Dist+ filtering question

[comfortably_numb]

I will soon be ordering parts for a modified Distortion+ and I'm looking into all of the available modifications to the circuit.  I want to make this as much "mine" as I can.  One thing that confused me was the 10uF cap in the feedback loop.  Technically it creates a high pass filter, correct?  But I calculated the rolloff with the 1M resister as .05something...obviously completely neglegible with regard to the audible spectrum.  What then does this capacitor do in the Dist+ that it is absent in the DOD 250?

Also, can I make a SWTC out of the 10k output resistor and the .001uF cap to ground?  Values adjustable of course.  The question is, can I move that resistor post diodes without a problem?  I suppose this would lower the clipping threshold...sort of...but I'll be using LEDs and Sis anyway.  Any thoughts?

[Mark Hammer]

Whoa, camel.  I said WHOA camel.  I said WHOA!!!!!

10uf in the feedback loop?  That's just plain wrong.

If you use a 10pf cap in the feedback loop, in parallel with 1M, that results in a lowpass filtering effect.

Why?  Because the relative gain of any part of the spectrum depends on how much negative feedback makes it from the output back to the input.  So, yes, the 10pf cap provides an easy path for high end, but that just means that the high end in the negative feedback does a better job at suppressing gain for that part of the spectrum.

10pf in parallel with 1M will roll things off around 1/[2*pi*1*.00001]=15,915hz, which isn't terribly low.  Actually, it is probably done just to eliinate high-frequency instability, rather than for filtering in a tonal sense.  Raise that cap to 22pf, and you'll start to hear some filtering as the rolloff gets dropped to 7.2khz (4.8khz with 33pf).

The 10k resistor limits the current seen by the diodes.  I couldn't quote you chapter and verse on how, but suffice to say that I've seen and built all sorts of diode clippers that vary the resistance leading up to the diodes (and/or in series with the diodes to ground), and it changes the flavour.  Not in a bad or good way, just different.

Given that you plan to use LEDs for clipping, the output level will be hot, so you can afford to lose a couple db on the output from something like an SWTC and the added series resistance it provides.  On mine, I use a 10k SWTC pot in series with the 100k output pot.  I also have a switch for Ge vs Si diodes.  With Si diodes, even at medium gain, there is still plenty of volume boost available with the SWTC inserted. 

If you are planning to use an LED in there, then the ceiling on output will be raised even higher, as will the clipping threshold.  You should probably compensate for this by raising the maximum gain so that there is some likelihood of clipping.  Do this by dropping the value of the 4k7 resistor in series with the gain pot to 3k3, or even as low as 2k7.  2k7 gives a max gain of x371.  3k3 gives a max gain of x304.  When you consider that the Rat aims for max gains greater than 2000 for parts of the spectrum, that's not so crazy.  The TS-9 aims for max gains of around 118, but then the clipping threshold is one third of what an LED's is.

Note that by dropping the 4k7 downwards in value, you run into the issue of bandwidth changes at max gain.  One of the curses (or virtues, depending on your perspective) of the Dist+ is that bass gets cut with increased gain.  This relationship can also be calculated by the F = 1/(2piRC) formula.  Using the stock .047uf cap and 4k7 resistor rolls off bass around 720hz at maximum gain.  Changing to 3k3 or 2k7 would make that even worse (1254hz with a 2k7 resistor -    where'd that fundamental go?!).  So, dropping that resistor to get more gain and oomph will require a change in cap value.  You should probably aim for .22uf or larger.  .22uf will roll off bottom around 268hz at max gain, which isn't unbearably thin.  MXR did not use fancy plastic caps for these parts, so you should be able to easily stick a ceramic .22uf cap on the board in the spot allocated for a .047uf plastic cap.

Between the added bottom, a bit of top end shaved off by the larger feedback cap (22pf-33pf), the added gain of a smaller gain-setting resistor, the higher clipping threshold of an LED, and the fizz-taming of a SWTC, you should be able to get a pretty loud, warm and meaty-sounding output that does not require you to either turn down yur guitar's tone control or the treble on the amp for it to be usable.

[comfortably_numb]

Does the 1M feedback resistor not interact with the 0.047uF cap to form a low pass filter also?  I suppose this doesn't make sense however, as I calculate a rolloff frequency of 3.39 Hz.  Obviously not a possibility for audio processing. 

I'll most likely be leaving the 10pF cap, and letting the SWTC shave the fizzies.  What size cap would you recommend?  I want a full audio spectrum with the ability to tone down the bite if necessary.

You mentioned that 1254Hz would be removing the fundamental...this is obvious...but I would say that 268Hz is also a little low, as the low E fundamental is around 82Hz, correct?  I would like to keep as much of this intact as possible, but I also don't want the signal to get muddy.  Any particular rolloff frequency that makes a good balance between this?  Maybe 100Hz?  Also, I am playing with a humbucker equipped guitar, so take that into account.

I may use the lower series resistor to increase gain range also. 

Thanks a lot Mark.  I'm always very appriciative of your help.

[Mark Hammer]

You need to think about the negative feedback in terms of "what am I suppressing?".  The feedback from the output encounters a kind of volume pot, comprised of the feedback elements, and the ground leg.  If I had a 500k feedback resistor, and a 500k resistance to ground, then I have essentially produced a 1M pot turned down to half.  Since the "wiper" of that pot presents an attenuated signal to the '-' input, the resulting gain from the op-amp will be less than the maximum possible from it.

If one reduces feedback resistance or provides a means for some output to find its way to the '-' input, then you suppress the op-amp more.  The same way a compensation/bypass cap on a Fender volume pot lets treble through even though the volume is turned down, a feedback cap on an op-amp lets treble feedback pass easily, which suppresses the gain of the op-amp even more (gotta think opposite, right?). 

