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.
