cascading filters question

[Jeremy]

In the schematic for Runoffgroove's Professor Tweed:

http://runoffgroove.com/professor.html

There are two cascaded low-pass filters at the end, just before the volume control.  They look like two simple 6db/octave 7.2kHz rolloffs forming one big 12dB/octave rolloff.

My question is, is that really what those filters are doing? 

Because from what little I know of electronics, I thought that the impedance of the signal going into the filter would drop the cutoff frequency quite a bit.  That means, I think, that the output impedance of the last amp stage is going to affect the cutoff frequency of the first filter, and both that impedance and the first filter's impedance will affect the frequency of the second filter.

Is what I'm asking making sense?

Which is it?  Is it one big low-pass at 7200 Hz or is it two lower low-passes?

[Mark Hammer]

On paper, it is just meant to mimic what happens when you feed an amp into a speaker with limited bandwidth.

Having said that, the ways of circuit fragments whose properties change depending on what follows them is a complete mystery to me.  Those 2-pole filters MAY well work a little differently than intended, but I suspect they were planned to have certain properties ignoring what comes after them.

One of the nice things about steeper filters is that they can often permit a wider usable passband than shallow ones.  If I'm concerned about 12khz fizz, a single-pole lowpass at 7.2khz won't do a whole lot for me.  I would be wiser to set my rolloff much lower to achieve a noticeable reduction of fizz in that region.  On the other hand, if the filter is steeper, I may very well get the same attenuation at 12khz using a 2-pole 7.2khz filter (and even more higher up) that I would have gotten with a single-pole 6khz filter...except that I don't affect content between 6khz and 7.2khz.

[Rob Strand]

>That means, I think, that the output impedance of the last amp stage is going to affect the cutoff frequency of the first filter,

Yes.  The only thing that remotely saves it is that last stage has negative feedback which will lower the output impedance (I would have to analyse it to determine whether it is successful or not).

>  and both that impedance and the first filter's impedance will affect the frequency of the second filter..

and yes.  The two stages interract and this precludes using the 1/RC cut-off formulas directly.  If the resistor of the second stage is somewhat larger than that of the first stage then the two stages act independently

In addition the volume pot affects the behaviour of the last filter, by a small and just noticeable amount.

When stages are cascaded you are correct in suspecting that stages interract (something which is overlooked all too often in the effects world, even in commerical devices).  The interraction does change the behaviour.  The trick is to recognise when tyou can ignore it, or when it happens, how to compensate for it.  You can do this theoretically but equations get harder to manage - sometimes you can do a good approximation and keep them manageable.

You will find some people design circuits ear then do a write up with simple equations.  The circuit is *usually* "right/intended"  but the write-up is technically incorrect!


>Which is it?  Is it one big low-pass at 7200 Hz or is it two lower low-passes?

It is two low passes (called a second order low-pass).  However the roll-off is not as steep as the case when the two RC networks are buffered from each other.

[Ge_Whiz]

You will have noted the precise wording in the Prof. Tweed article:

"Our "artistic license" is in the choice of the last JFETs output cap and the setting of the dual Low Pass Filters. Our goal was to produce the sound of a Jensen speaker. These are typically a little broader in frequency response than something like a Celestion."

The guys at ROG put a lot of effort into tweaking things by ear. It's possible that Brian has a tin ear, but as far as I can tell, his tin ear is a good match to my tin ear, so I like the sound of ROG circuits. I am, of course, free to carry out my own tweaking. Having said that, resonance equations are not a bad place from which to start the tweaking process.

[Jeremy]

Thanks Mark, Rob, and Ge. 

That all makes sense. 

I'm not questioning ROG's circuit design, just my own ability to analyze it!  :-)  The mp3 examples of this circuit sound great.