TABLE OF CONTENTS As we have seen, designing L-C lowpass filters from the lowpass prototype involves only scaling of the resistance and cutoff frequency of the prototype by simple multiplication and division. The transfer characteristics of the prototype are exactly retained and no special realization difficulties are introduced.
The design of other structures, such as highpass, bandpass and bandstop filters, require transformation in addition to the scaling. These transformations naturally modify the attributes of the prototype and may introduce severe realization difficulties, especially for bandpass and bandstop structures. The "ideal" transformation does not exist, and it becomes necessary to consider alternative transformations and how they relate to specific filter requirements and applications. This chapter considers a number of network transformations and equivalences.
When 1/s is substituted for s in the lowpass transfer function, a highpass response results. However, instead of synthesizing a highpass prototype, it is only necessary to convert lowpass prototype series inductors to shunt capacitors and prototype shunt capacitors to series inductors while inverting the prototype values.
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These normalized highpass values are then scaled to the desired resistance and frequency using equations (65) and (66) in Chapter 2.
Bandpass filters are also designed by transformation and scaling the lowpass prototype. We will consider several alternative bandpass transformations. With the conventional bandpass transform, each lowpass prototype series inductor transforms into a series inductor and a series capacitor. Each prototype shunt capacitor transforms into a shunt inductor and a shunt capacitor. Therefore the...
