design = approximation + realization

The analog filters offered by this site exhibit linear phase responses, ideal for anti-alias use. They are optimized using software developed by the author many years ago, when analog was king! Before this software becomes obsolete I am making a last attempt to see if there is anyone out there who could still benefit from it.

What does the software do? It designs analog filters having unique characteristics. Specifically these include linear phase, equiripple group delay, Nyquist-I responses, or pulse shaping in general.

Those who work with filters apply the term design loosely to the whole process from conception to the final product. The process of design includes two distinct phases - those of approximation , and realization.

These terms, and others applicable to filters, are defined in a GLOSSARY, accessible from the home page.

optimization software features

This site is concerned principally with the design of analog filters. The software which produces their approximations operates in the s-plane. The transfer functions are defined as rational polynomials, typically broken up into a cascade of biquadratic (biquad) stages, plus a possible first order stage.

These filters all have zeros in the right half plane. This makes them difficult to realize in LC (passive) format. Typically they would be realized using operational amplifiers, as a cascade of biquadratic stages. This presents no problem below say 1MHz, but challenges the skills of the circuit designer at higher frequencies.

Each of the biquad stages will have a pair of poles. The biquad with the highest pole Q is considered to present the most difficulty in terms of physical realization. Thus a knowledge of the highest pole Q is of considerable interest to the circuit designer. In general terms Q`s of 10 or more are troublesome, and those of say 20 or more would be considered (by most of us) as being unrealistic.

Compared with systems composed of classical lowpass filters plus allpass equalizers, the approximations produced by this software have the following advantages (for the same amplitude specification):

The first item in the list above illustrates the major advantage of the joint optimization process. Note that this does not come at a cost. Instead, it brings with it added advantages, as illustrated by the next two items - these mean that physical realization is simplified.

As an example of a lowpass filter optimized jointly to equiripple amplitude and delay responses, see the Figure below.

lpf responses

This example filter has the following specification:


lowpass, order 9

passband ripple 0.1 dB, DC to 1 rad/s
stop band -50 dB at 1.8 rad/s

delay ripple 0.1 sec pp, DC to 1.3 rad/s
max pole Q = 3.7

This result cannot be achieved with a classical filter plus allpass equalizer, the whole being of order 9. Note the equiripple delay response extends into the transition band, and has no 'spike' at the high frequency end.

Now please go home to find out how you might obtain a filter produced to your own specification.