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1042 ⏐⏐⏐ DECIBELS, FILTERS, AND BODE PLOTS dB<br />

V i<br />

0<br />

V i<br />

V i<br />

0<br />

V i<br />

0<br />

V i<br />

V i<br />

=<br />

V i<br />

Since the characteristics of a stop-band filter are the inverse of the<br />

pattern obtained for the pass-band filters, we can employ the fact that at<br />

any frequency the sum of the magnitudes of the two waveforms to the<br />

right of the equals sign in Fig. 23.40 will equal the applied voltage V i.<br />

V o<br />

f 0<br />

fo Pass-band Stop-band<br />

FIG. 23.40<br />

Demonstrating how an applied signal of fixed magnitude can be broken down<br />

into a pass-band and stop-band response curve.<br />

+<br />

V i<br />

–<br />

+<br />

V i<br />

–<br />

f<br />

+<br />

0 fo f<br />

For the pass-band filters of Figs. 23.33 and 23.34, therefore, if we<br />

take the output off the other series elements as shown in Figs. 23.41 and<br />

23.42, a stop-band characteristic will be obtained, as required by Kirchhoff’s<br />

voltage law.<br />

For the series resonant circuit of Fig. 23.41, Equations (23.22)<br />

through (23.24) still apply, but now, at resonance,<br />

Stop-band filter<br />

R<br />

R l<br />

L<br />

C<br />

FIG. 23.41<br />

Stop-band filter using a series resonant circuit.<br />

Stop-band filter<br />

R l<br />

C<br />

L<br />

FIG. 23.42<br />

Stop-band filter using a parallel resonant network.<br />

R<br />

+<br />

V o<br />

–<br />

+<br />

V o<br />

–<br />

V omax = V i<br />

0.707V i<br />

V omin<br />

0<br />

V omax = V i<br />

0.707V i<br />

V omin<br />

V o<br />

0<br />

BW<br />

f 1 f s f 2 f<br />

V o<br />

BW<br />

f 1 f p f 2 f

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