gain of a ts-808

[TimWaldvogel]

i add the 500k, 4k7 and the 47k together and divide it my 4k7 right? so what is the gain of a ts808 about 117?
turkey must be giving me a brain fart, i feel encouraged to design my own distortion design. i read cook your own distortion article before but have never decided to calculate gain in a circuit where there is a resistor is at the minimum end of the pot

[Keppy]

This should help:
http://www.geofex.com/Article_Folders/TStech/tsxfram.htm

I've successfully designed a few gain stages based on the information in this article. Scroll down to the heading "Clipping Stage" for the answer to your question.

[Mark Hammer]

Well your calculations are correct.  One of the reasons why the TS series is considered an overdrive, rather than a "distortion" or "fuzz", is precisely because the gain is not high enough to elicit serious clipping.

The Boss SD-1 has higher max gain: [1M+39k+4k7]/4k7 = 222x, but also raises the clipping threshold a bit via use of a 2+1 diode complement.  Of course, in using a 39k minimum feedback-resistance value in conjunction with the 2+1 diode arrangement, it also achieves LESS gain than a TS, such that the TS has more dialability (i.e., less variation n gain, distributed across the full pot rotation), but the SD has more range for the same pot rotation.

Drop the 4k7 resistor in the TS down to 3k9, and your max gain goes up to 142x.  Drop the 51k fixed resistor down to 39k as well, and your gain range now goes from 11-139x, instead of the standard 12-117x.

Of course, change the gain-setting resistors, and you also change the various rolloffs.  With 3k9 instead of 4k7, the low end rolls off at 868hz instead of 720hz.  Bring the cap up to .068uf, and you get a rolloff starting around 600hz, which will bring back a bit of body, but not so much that it alters the essential nature of the TS sound.  

With a max feedback resistance of 500k+39k, you'll get a treble rolloff at just under 5.8khz, instead of  5.6khz.  When you factor in component tolerance of the resistor, cap and pot, that's no real change, so you can leave things be.  Although, with greater max gain, a person might be tempted to stick in a 68pf cap instead of 51pf, for a rolloff at 4.3khz at max gain.  Keep in mind that at a gain equivalent to a stock TS, that would put the gain pot at around 420k, which would provide a rolloff around 5.1khz.

A low-end rolloff around 600hz, and top end rolloff around 5.1khz, would actually deliver a slightly warmer fuller-bodied sound for settings similar to a standard TS, plus you'd get a little more seriousness at max gain, without seriously compromising dialability.

Dontcha love math?

[TimWaldvogel]

Mark little did you know you just greatly aided me inte design of my first OD/distortion pedal.
Thank you sir :-)

[TimWaldvogel]

How do you do it if our using two op amp gain stages?
How do you configure the overall gain

[Mark Hammer]

Gain is multiplicative.  So one gain stage of 10x, immediately followed by another of 10x, gets you 100x. 

Of course, it gets a little more complex to get a sense of amount of boost in output when there is any sort of attenuation between stages.  If stage A applies a gain of 300x, stage B applies a gain of 4x, and there is a signal-sucking passive tonestack between those two stages, what you get at the output will NOT be 1200x the input amplitude. 

Moreover, since there are limits on how much voltage swing the semiconductors in the circuit can produce with the supply voltage, the gain figures really only apply to very small signals. For instance, if one uses a dual op-amp that can only swing to within a volt of either rail, AND the circuit is powered by 9vdc, then the maximum swing in the signal is only 7v "wide", or +/-3.5v.  Let's say that the average input signal from a guitar is +/-100mv.  That means we can, on average, apply a gain of 35x without running into headroom issues.  For the peaks on pick attack, we are likely to exceed 100mv several fold, and shortly after pick attack we are likely to descend below100mv.

One of the implications of this is that some of what we are hearing in overdrive/distortion pedals that use diodes is not the diodes, but rather the limitations of the chip itself.  This is partly why folks will find they like the nuances of the tone more with this chip than that one.  Of course there are circumstances where the diodes play greater and lesser roles than the properties of the op-amp under duress.

