Chapter 14

Q. 14.12

Design a lowpass active filter with a dc gain of 4 and a corner frequency of 500 Hz.

Step-by-Step

Verified Solution

From Eq. (14.61), we find

ω_{c} = \frac{1}{R_{f}C_{f}}                 (14.61)

ω_{c} = 2πf_{c} = 2π (500) = \frac{1}{R_{f}C_{f}}               (14.12.1)

The dc gain is

H(0) = – \frac{R_{f}}{R_{i}} = – 4             (14.12.2)

We have two equations and three unknowns. If we select C_{f} = 0.2  μF , then

R_{f} = \frac{1}{2π(500) 0.2  ×  10^{-6}} = 1.59  kΩ

and

R_{i} = \frac{R_{f}}{4} = 397.5  Ω

We use a  1.6-kΩ resistor for R_{f}   and a 400-Ω  resistor for R_{i}   Figure 14.42 shows the filter.

تعليق توضيحي 2023-02-14 183009