c. The general transfer function of a 2nd order Butterworth active filter is: Ao H(s) = This filter can be implemented using a Sallen and Key second order filter section as illustrated in Figure Q3(c). R, R, ww Ov ww Figure Q3(c) The transfer function of such a structure is given by

c. The general transfer function of a 2nd order Butterworth active filter is: Ao H(s) = This filter can be implemented using a Sallen and Key second order filter section as illustrated in Figure Q3(c). R, R, ww Ov ww Figure Q3(c) The transfer function of such a structure is given by

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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Concept explainers

Filter

A filter is a device or process which removes some of the unwanted features or components like frequencies from a signal in signal processing. The feature of filters is the complete or partial suppression of some part of the signal, and filtering is a class of signal processing. This most often means removing some frequency bands or some frequencies. In the frequency domain, the filters do not exclusively act, especially in the image processing field many other targets for filtering exist. Without having to act in the frequency domain, the correlations can be removed for certain frequency components and not for others. The filters are widely used in electronics and telecommunication, in television, radio, radar, audio recording, music synthesis, control systems, computer graphics, and image processing.

Question

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
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 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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