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An active low pass filter is required. The filter should have a cut off frequency of 2 kHz and a 40 dB per decade roll off. A second order Sallen Key filter prototype, as illustrated in figure Q3(c), is used for this purpose. i. Explain briefly why a second order filter is an adequate choice here? ii. Express the gain Ao, the natural frequency on and the damping ratio ç in terms of the circuit elements R1, R2, R and C. ii. If R: = 10kn and C =10* F, what are the values of R and R2? %3D

An active low pass filter is required. The filter should have a cut off frequency of 2 kHz and a 40 dB per decade roll off. A second order Sallen Key filter prototype, as illustrated in figure Q3(c), is used for this purpose. i. Explain briefly why a second order filter is an adequate choice here? ii. Express the gain Ao, the natural frequency on and the damping ratio ç in terms of the circuit elements R1, R2, R and C. ii. If R: = 10kn and C =10* F, what are the values of R and R2? %3D

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Q3 c
c. The general transfer function of a 2nd order Butterworth active filter is: Ao H(s) = + 23 ) + 1 This filter can be implemented using a Sallen and Key second order filter section as illustrated in Figure Q3(c). R, R2 ww ww Ov R ww ov Figure Q3(c) The transfer function of such a structure is given by
Transcribed Image Text:c. The general transfer function of a 2nd order Butterworth active filter is: Ao H(s) = + 23 ) + 1 This filter can be implemented using a Sallen and Key second order filter section as illustrated in Figure Q3(c). R, R2 ww ww Ov R ww ov Figure Q3(c) The transfer function of such a structure is given by
R, +R2 Vout (s) H(s) = Vin (s) (RCs)² + (3 – Ao)RCs + 1 An active low pass filter is required. The filter should have a cut off frequency of 2 kHz and a 40 dB per decade roll off. A second order Sallen Key filter prototype, as illustrated in figure Q3(c), is used for this purpose. i. Explain briefly why a second order filter is an adequate choice here? ii. Express the gain Ao, the natural frequency on and the damping ratio ç in terms of the circuit elements R1, R2, R and C. iii. If R1 = 10k and C =108 F, what are the values of R and R2?
Transcribed Image Text:R, +R2 Vout (s) H(s) = Vin (s) (RCs)² + (3 – Ao)RCs + 1 An active low pass filter is required. The filter should have a cut off frequency of 2 kHz and a 40 dB per decade roll off. A second order Sallen Key filter prototype, as illustrated in figure Q3(c), is used for this purpose. i. Explain briefly why a second order filter is an adequate choice here? ii. Express the gain Ao, the natural frequency on and the damping ratio ç in terms of the circuit elements R1, R2, R and C. iii. If R1 = 10k and C =108 F, what are the values of R and R2?
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