Explanation Given data: Refer to Figure 14.49 in the textbook. The value of the corner frequency before scaling ( ω ) is 1 rad s . The value of the cutoff frequency after scaling ( f ′ ) is 10 kHz . The value of the scaled capacitor ( C ′ ) is 15 nF . Formula used: Consider the equations used in magnitude and frequency scaling. Write the expression to calculate the scaled resistor 1. R 1 ′ = K m R 1 (1) Here, K m is the magnitude scaling factor, and R 1 is the value of the resistor 1. Write the expression to calculate the scaled resistor 2. R 2 ′ = K m R 2 (2) Here, R 2 is the value of the resistor 2. Write the expression to calculate the scaled inductor L ′ = K m K f L (3) Here, K f is the frequency scaling factor, and L is the value of the inductor. Write the expression to calculate the scaled capacitor 1. C ′ 1 = 1 K m K f C 1 (4) Here, C 1 is the value of the capacitor 1. Write the expression to calculate the scaled capacitor 2. C ′ 2 = 1 K m K f C 2 (5) Here, C 2 is the value of the capacitor 2. Write the general expression to calculate the scaled corner frequency. ω ′ = 2 π f ′ (6) Here, f ′ is the value of the scaled cutoff frequency. Write the expression to calculate the scaled corner frequency. ω ′ = K f ω (7) Here, ω is the value of the corner frequency. Rearrange the equation (7) to find K f . K f = ω ′ ω Substitute the equation (6) in above equation to find K f . K f = 2 π f ′ ω (8) Calculation: The given circuit is redrawn as Figure 1. Substitute 10 kHz for f ′ and 1 rad s for ω in equation (8) to find K f . K f = 2 π ( 10 kHz ) ( 1 rad s ) = 20 π × 10 3 Hz ( 1 1 s ) { ∵ 1 k = 10 3 } = 20 π × 10 3 ( 1 s ) ( 1 1 s ) { ∵ 1 Hz = 1 1 s } = 2 π × 10 4 Substitute 15 nF for C ′ , 2 π × 10 4 for K f and 1 F for C 1 in equation (4). ( 15 nF ) = 1 K m ( 2 π × 10 4 ) ( 1 F ) Rearrange the above equation to find K m

6th Edition

ISBN: 9780078028229

Author: Charles K Alexander, Matthew Sadiku

Publisher: McGraw-Hill Education

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Chapter 14.9, Problem 14PP

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Scale the third-order Butterworth filter shown in Figure 14.49.

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Chapter 14.8, Problem 13PP

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Chapter 14 Solutions

Fundamentals of Electric Circuits

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Scale the third-order Butterworth filter shown in Figure 14.49.

Solution Summary: The author explains how to scale the third-order Butterworth filter shown in Figure 14.49.

Scale the third-order Butterworth filter shown in Figure 14.49.

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Chapter 14 Solutions