 S = − 6.25 × 10 − 7 Substitute 40 for h 21 in equation (4) to find a 22 ' . a 22 ' = − 1 40 = − 0.025 Find the a parameters for the second two-port circuit. The given circuit of Figure (b) is redrawn as shown in Figure 1 (star to delta transformation). In the given circuit, tee network with resistance R is converted into delta network with the resistance 3 R as shown in Figure 1. The new value of resistance in the delta network is calculated as follows. Resistance in delta network = R R + R R + R R R = R 2 + R 2 + R 2 R = 3 R 2 R = 3 R In Figure 1, since R and 3 R are connected in parallel. Therefore, the equivalent resistance for parallel connection is calculated as follows. R | | 3 R = R × 3 R R + 3 R = 3 R 2 4 R = 3 4 R The modified circuit is shown in Figure 2. The circuit is redrawn as shown in Figure 3 when the current I 2 = 0 (open-circuit). In Figure 3, the voltage V 1 is calculated by using Ohm’s law as follows. V 1 = ( 3 R | | ( 3 4 R + 3 R ) ) I 1 = ( 3 R | | 15 4 R ) I 1 = ( 3 R × 15 4 R 3 R + 15 4 R ) I 1 = 5 3 R I 1 In Figure 3, the voltage V 2 is calculated by using voltage division rule as follows. V 2 = V 1 × 3 R 3 4 R + 3 R = V 1 × 1 1 4 + 1 = V 1 × 1 5 4 V 2 = 4 5 V 1 (15) Rearrange the equation as follows, V 1 V 2 = 5 4 Substitute 5 4 for V 1 V 2 in equation (6) to find a 11 " . a 11 " = 5 4 = 1.25 Substitute 5 3 R I 1 for V 1 in equation (15)

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Z parameter

The Z-parameters that are the impedance parameters of a two-port network are defined by expressing the two-port voltages V1 and V2 in terms of two-port currents I1 and I2. The Z-parameters are calculated by open circuiting one of the two ports at a time …

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Chapter 18, Problem 39P

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Find the voltage vo in the given interconnected cascade network.

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Electric Circuits. (11th Edition)

Ch. 18.2 - Find the y parameters for the circuit in Fig....Ch. 18.2 - Prob. 2AP Ch. 18.2 - Prob. 3AP Ch. 18.2 - Prob. 4AP Ch. 18.2 - Prob. 5AP Ch. 18.3 - Prob. 6AP Ch. 18.4 - Each element in the symmetric bridged-tee circuit...Ch. 18 - Prob. 1P Ch. 18 - Prob. 2P Ch. 18 - Prob. 3P

Ch. 18 - Find the b parameters for the circuit shown in...Ch. 18 - Find the y parameters for the circuit shown in...Ch. 18 - Prob. 6P Ch. 18 - Prob. 7P Ch. 18 - Prob. 8P Ch. 18 - Find the g parameters for the operational...Ch. 18 - Find the a parameters for the circuit in Fig....Ch. 18 - Use the results obtained in Problem 18.10 to...Ch. 18 - Prob. 12P Ch. 18 - Prob. 15P Ch. 18 - Prob. 16P Ch. 18 - Prob. 17P Ch. 18 - Prob. 18P Ch. 18 - Prob. 19P Ch. 18 - Use the defining equations to find the s-domain...Ch. 18 - Prob. 21P Ch. 18 - Prob. 22P Ch. 18 - Prob. 23P Ch. 18 - Prob. 24P Ch. 18 - Prob. 25P Ch. 18 - Prob. 26P Ch. 18 - Find the Thevenin equivalent circuit with respect...Ch. 18 - Prob. 28P Ch. 18 - Prob. 30P Ch. 18 - The h parameters for the two-port amplifier...Ch. 18 - For the terminated two-port amplifier circuit in...Ch. 18 - Prob. 33P Ch. 18 - The linear transformer in the circuit shown in...Ch. 18 - The following measurements were made on a...Ch. 18 - Find the z parameters for the two-port network in...Ch. 18 - Find the s-domain expressions for the h parameters...Ch. 18 - The g and h parameters for the resistive two-ports...Ch. 18 - The h parameters of the first two-port circuit in...Ch. 18 - The networks A and B in the circuit in Fig. P18.40...Ch. 18 - Prob. 41P Ch. 18 - Show that the circuit in Fig. P18.42 is an...Ch. 18 - Prob. 43P Ch. 18 - Prob. 44P Ch. 18 - Prob. 45P

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Z Parameters - Impedance Parameters; Author: Electrical Engineering Authority;https://www.youtube.com/watch?v=qoD4AoNmySA;License: Standard Youtube License