Why do active and passive filters have such fundamentally different responses?

Question

I'm a first-year electrical engineering student and we have an exam coming up on active filters. Before studying engineering, I had played around with active filters, even designing and building a guitar pedal once that was essentially just a filter in a box.

My coming exam got me thinking, though: what is it about active filters that makes their response so fundamentally different to passive filters'?

For instance, the Chebyshev topology has passband ripple. Why? Why don't passive filters ever have passband ripple?

Nothing in my textbook explains this.

Answer 1

Active analogue filters have an advantage over passive analogue filters in that they use near perfect voltage sources - this means you can mimic inductors with op-amps, capacitors and resistors and build multi-stage high order filters like Chebyshev.

But, theoretically you can build just as complex a filter in passive components as you can with active components - just look at some antenna filters - they can use ceramic resonators to kill-off unwanted transmitter harmonics and ceramic resonators can also used to reject the transmission frequency in cell-phone handsets allowing full-duplex simultaneous send and receive.

Here's a quick simulation I did: -

It's got a couple of dB of passband ripple and certainly rolls off the frequency nicely above 600kHz but it's a passive implementation.

In conclusion there is no theoretical fundamental difference between active and passive analogue filters.

Answer 2

It's all a matter of where the zeroes and poles are. Active or pasive are just ways to achieve these zeroes and poles, by means of feedback, or gain... but at the end, the response depends on the zeroes and poles (and vice versa).

Also, you can have a passive Chevyshev filter, with the pass band ripple included. Chevyshev (as also does Butterworth, Eliptic, etc) only fixes the position of the zeroes and poles.