TABLE OF CONTENTS 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 in Subsections 11.2.1 through 11.2.4 below.
The RC network shown in Figure 11.2 is a basic analog low-pass filter. We will derive expressions for its magnitude and phase.
Application of the voltage division expression yields
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 script below to plot G(j ?) versus radian frequency ?. This is shown in Figure 11.3 where, for convenience, we let RC = 1.
w=0:0.02:10; RC=1; magGjw=1./sqrt(1+w.*RC); semilogx(w,magGjw);...xlabel('Frequency in rad/sec - log scale'); ylabel('Magnitude of Vout/Vin');...title('Magnitude Characteristics of basic RC low-pass filter'); grid
We can also obtain a quick sketch...