Occasionally, you'll see little T-networks in the feedback loop, with 2 caps in series, and a resistor to ground from their junction.  These networks provide selective boost.  How?  Well, again, think of what does and doesn't make it back to the '-' (inverting) input pin.  The first of the two caps (starting from the output and working back to the input) is followed by two paths to follow.  The resistor to ground, in combination with that first feedback cap, forms a highpass filter, bleeding lower frequency content to ground.  But the two caps in series provide a path for treble to get to the inverting input, so what happens?  Combine a highpass and a lowpass filtering effect, and you end up with a bandpass.

But what about the so-called "ground leg" of our imaginary pot?  Say we have a 1M feedback resistor, and a 500k ground resistor.  That's kind of like a 1.5M pot turned down 2/3, isn't it?  If the feedback to the inverting input is reduced by virtue of the action of our imaginary pot, then there is less suppression of gain and gain is higher.  What if we stuck a cap in series with that 500k, between the 500k and ground.  We would have a pot with a ground leg of 500K plus zero ohms for HF content (since HF passes through the cap easily), and a ground leg of 500K plus some additional resistance for lower-frequency content.  If we are "bleeding" more treble content to ground through that cap, then that means less suppression and more gain for higher frequency content than for lower frequency.

One of the best known examples of this is the Rat.  There ( http://www.diystompboxes.com/pedals/PCRAT1.GIF ), you will see two different ground legs.  One is 560R through a 4u7 cap, and the other is 47R through a 2u2 cap.  What do these do?  Since the lower resistance of a ground leg means more signal bleed-off by our feedback+groundleg "pot", that means greater gain.  But how much is being bled off at different parts of the spectrum?  Here, two formulas come to our rescue.  One calculates gain: R-feedback plus R-ground divided by R-ground.  The other calculates rolloff F = 1/(2piRC).  The 560R path delivers maximum gain of (100k+560R)/560R=178, with gain being flat above 1/(6.283*.000560*4.7) = 60.5hz.  The other path, meanwhile, provides a max gain of 2,129 (  ), which is flat above 1/(6.283*.000047*2.2) = 1539hz.  We end up with this because the point where bleed-off becomes frequency-sensitive depends on the joint product of R and C.  So, one path produces huge bleed-off for content above 1539hz (less suppression = more gain) and the other produce modest bleed-off for most of the audio spectrum (above 60hz) and much less bleed-off (hence more suppression and less gain) for content below that point).

Because you don't want to take a DC drift from the output of the op-amp and multiply it by 100, 200, or 2129, it is always wise to provide no bleed-off of DC from the output back to the inverting pin.  ANY capacitor in series with the ground resistance will pose a high-resistance path to ultralow frequencies and DC.  Again, no bleed-off means complete suppression by negative feedback.  So that cap to ground assures you won't inadvertently turn a 1mv "output error" into a 300mv problem.  Happily, though, you can use it to shape tone because it not only bleeds off DC but bleeds off lower frequencies above DC to whatever point you desire.  If the RC combination provides for gain-increasing bleed-off above 3.39hz, then you know you won't have problems with DC, but it also means that any 60-cycle hum coming in via your cable will receive the mixed "blessings" of all the gain you apply to the audio signal.  As a result, while most pedals are generally designed to permit for full bandwidth, even when you string 10 of them end to end (and shaving off 2db at 16hz and below would give you something like that), very high-gain pedals are often designed to provide less gain where it might risk boosting objectionable components, such as 60hz hum.

The Dist+ was designed to provide for a rolloff below 6.7hz at min gain, and 720hz at max gain.  At near-unity min gain, one is not quite that concerned with accidentally boosting 60hz hum from single-coil pickups, so a passband that extends down to under 7hz is fine.  As gain increases though, multiplying the amplitude of 60-cycle hum by 50, 100, and finally 214 (max gain of a stock Dist+) is not something you really want to do.  So, the cap value is selected such that gain changes resulting from reducing the resistance value, also reduce gain for low frequencies.  As with lots of things, the same gain control also ends up producing supplemental tone changes because the rolloff changes location so dramatically.

To tie this all together (because I do have to get some work done today), you want to aim for something that keeps that dang 60hz out of there as the gain starts to add up, wihout presenting so much of a bass-chop at high gain that the sound wimps out.  That can be with one well-chosen cap, complemented by the gain pot inserted in a manner I described the other day in another Dist+ thread.  Alternatively, you can consider a toggle with several choices of cap value depending on where you want to set the gain.

Although your idea of tending to the fizzies with the diode-paralled cap and SWTC is fine, understand that the harmonics you end up having to control are a function o the frequencies you try and sneak by the clipping diodes.  If the bandwidth of the audio signal being clipped is limited, then you don't end up with harmonics of harmonics of harmonics to shave off down the line.  As such, taming the high end in the gain stage can do wonders for having the tone controls down the line accomplish what you need them to.  Personally, I would advocate for a 22pf cap replacing that 10pf unit, unless noisiness and audio splatter is what you want and need from the pedal.

[LyleCaldwell]

This should be retitled and stickied.  Great post, Mark.

[Mark Hammer]

Thanks.  I think it needs to be accompanied by a drawing of an op amp with the feedback and ground path drawn as a pot.  I, um, don't have schematic-drafting software installed on my work machine.  If somebody wants to draw that and label it, I'd be honoured to revise the post and use the reference labels included in the drawing.

[DryRoasted]

sorry to revisit an old thread but if anyone takes up Marks offer and runs off a diagram, I for one would find it of great value

[wampcat1]

And yet ANOTHER great post by Mr Hammer...

a book I tells ya! You need to write it all down in one place brotha!!!! 

bw