The Marshall Bluesbreaker provides an interesting instance of gain multiplication.  The Gain pot forms part of the feedback resistance of stage 1 with the resistance on one side of the wiper, and part of the input resistance of stage 2 with the remanider of the resistance on the other side of the wiper.  When the Gain is turned down fully, the feedback resistance of stage 1 is 1x, and the 100k is added to the input resistance of stage 2, giving it a gain of 2x.  If we bring the Gain pot up halfway, so that feedback resistance is 50k in stage 1, and input resistance is 50k+10k in stage 2, we get a basic gain of 11.6 in stage 1, and a gain of 3.7 in stage 2, yielding a combined gain of around 42.7.  I say "around" because the gain-setting loops in that circuit have a number of other things going on.  The point is, however, that use of the multiplicative principle in this design, can get us some considerable gain fairly quickly.

[TimWaldvogel]

So when people stack op amps that's to help create a larger potential headroom without the larger supply voltage?
Because they are in parallel they can potentially can have  a larger voltage swing without taking more than 9v. Of course I'm sure the mA gets bumped up as well

[Mark Hammer]

No, it's to be able to put out more current.  As I understand it, the behaviour of diodes can be a function of the amount of current they are being asked to pass.

There is also op-amp stacking used for purposes of feeding current into low-impedance loads like headphones.

Here, I shall stand back and eagerly await the comments of my betters, who actually HAVE training in this area.

[TimWaldvogel]

I think I get what you mean a bit. For some reason I though stacking op amps gave you a little bit more headroom

[TimWaldvogel]

Obviously resistors mean noise, but you can also reduce clipping by putting resistors in series with the diodes right?

[Mark Hammer]

yes.  Try to think of diodes as a more extreme version of a capacitor.  Where a cap serves as a lower-impedance path, the higher the frequency of AC content coming its way, a diode acts in a largely all or none fashion, acting as a brick wall up to the "knee" of the forward voltage, then like an expressway once the forward voltage is exceeded.  If there is a resistor or cap in series with the diode, then it's like a gate that opens up to a less efficient gravel road, rather than an expressway.

If I put a pair of diodes in the feedback loop of an op-amp, then the gain of the op-amp is set by the usual factors - feedback resistance, etc. - until the forward voltage of the diodes is reached.  Remember that, in an op-amp, the gain is determined by how much negative feedback is applied.  The analogy I like to use is that an op-amp behaves like a car whose accelator is on full (pedal to the metal), and you regulate the speed by how hard you step on the brakes.  If there is a feedback resistance, that provides some attenuation of the negative feedback (i.e., less brakes applied), and you start to move in the direction of full open-loop gain (where there are NO brakes applied).  When the signal level exceeds the forward voltage of the diodes, however, you provide an essentially zero-ohm path for that negative feedback to actively reduce the gain of the op-amp (slam on the brakes).  Naturally, when the op-amp gain is forced low by the diodes passing signal, that precipitates the production of a signal that, in turn, falls below the forward voltage of the diodes.  That's how the signal is "clipped" and held to some constant maximum, and now the gain is once again set by all those other passive components.

If there is a resistance in series with diodes, then even when the diodes open up and pass signal, there is still an impediment to that negative feedback affecting the op-amp's gain.  The result is that the "clipping" produced is not so hard, and not so low in amplitude.

I sold a modded TS-808 clone to one of Canada's more distinguished blues guitarists (Tony D of Monkeyjunk) about 4 or 5 years ago, where I had inserted a 10k pot between one of the clipping diodes and the inverting pin of the clipping stage.  This resulted in harder clipping for one half cycle than for the other (assuming the pot was set for other than zero ohms), because of the series resistance.  The result was continuously variable dynamics, and a somewhat more open feel.  Don't know if he still uses it, but he loved it at the time.

[TimWaldvogel]

Now I just need to find out/research/read about how the series resistor at the input of a second gain stage etc. affects the gain multiplication

[Mark Hammer]

Any basic reference on inverting vs non-inverting op-amp configurations will explain it.  But basically, it works like this.  All other things being equal, the gain of an inverting op-amp is dictated by the ratio of the feedback resistance  to the input resistance.  A 10k input and 100k feedback gets you 10x.

For non-inverting op-amps, the gain is set by the combination of the feedback resistance and "ground leg" (the resistance from the '-' pin to either ground or Vref), divided by the ground leg.  So, feedback of 470k and ground leg of 10k = (470+10)/10 = 48x.

[TimWaldvogel]

So if I were to do a modded copy of a ROG tube reamer with a modded BMP tone stack would it be better between the two stages or after them both? Should I modify the second stage if I put it in between the two?

