Page 92 - Schaum's Outline of Theory and Problems of Electric Circuits

AMPLIFIERS AND OPERATIONAL AMPLIFIER CIRCUITS
CHAP. 5]

Fig. 5-28 81

Fig. 5-29

5.13 LOW-PASS FILTER
A frequency-selective amplifier whose gain decreases from a finite value to zero as the frequency of
the sinusoidal input increases from dc to infinity is called a low-pass filter. The plot of gain versus
frequency is called a frequency response. An easy technique for finding the frequency response of filters
will be developed in Chapter 13. The leaky integrator of Fig. 5-24 is a low-pass filter, as illustrated in
the following example.

3
5
4
EXAMPLE 5.22 In Example 5.18 let v 1 ¼ sin ! t. Find jv 2 j for ! ¼ 0; 10; 100; 10 ; 10 , and 10 rad/s.
By repeating the procedure of Example 5.18, the frequency response is found and given in Table 5-1. The
response amplitude decreases with frequency. The circuit is a low-pass filter.
Table 5-1. Frequency Response of the Low-pass Filter

!, rad/s 0 10 100 10 3 10 4 10 5
f , Hz 0 1.59 15.9 159 1:59 10 3 15:9 10 3
jv 2 =v 1 j 1 1 0.995 0.707 0.1 0.01