What is the practical purpose of a Biquadratic Filter(Tow Tohmas Filter)?

[MrBinns]

With a Biquadratic Filter(TT filter) you can adjust the gain, central frequency, and bandwidth independently.

With a State Variable Filter(SVF) you can adjust the gain, central frequency, and quality factor independently.

The difference is with a SVF as you adjust the central frequency the bandwidth changes. This allows you to set the bandwidth as a percentage of the central frequency, like 3 octaves, as you adjust the central frequency. So a 3 octave bandwidth at 1000Hz is still a 3 octave bandwidth when you move the central frequency down, without adjusting anything else.

I don't see the purpose of using a TT filter. You set the bandwidth to be say 11.049Hz, and central frequency at 15.625Hz. That's a one octave bandwidth centred at 15.625Hz. As you move the central frequency up to 1000Hz the bandwidth stays at 11.049Hz. That's way less than one octave.

It would mean you would get an increasingly narrower band filter.

[R.G.]

Most active filters are not built to be tuned. For a non-swept filter, the BiQuad is a reasonable competitor to the SVF, and choices would be made on things other than the actual filter characteristics.

Typically your ear wants to hear constant Q. For audio swept filters, you'd likely want the SVF. For fixed frequency filters, the choice is not so clear.

[PRR]

Just to be argumentative---

> You set the bandwidth to be say 11.049Hz, and central frequency at 15.625Hz. That's a one octave bandwidth centred at 15.625Hz. As you move the central frequency up to 1000Hz the bandwidth stays at 11.049Hz.

The AM Broadcast band runs from 500KHz to 1600KHz with stations every 10KHz (9KHz in Europe). The proper filter to select one station holds a constant 10KHz bandwidth over a 3:1 range of frequency.

Of course after early (1920-1935) contraptions with semi-constant passband over 3:1 of range, most radios settled for taking ~~50KHz at the input and then shifting (superhetrodyne) everything to a constant 455KHz 10KHz-wide "IF" filter. An alternate does direct conversion to LF with a 5KHz low-pass at the output.

And true: with low-cost op-amps it is not easy to do very narrow filtering around 1MHz. Good AM radio needs several Q=100 filters, so op-amps need GBW far over 100MHz, and while such beasts are no longer costly, they are tricky. OTOH a few coils+caps do the job for a few bucks, ceramic filters maybe better/cheaper, and the ADC guys offer whole new ways to extract voices from the ether

> I don't see the purpose of using a TT filter.

It is mathematically neat for many problems. But probably not many *audio* problems.

[MrBinns]

>The AM Broadcast band runs from 500KHz to 1600KHz with stations every 10KHz (9KHz in Europe). The proper filter to select one station holds a constant 10KHz bandwidth over a 3:1 range of frequency.

o very cool. I did not know this.

[blackieNYC]

A guy I know here in the US was proud to show us the cool tuner he brought home from somewhere across the pond.  Digital. 9k steps, which didn't happen to land on many stations.
Are you looking to do a wah/fixed wah and notch?  Perhaps just a general question. 

[PRR]

> 9k steps, which didn't happen to land on many stations.

About 10%.

However, look inside. There is usually a 9KHz/10KHz jumper.

[MrBinns]

>
A guy I know here in the US was proud to show us the cool tuner he brought home from somewhere across the pond.  Digital. 9k steps, which didn't happen to land on many stations.
Are you looking to do a wah/fixed wah and notch?  Perhaps just a general question.  

I'm about to prototype a parametric eq design. I worked out the math for a TT filter before realizing that it wouldn't work like I wanted. This post was just a general question. I read about them in a book.

I might prototype one for fun. I did the math already so I might as well. I have to buy parts to build up stock though. I'm currently reading the wiki: http://www.diystompboxes.com/pedals/buy.html