Generalized Chebyshev Filter

In this week article, lets discuss the Generalized Chebyshev class filter. Firstly, here’s a video on a Generalized Chebyshev class filter constructed using our EDS HF software.

The Design

The Generalized Chebyshev filters have equiripple passband characteristics and flexibility in placing transmission zeros arbitrarily. The synthesis of this type of filter is based on the locations of the zeros in the complex plane placed symmetrically or asymmetrically, and the degree of the filter. In the video demonstration, the 5th order Generalized Chebyshev lowpass filter is synthesized with the ladder-type network with the prescribed zeros at ±1.2 rad/s, ±1.4 rad/s and ∞.

lumped 5th order Generalized Chebyshev

After synthesizing the ideal lowpass filter network, the highpass Generalized Chebyshev filters can also be constructed. Under the Richards highpass transformation, the transformed highpass network has series open circuited stubs. With a single transmission zero at infinity, the series inductors can be realized as an open circuited stub with characteristic impedance of Lr (r is the rth inline inductor) and the electrical length of 45o at the cutoff frequency fc. For the resonators in the lowpass network can be realized as a shunt open circuited stubs with the characteristic impedance of 2/Cr and electrical length of 90o at the cutoff frequency fc. Based on the highpass Richard transformation, the 5th order Generalized Chebyshev highpass filter network, cutoff at 1GHz, can be synthesized and realized as:

Distributed equivalent circuit

In summary, the Generalized Chebyshev filter, though harder to design than the common Chebyshev, is popular due to the unique characteristic to arbitrarily place transmission zeroes in the response. It is a good design to understand. Perhaps it may come in handy in your future designing work!