Explanation Given data: Refer to given circuit in the textbook. Formula used: Write a general expression to calculate the impedance of a resistor in s -domain. Z R = R (1) Here, R is the value of resistance. Write a general expression to calculate the impedance of an inductor in s -domain. Z L = s L Z M = s M (2) Here, L is the value of inductance, and M is the value of mutual inductance. Write a general expression to calculate the impedance of a capacitor in s -domain. Z C = 1 s C (3) Here, C is the value of capacitance. Write a general expression to calculate the poles and zeroes from the transfer function. H ( s ) = k ( s − z 1 ) ( s − z 2 ) .... ( s − z n ) ( s − p 1 ) ( s − p 2 ) .... ( s − p n ) (4) Here, z 1 , z 2 .... z n are the zeroes of a system, and p 1 , p 2 .... p n are the poles of a system. Calculation: The given circuit is redrawn as shown in Figure 1. The T-equivalent circuit of the mutually connected series aiding inductors is shown in Figure 2. Implement the Figure 2 in Figure 1 as shown in Figure 3. Consider, L eq1 = L 1 + M L eq2 = L 2 + M M eq = − M Now, the Figure 3 is drawn as shown in Figure 4. Substitute 10 k Ω for R in equation (1) to find Z R . Z R = 10 k Ω = 10 × 10 3 { ∵ 1 k = 10 3 } = 10000 Use equation (2) to find Z L eq1 . Z L eq1 = s ( 15 H ) = 15 s Use equation (2) to find Z L eq2 . Z L eq2 = s ( 35 H ) = 35 s Use equation (2) to find Z M eq Z M eq = s ( − 10 H ) = − 10 s Substitute 62.5 nF for C in equation (3) to find Z C . Z C = 1 s ( 62.5 nF ) = 1 s ( 62.5 × 10 − 9 F ) { ∵ 1 n = 10 − 9 } = 16 × 10 6 s Convert the Figure 4 into s -domain as shown in Figure 5. Apply mesh analysis for Loop 1 in Figure 5. − V g − 10 s I 1 + 35 s ( I 1 − I o ) = 0 − V g − 10 s I 1 + 35 s I 1 − 35 s I o = 0 − V g + 25 s I 1 − 35 s I o = 0 V g = 25 s I 1 − 35 s I o (5) Apply mesh analysis for Loop 2 in Figure 5. 15 s I o + 10000 I o + ( 16 × 10 6 s ) I o + 35 s ( I o − I 1 ) = 0 15 s I o + 10000 I o + ( 16 × 10 6 s ) I o + 35 s I o − 35 s I 1 = 0 50 s I o + 10000 I o + ( 16 × 10 6 s ) I o − 35 s I 1 = 0 [ 50 s + 10000 + ( 16 × 10 6 s ) ] I o = 35 s I 1 Simplify the above equation to find I 1

11th Edition

ISBN: 9780134746968

Author: James W. Nilsson, Susan Riedel

Publisher: PEARSON

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Question

Chapter 13, Problem 60P

To determine

Find the poles and zeros of the transfer function for the given circuit.

Expert Solution & Answer

Chapter 13 Solutions

Electric Circuits. (11th Edition)

Ch. 13.2 - The parallel circuit in Example 13.1 is placed in...Ch. 13.3 - Prob. 2AP Ch. 13.3 - The energy stored in the circuit shown is zero at...Ch. 13.3 - The dc current and dc voltage sources are applied...Ch. 13.3 - Prob. 6AP Ch. 13.3 - Using the results from Example 13.7 for the...Ch. 13.3 - The energy stored in the circuit shown is zero at...Ch. 13.4 - Derive the numerical expression for the transfer...Ch. 13.5 - Find (a) the unit step and (b) the unit impulse...Ch. 13.5 - The unit impulse response of a circuit is υo(t) =...

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