Explanation Given Data: The transfer function of low-pass filter is given as follows: H ( s ) = 1 s 4 + 2.613 s 3 + 3.414 s 2 + 2.613 s + 1 Formula used: Refer to Equation 19.82 in the textbook and write the expression for transfer function of an LC ladder network as follows: H ( s ) = − y 21 / Y L 1 + y 22 / Y L (1) Calculation: Consider the LC ladder network is terminated in a 1 Ω resistor. As the network is terminated with 1 Ω resistor, the value of Z L is 1 Ω . Therefore, the value of Y L is obtained as follows: Y L = 1 Z L = 1 1 Ω = 1 S Substitute 1 for Y L in Equation (1) and obtain the transfer function for the given LC ladder network as follows: H ( s ) = − y 21 / 1 1 + y 22 / 1 H ( s ) = − y 21 1 + y 22 (2) From the denominator of given transfer function, it is clear that, the given network is a 4 th order network. Therefore, draw the network with two inductors and two capacitors as shown in Figure 1. Separate the odd and even terms in the denominator of the given transfer function and rearrange the given transfer function as follows: H ( s ) = 1 ( s 4 + 3.414 s 2 + 1 ) + ( 2.613 s 3 + 2.613 s ) = 1 ( 2.613 s 3 + 2.613 s ) [ 1 + ( s 4 + 3.414 s 2 + 1 2.613 s 3 + 2.613 s ) ] H ( s ) = 1 2.613 s 3 + 2.613 s 1 + s 4 + 3.414 s 2 + 1 2.613 s 3 + 2.613 s (3) Compare Equation (3) with Equation (2) and obtain the terms y 21 and y 22 as follows: y 21 = − 1 2.613 s 3 + 2.613 s y 22 = s 4 + 3.414 s 2 + 1 2.613 s 3 + 2.613 s As y 22 is the output admittance of the network with input short-circuited, redraw the network in Figure 1 as shown in Figure 2. From Figure 2, write the general expression for y 22 as follows: y 22 = s C 4 + Y A (4) Rewrite the expression of y 22 as follows: y 22 = s 4 + 1 s 2 + 2.414 s 2 + 1 2.613 s 3 + 2.613 s = s 4 + 1 s 2 2.613 s 3 + 2.613 s + 2.414 s 2 + 1 2.613 s 3 + 2.613 s = ( 1 2.613 ) [ s ( s 3 + 1 s ) s 3 + s ] + 2.414 s 2 + 1 2.613 s 3 + 2.613 s y 22 = 0.383 s + 2.414 s 2 + 1 2

EE 98: Fundamentals of Electrical Circuits - With Connect Access

6th Edition

ISBN: 9781259981807

Author: Alexander

Publisher: MCG

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Chapter 19, Problem 96P

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Design an LC ladder network to realize the given transfer function of low-pass filter.

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Chapter 19 Solutions

EE 98: Fundamentals of Electrical Circuits - With Connect Access

Ch. 19.2 - Find the z parameters of the two-port network in...Ch. 19.2 - Calculate I1 and I2 in the two-port of Fig. 19.11....Ch. 19.3 - Obtain the y parameters for the T network shown in...Ch. 19.3 - Obtain the y parameters for the circuit in Fig....Ch. 19.4 - Determine the h parameters for the circuit in Fig....Ch. 19.4 - Find the impedance at the input port of the...Ch. 19.4 - For the ladder network in Fig. 19.30, determine...Ch. 19.5 - Find the transmission parameters for the circuit...Ch. 19.5 - Prob. 9PP Ch. 19.6 - Determine [y] and [T] of a two-port network whose...

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Design an LC ladder network to realize the given transfer function of low-pass filter.

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Design an LC ladder network to realize the given transfer function of low-pass filter.

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Chapter 19 Solutions