Confusion about analog filters

Question

I'm mixed about the concepts of analog filters, so I hope someone can explain me, or point to information, to unentangle the ideas. I know there are filters (analog) as Chevyshev, Butterworth, elliptical... And each one can be configured to have a LP,HP,BP response. Right?

And to change the type or mode of the response (between Chevyshev,Bessel and Butterworth), it's simply playing with the transfer functions based in the specifications, to set the poles and zeros to obtain the desired response.

Is there a method to do this? or its trial and error? I have been using the wizards of ti, multisim and matlab, but I want to be able to do it analytically, Im guessing you have to work out the transfer function and Im taking a LP filter as starting point.

Is this concept right? I'm missing some theory? I work with electronics, but Im trying to apply signal processing into a smart grid to filter and rectify electricity. But the results are not as expected and perhaps I didn't designed right filters or selected an inappropriate IC.

Thanks!.

Answer 1

The classic analog filter types -- Butterworth, Chebychev, elliptic, Bessel, were all designed to meet certain critera with transfer functions that could be generated analytically.

Basically, if I tell you I want an $N^{th}$-order Butterworth low-pass filter with a $3\mathrm{dB}$ transition point at $f_0$, you can go look things up in a handbook, or run a few lines of computer code and generate me a filter -- and if I change my mind about what $N$ I want, you can go do it again, quickly.

Ditto the Bessel, and with a few more parameters, the Chebychev and elliptic.

If I want a bandpass or a bandstop or a high-pass, there's conversions from a low-pass prototype to those filter types.

That's a really good starting point for understanding what you're doing when you're designing analog filters, and the circuits that realize them.

What these filter types don't do is give you the very best filter for any given job -- they give you filters that, in the days of slide rules, you could look up in a book. So when you have a job for a filter, you look at the characteristics you need, you fit those characteristics to the filter types available, and you look in that chapter of your filter tables book.

I haven't done any radio design for money since 1989, and I was just a grad student then, so I suspect things have changed. Today, if you want the very best analog filter for a job, you probably want to start with an actual specification of what it must do (usually in the form of amplitudes vs. frequencies, and possibly allowable phase shifts or group delays), and then let some computer optimization program run with it. If you're smart, you'll probably use a program that takes component variation into account (or maybe you'll start with one of the big name filters, put it all into SPICE, and alternate between monte-carlo analysis and tweaking -- that works pretty well).