Electronic – How was the design of active filter topologies arrived at, invented or discovered


Active filters make use of Op-Amps. This can make it possible to avoid using inductors and get the same effect by "reversing" a capacitor. There are multiple topologies in existance for these active filters:

Chebyshev filter
Butterworth filter
Bessel filter
Elliptic filter

I can see that they have different role off and amount of ripples in pass band and stop band. What I do not understand is how these were discovered or invented in the first place. I fully understand passive filters made up of RLC. It is evident how they work and why they are the way they are. However, for the active filters it is not clear. Did the designers get a hypethetical transfer function first and then realize it in electronics?

Best Answer

A filter topology, whether it's a passive one like a pi-section or an active one like the Sallen-Key circuit, is just a way to produce some poles and zeros. Generally, you can tune the circuit values (resistances, capacitances, inductances) to move those poles and zeros around in the s-plane.

A filter design, like Butterworth or Chebychev, is a choice of pole and zero locations that gives a certain performance (Butterworth has maximally flat pass-band, and Chebychev filters minimize the error between the real filter and a boxcar filter, for example).

You can use whatever filter topology you like to implement whichever filter design you like. First determine the desired pole and zero locations from the filter design. Then tune your component values to achieve those locations. However, you might find that some topologies require unreasonably large or small component values for certain filter designs, or be excessively sensitive to errors in the component values, and that kind of issue might motivate you to use a different topology.

As to how they were invented, I suspect the guys who came up with them were simply very very clever.