Output cap + volume pot cutoff frequencies question [fuzz content]

[midwayfair]

I can use a calculator to just calculate the cutoff frequency based on the cap and volume pot forming a low high-pass filter, but this seems to be missing something once the circuit exists in the real world.

I'll use the Fuzz Face as an example, where just using the stock 500K and 10nF cap results in a calculator telling me the cutoff is 33Hz, but my ears tell me that there's bass being cut, even though clearly there's no guitar note content down that low. RG notes in the Technology Of that 47nF results in more usable bass, and of course it does ... but the cutoff is then 6Hz, which only increased the range by 13Hz within the range of human hearing!

So I must be missing something. Is it simply that the curve is extreme enough that it just BOTTOMS OUT at 33Hz, and the roll-off starts happening much, much higher (so the bass frequencies are just not prominent enough to notice), or is it because in a fuzz like this the bass is so completely clipped and overwhelmed, or am I missing something else?

I know I'm not factoring in the output impedance of the transistor, but I was under the impression it was only a few hundred Ohms, so I figured it was neligible when we're talking about 500K in the volume pot.

[thelonious]

Here's some conjecture for you, which might or might not be correct:
-I think those calcs don't give you the frequency where roll-off starts; they give you the corner frequency, which is usually the -3dB point like this:

Because of that, yes, you are losing some content beyond the corner frequency.

-Especially in a fuzz (and you actually hinted at this in your question), the larger amplitude of the bass frequencies is going to cause significant compression of all frequencies. Think about the sound of cranking a fuzz into meltdown territory with a large input cap, or the sound of a misbiased transistor farting out. The entire frequency spectrum is getting compressed as the transistor clips. When you reduce the input cap, allowing less low frequency content through, there's more headroom left for amplifying the entire spectrum, so higher frequencies will actually be louder than before.

[midwayfair]

This is the caluculator I like to use:
http://sim.okawa-denshi.jp/en/CRtool.php

It gives a frequency analysis, but doesn't specify that I can see whether it's providing corner frequencies or just cutoffs.

P.S. obviously I meant high-pass filter throughout.

[GGBB]

Here's some conjecture for you, which might or might not be correct:
-These calcs don't give you the frequency where roll-off starts; they give you the corner frequency, which is usually the -3dB point like this:

Because of that, yes, you are losing some content above the corner frequency.

And at 6dB/octave - there's at least half an octave above the knee that is affected.  If that diagram is reasonably accurate it is probably closer to 2 octaves due to the rounding of the knee.  So with a 33Hz knee, you could see things actually start to roll off at about 132Hz.

[GGBB]

This is the caluculator I like to use:
http://sim.okawa-denshi.jp/en/CRtool.php

It gives a frequency analysis, but doesn't specify that I can see whether it's providing corner frequencies or just cutoffs.

P.S. obviously I meant high-pass filter throughout.

Looks like it's -3dB - corresponds to 1/(2*PI*R*C).  Nice tool - wish the graphs were bigger.

[thelonious]

This is the caluculator I like to use:
http://sim.okawa-denshi.jp/en/CRtool.php

Nice. That has a lot of options and information. I've always used Jack's, which specifies that it's finding the corner frequency: http://www.muzique.com/schem/filter.htm. I compared them, and it looks like the Okawa calc is giving a very similar result. Any difference is likely because the Okawa calc is spitting out resistors that have been rounded to an E-series. When I chose E96 the results were very similar, though.

Also, I was under the impression that cutoff frequency and corner frequency are essentially the same thing---the "knee" of the curve where the filter really takes effect.

[thelonious]

And at 6dB/octave - there's at least half an octave above the knee that is affected.  If that diagram is reasonably accurate it is probably closer to 2 octaves due to the rounding of the knee.  So with a 33Hz knee, you could see things actually start to roll off at about 132Hz.

Huh. It would be interesting to do a listening test comparison to a filter with like 24db/octave or something, set to the same corner frequency, and see what the sound difference was.

[samhay]

And at 6dB/octave - there's at least half an octave above the knee that is affected.  If that diagram is reasonably accurate it is probably closer to 2 octaves due to the rounding of the knee.  So with a 33Hz knee, you could see things actually start to roll off at about 132Hz.

Huh. It would be interesting to do a listening test comparison to a filter with like 24db/octave or something, set to the same corner frequency, and see what the sound difference was.

