Filter Response Types

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Pafnuty Chebyshev is in the Microwave Hall of Fame

New for November 2018: on this page we offer a primer on the differences between Chebychev, Bessel, Butterworth, Gaussian and Elliptical filter responses.  Note that these responses can be applied to low pass, bandpass and high-pass filters types. If anyone has any further knowledge to impart on this topic (or figures!) please get in touch.

Here's a handy video that covers the most popular filter responses from Matt Duff over at Analog Devices:

In the video, Matt references an awesome filter calculator at It will allow you to quickly compare Chebychev, Butterworth and Bessel filter responses for your design. However, it is intended for lower frequency work where op-amp filters are used.  The last time we heard of someone designing a microwave op-amp, it was well diguised as an oscillator.

Tonnesofteware used to have free filter calculators for lumped element filters and diplexers.  Looks like they now want to charge money for their tools.

Critical thinking exercise for military contractor engineers.... what could go wrong when you enter the frequency band of your new missile or radar on a public website?

Here's our breakdown of the reponses for different filters. For demonstration purposes, these are all high-pass filters. We've included the Passband, S-Parameters, and Group Delay for each type - you can click on any of the graphs for a bigger image. 

Chebyshev (equal-ripple amplitude)
The Chebyshev filter is arguably the most popular filter response type. It provides the greatest stopband attenuation but also the greatest overshoot. It is the worst for group delay flatness (OK for CW applications such as a frequency source).

Bessel-Thomson (maximally flat group delay)
Best in-band group delay flatness, no overshoot, lowest stopband attenuation for given order and percentage bandwidth (ideal for receiver applications such as image-rejection filters).

Butterworth (maximally flat amplitude)
Best in-band amplitude flatness, lower stopband attenuation than Chebyshev, better than Chebyshev for group delay flatness and overshoot (usually used as a compromise). All of the above are realizable in parallel-coupled, direct-coupled, and interdigital filter topologies.

This filter provides a Gaussian response in both frequency and time domain. It is useful in IF receiver matched filters for radar.

This type of filter has a sharp response but the rejection band isolation is not as good as Chebychev.


Author : Unknown Editor