Commonly Used Functions for Approximating Constant Gain or Linear Phase

Fig. 9-1 Assumed ideal passband shape

In the filter amplifier the usual problem is to approximate an "ideal" amplitude response, such as that shown in Fig. 9-1, where the gain is constant in some passband region (wi to co2) and zero outside this passband.

In practice, with only lumped, linear networks neither the constant gain in the passband nor the infinite rejection of signals outside the passband can be obtained. Therefore our problem is to discover suitable gain func-

for a filter amplifier. tions which are Physically realizable and which come satisfactorily close to our ideal. In other words we must try to approximate our ideal in a manner suitable for our application. As examples, a radar intermediate-frequency amplifier does not usually require extremely constant gain in the passband, nor does it have particularly stringent requirements on the out-of-band attenuation; conversely an amplifier for telephone repeater service must have extremely constant gain in the passband and possibly very high attenuation out of the passband to remove signals at other carrier frequencies.

Notice that a cascade of identical single-tuned stages provides a crude approximation to constant gain. If we consider the bandpass of Fig. 9-1 moved down to zero frequency, as shown in Fig. 9-2, we can compare the

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