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One way to design a filter is to use the element values of well-known filter prototypes, such as maximally flat or equal-ripple low-pass filters. It is easier to fabricate a distributed element filter on a microwave substrate than a lumped element filter, since it is cumbersome to find off-the-shelf capacitors and inductors that are exactly matched to the frequency-scaled element values of the filter prototype.

This tutorial model demonstrates the design process of a distributed element filter using Richard’s transformation, Kuroda’s identity, and the Transmission Line interface. This approach is very fast compared with solving Maxwell’s equations in 3D. The model simulates a three-element 0.5-dB equal-ripple low-pass filter that has a cutoff frequency at 4 GHz. The resulting S-parameter plot shows a low-pass frequency response that is also periodically observed at a higher frequency range.