You don't have to go that high. A 2 pole HPF is noticably sharper than a 1 poler filter. I think it is a little harder to hear the difference in a LFP, but I bet you could hear the difference with a 4-pole (24db/octave) filter.

[samhay]

Jon - if you want to make it more complicated, you could add (in parallel) the load impedance/resistance to the half of the pot going to ground. If the load is 1M though, this is only going to matter with a large pot when the volume is almost all the way up.

Edit - not volume down, but volume up - most of the pot resistance going to ground.

[midwayfair]

So with a 33Hz knee, you could see things actually start to roll off at about 132Hz.

I have a feeling this is what I'm missing, and I'm sure you or someone else has explained it to me before. I have a bit of a mental block in getting what I'm hearing in-circuit to correspond to what's on the page with frequency filtering. This despite having a decent handle on multiband EQs in recordings and live sound.

[thelonious]

I have a bit of a mental block in getting what I'm hearing in-circuit to correspond to what's on the page with frequency filtering. This despite having a decent handle on multiband EQs in recordings and live sound.

Me too. I think the slope creates a significant feel difference between the filters we use in pedal work and the average mixer or software EQ. In my experience those tend to have at least 12dB/octave slope, and usually higher.

You don't have to go that high. A 2 pole HPF is noticably sharper than a 1 poler filter. I think it is a little harder to hear the difference in a LFP, but I bet you could hear the difference with a 4-pole (24db/octave) filter.

Sounds like I might have a new experiment to perform now. 

[thelonious]

I finally remembered where I had seen a calculator that showed both voltage gain and decibels, in numbers, at multiple frequencies of particular interest to guitarists. This ampbooks calculator is intended for amps/tubes, but it clearly shows how much the gradual slope affects frequencies above the corner frequency:
http://www.ampbooks.com/home/amplifier-calculators/coupling-capacitor/



(Note the "Volume Setting" slider - it's set at 50% by default, which is why frequencies fully passed by the filter are still at -6.34dB in this image)

[midwayfair]

I finally remembered where I had seen a calculator that showed both voltage gain and decibels, in numbers, at multiple frequencies of particular interest to guitarists. This ampbooks calculator is intended for amps/tubes, but it clearly shows how much the gradual slope affects frequencies above the corner frequency:
http://www.ampbooks.com/home/amplifier-calculators/coupling-capacitor/

This is one of the best calculators I've ever seen. Thank you so much for the hook-up!

[thelonious]

No prob. They have loads of great calculators on that site.

[GGBB]

Yes - very cool.  Any idea what output impedance would be appropriate for op-amps, FETs, or transistors?  I'm guessing as low as possible (calculator only goes down to 1K).  Seems like the higher the output impedance, the greater the rounding of the knee - but only slight.

[samhay]

thelonious  - just realised I got another thing backwards. If my hazy recollection is correct, you can hear the steepness of a filter more easily in a LPF than a HPF. I vaguely recall a thread around here, perhaps by Mark Hammer, that says something similar (or quite possibly not). Either way, playing with higher order filters is a great way to spend some time.

[PRR]

> calculate the cutoff frequency based on the cap and volume pot forming a low high-pass filter

Draw the WHOLE circuit.

*Usually* a "volume pot" drives a LOAD. When pot is full-up, that load parallels the pot. If pot is 500K, and load is 500K (not atypical amp input), then your "33Hz" is really 66Hz, and -1dB to -2dB over the bottom half-octave of guitar.

If load is 50K, then 33hz becomes 330Hz and a severely gut-less guitar. (Also a very weak output when pot is turned lower than "9", though the bass response improves.)

*Usually* what you want is all bass-cut caps MUCH larger than necessary. Like 1Hz. Especially any place where such a target moves you to a small Electrolytic instead of a large Film cap.

Remember that a Whole System is not "one cap". There may be twenty bass-cut caps between axe and speaker. If each one is "only" 1 dB down at 82hz, that's *20* dB down on your low note.

There are places where you want to limit bass. Fuzz circuits sorta hafta cut-back bass or the sound gets muddy. A guitar amp probably should have at least one fairly-tight bass-cut to reject subsonic thumps and to limit the damage a bass player can to to guitar speakers. SE transistor audio amps need a HUGE capacitor to the speaker, and we don't make this any more huge than absolutely needed (one reason such designs are now uncommon).