Rat gain control vs. Dist+ gain control?

[the_floyd]

The Rat uses a 100K pot in place of a feedback resistor in series with the NFB loop, whereas the Distortion+ uses a fixed 1M feedback resistor, and a 500K pot between the 4k7/47n "feedback leg" and ground. How would these two types of gain adjustment behave differently (if at all)?

Help would be much appreciated, as I'm still working to understand these sorts of things.

[Mark Hammer]

I've described this before.  Maybe this time I can do it in fewer words.

The feedback resistance, and resistance to ground form a virtual potentiometer, with the virtual wiper going to the "-" pin of the op-amp.

Op-amps are built to go full-tilt, with gobs and gobs of gain, unless you do something to tame them.  Like horses on speed, that will run themselves ragged unless you pull back on the reins. 

What brings the op-amp back from  the edge of all that unrestricted gain is negative feedback from the output to the inverting input.

Going back to or "virtual pot", it may have occurred to you that the output side of the feedback resistance is kind of the "input lug" of our virtual pot. 

Now, the amount of attenuation a pot provides to whatever is coming into it (and leaves via the wiper) is a function of the ratio of the resistance between input and wiper, to the total resistance of the pot.  What this means is that the smaller the feedback resistance is, relative the ground-leg resistance, the less attenuation of feedback there will be.  Conversely, the smaller the ground-leg resistance is, relative to the feedback resistance, the more attenuation there will be of that feedback.  The output feedback comes through the feedback resistance, but if the path from inverting input to ground is tiny, then most of that feedback is dumped.

But hold on a sec!  The feedback is what keeps the op-amp "behaving", and more feedback will pull the reins tighter, and reduce gain.

Okay, starting to gel?   The less negative feedback arrives at the inverting input pin, the more "unrestrained" the op-amp will be, and the more able it is to move towards its maximum gain.  The more negative feedback there is, the lower the gain will be.

So, if you increase the feedback resistance, as in the Rat, and leave a small ground-leg resistance, you are attenuating the negative feedback more, thereby increasing gain.  If you hold the feedback resistance constant, but reduce the ground leg resistance from where it is, you are again, reducing the amount of negative feedback and thereby increasing gain.

But why does this matter?  You ask an excellent question!  It matters because the feedback cap that sets the treble rolloff point, and the ground leg cap that sets the bass rolloff, interact with their respective resistors in opposite ways.  They both conform to the F = 1 / [2 * pi * R * C] rule, but with a different impact.

On the ground leg, smaller resistance values increase gain.  Holding the cap value constant, decreasing the resistance also moves the bass rolloff upwards.  With a .047uf cap, the 500k Gain pot (+ 4k7 series resistor) on the Dist + and DOD250 move the bass rolloff from about 7hz at minimum gain (when ground leg resistance is 504.7k) to 720hz with the gain maxed. 

On the feedback part, increasing feedback resistance (to increase gain), while holding cap value constant, will decrease the treble rolloff.  So, a Tube Screamer uses a 51pf cap, a 51k fixed resistor and 500k pot.  At min gain (pot = 0k), the treble rolls off at 61khz.  At max gain (pot = 500k), that hikes on down to just under 5.7khz.

So, to sum up, if you adjust gain by the feedback resistance, you roll off more treble as gain goes up.  If you adjust gain by means of the ground leg, you lose bass as gain goes up. 

Both are useful in their own way.  Since distortion generates more harmonic content, losing more treble by having your gain adjustment in the feedback path "smooths out" the resulting tone, depending on what cap value you've selected, and what the actual range of adjustment is.  BUT, high gain applied to unshielded signals tends to result in more audible hum.  This is partly what I think the ground-leg adjustment on the Dist+/DOD250 was intended to do.  Remember, when they both first came out, there was nowhere near the choice hum-rejecting pickups with single-coil tone that we have available now.  So, a pedal that push the 60hz hum to the background as it gave you more crunch and distortion was killing 2 birds with one stone.  And since so much of the signal lives in the bass-ment, trimming back the bass as gain is increased also provides for a smoother transition in distortion tone.

Some time back I tried to sidestep this dilema with a booster I called The Crank.  I tried to put both principles to work with two cascaded op-amp gain stages.  One adjusted gain via the ground leg, and the other adjusted it via the feedback resistance.  Since gain is multiplicative (gain of 2x, followed by gain of 5x = total gain of 10x), all I had to do was provide a small increase in gain in each stage to get a total gain that was reasonably substantial.  And because the amount of resistance adjustment in each stage was small, there was very little bass or treble loss as gain was increased (though I rigged it to provide more treble loss than bass loss, simply because amps like that sort of boosting).

Clearer now?

[the_floyd]

Much clearer, thank you! It took a couple of reads to understand, granted, but I certainly understand it now. As an aside, it's great having experts such as yourself around here, Mr. Hammer - I've come across many of your postings while researching, and they've taught me a lot. Thanks again!

[John Lyons]

Good question, good explanation.
Thanks guys! 

[Mark Hammer]

Much clearer, thank you! It took a couple of reads to understand, granted, but I certainly understand it now. As an aside, it's great having experts such as yourself around here, Mr. Hammer - I've come across many of your postings while researching, and they've taught me a lot. Thanks again!

It probably needed some pictures to help out, but we got there eventually.  Glad it helped.  Thanks for the nod.

[ashcat_lt]

There's also that thing where the Rat can actually get down to unity, while the other always has some (about 2.5 x?) gain.

[Mark Hammer]

The Rat's ground leg resistors are so low that it makes little sense to try and stick something in series with the Gain pot to achieve a minimum gain.  In the case of the Dist+/DOD250, you have to have something on the ground leg or else you just elicit unstable behaviour from the op-amp.

If you find the 250 or D+ lacks enough zip/oomph for your needs, you can do two simple things without changing the board in any way:

1) replace the 4k7 resistor with 3k9 or even 3k3 to increase the max gain from 213x to 304x,
2) replace the .047uf cap with .1uf or even .22uf to retain more bass as you increase gain, resulting in a larger amplitude output signal from the op-amp, and more clipping from the diodes at medium and higher gain settings.