[Mark Hammer]

If all your second stage is doing is adding some boost, to compensate for what the compressing effect of the clipping diodes is doing, then there is no major effect of the tonestack on the resulting tone, by virtue of its location.

At the same time, adding that second stage allows you to fritter around with the sound, using the feedback cap and ground-leg cap of that 2nd stage (I assume your intent is to have the output be in-phase with the input), which can:
a) help tame some of the hiss or fizz
b) "pre-shape" the tone before the tone-control

The other thing is that any pre-shaping, via the 2nd stage, can free you up for the tone-control to be more nuanced or selective in its action.  So, my own preference would be clipping stage -> gain-recovery/pre-shaping stage -> tone-control -> output level.  BUt that's just me.

[TimWaldvogel]

Keeping in min this is all completely hypethetical and trial and error for sake of my curiosity.
My IDEA is that the tone circuit will be clipping.
I using the soft clipping of a tube screamer type gain stage. After that I put plan on buying the simple BMP tone stack which I may tweak values to taste. AMZ has an article about using diodes to ground clipping. infusing hard clipping and soft clipping together.
My idea is to have the higher frequencies clip differently and clip more than the low end. I personally love the sound of a cleaner more lightly rounded bottoms end with a heavier high end. Keeps the issuksion of clarity.
I want something that sounds potentially heavier than a tubescreamer, so this might be up my alley. The part of the tone stack for the low end will have a higher Threshold than the top end. And the gain recovery stage may be used to tame any overly harsh high end and bo the signal back up a bit

[Mark Hammer]

The whole point of the TS "engine" is to differentially clip the top, mid, and low end.  That's what tone-shaping is for: to keep the lows roughly the same distance from the clipping threshold as the highs and mids.  The lowpass filter, post-clip is simply to even out the harmonic content added by clipping.

Seems to me that your optimal strategy is to play with the signal parameters in the clipping stage itself, rather than have to grapple with trying to make the diodes in the tone-control do what you want them to do.  Just saying.

FWIW, I whipped up this circuit a few years ago.  What Jack posted in the linked-to AMZ document is a cousin of this circuit.  It splits the signal with some simple filtering and clips each portion separately, blending in the two signals for the output.  I had intended it to be as simple as possible, with 3 controls governing the whole shebang.  In retrospect, it was hard to identify a set of values that would permit a "reciprocal" pot (one direction turns up the gain for thew one part and turns it down for the other) to provide pleasing changes, so I think separate gain pots would have been optimal.  Produces a broad array of sounds, including both the familiar, and the very unfamiliar.  You will note that the clipping diodes are used in two different ways.  The absence of a tone control stems from the nature of the filtering already present.  All one needs to do to get a different tone is adjust the balance and relative drive.

[TimWaldvogel]

Hmmmm not quite what I'm thinking of.
Cool design though !
I actually want different clipping characteristics in an attempt at a "best of both worlds" diode clipping.
I may scratch the idea all together an reimpliment my original idea of a hard clipping stage flowing into a soft clipping stage simulating a simpler single pedal version of my visual sound Jekyll and Hyde. Where te hard clipping is rolled very far back and Just adds a crunch esc with just clipping the top of the circuit a tad and running into a smooth overdrive with great tonal balance.

I believe it's time to get to my breadboard

[Keppy]

Mark, can you explain the effect of having multiple lowpass filters after the clipping stage on top of the schem? I'm kind of fuzzy on how the math works. For example, is the resistance for the second filter stage 4k7 or 9k4 (4k7 x 2)? And how does the additional 4k7 resistor after these sections affect things? Basic stuff I know, but I'd appreciate an explanation or convenient link if you have one.

[TimWaldvogel]

this is the design im working on.
this has not been tested, this is simply the basic idea. the BMP tone control is gonna function more as a "shape" control. im gonna tweak more frequency corner filters on the stages is if sounds THAT horrible. the high threshold of the first clipping stage is meant for asymmetrical  smooth clipping with less saturation before the tone control which adds hard clipping into the circuit. the gain recovery stage has been tweaked for a gain of "5" instead of "4.25" like the original tube reamer schematic. considering the tone stack has insertion loss. i may need to tweak the capacitor value of the 2nd gain stage for LESS bass, not sure yet.
i have NO clue how this will sound. and even though not everybody will think this is a good idea. its my curiosity and the fact that more fortune cookie yesterday said "follow your creative instinct, it will produce fine results"

EDIT **unlabeled diodes are LEDS**