11.2 Basic Analog Filters

An analog filter can also be classified as passive or active. Passive filters consist of passive devices such as resistors, capacitors and inductors. Active filters are, generally, operational amplifiers with resistors and capacitors connected to them externally. We can find out whether a filter, passive or active, is a low-pass, high-pass, etc., from its the frequency response that can be obtained from its transfer function. The procedure is illustrated with the examples that follow.

Example 11.1

Derive expressions for the magnitude and phase responses of the series RC network of Figure 11.2, and sketch their characteristics.

Figure 11.2: Series RC network for Example 11.1

Solution:

or

The magnitude of (11.1) is

and the phase angle, also known as the argument, is

We can obtain a quick sketch for the magnitude G( j ?) versus ? by evaluating (11.2) at ? = 0, ? = 1/ RC, and ? ? ?. Thus,

as ? ? 0,

for ? = 1/ RC,

and as ? ? ?,

We will use the MATLAB code below to plot G( j ?) versus radian frequency ?. This is shown in Figure 11.3 where, for convenience, we let RC = 1.

<span class="serif">w=0:0.02:10; RC=1; magGs=1./sqrt(1+w.*RC); semilogx(w,magGs); grid</span>

Figure 11.3: Amplitude characteristics of a series RC low-pass filter with RC = 1

We can also obtain a quick...