dB of Distortion

[Koreth]

I was reading the Tube Amp FAQ on geofex, and came across the following statements:

A recently voiced although intuitively applied idea in distortion is that tube distortion sounds best when each successive distortion stage is overdriven by less than about 12db. This has the effect of keeping the tubes inside the area where the signal is more compression-distorted than clipped. That is what those resistive divider chains between distortion stages are for inside those distortion preamp schematics. Mesa's distortion preamps are another good example.

Overdriving a tube stage too much gives you harsher clipping, not the singing, sweet distortion we want. To really get sweet, crunchy distortion, keep each stage that goes into distortion no more than 6-9db into distortion.

I am trying to understand this. What is meant here being overdriven by so many dB or being so many dB into distortion? Does it mean that the signal in question would be X dB larger if the amplifying stage had the headroom to amplify that much instead of compressing or clipping the signal? Does it mean X dB worth of harmonic distortion is now added to the signal? Something else entirely? Are those two the same thing?

[R.G.]

What I meant was that the input signal was X db larger than the amount necessary to be just below distortion.

Obviously, this is a little slushy, as tubes don't (usually) enter distortion at some well-defined point. It's approximate.

I did not mean X db of distortion added to the signal.

[Koreth]

Okay, then let me apply this to a hypothetical case to see if I understand.

Let's take a 12AX7 gain stage. 300V B+, 68k grid stopper, 1Meg grid leak, 100k plate, 1.5k cathode, 22µF bypass cap (fully bypassed). Plugging those values into Merlin's load line spreadsheet says gain should be about 60, and bias should settle to about -1.5 at the grid. Thus it would take an input signal of 1.5Vp (or thereabouts) to bring about the onset of distortion. If I have the math correct, 12dB would be a ratio of 4:1, so to keep the overdrive of this particular stage at or below 12dB, we wouldn't want more than 6Vp at the grid. Am I on the right track here?

Another example, let's take the Marshall 2203 preamp, and the pickup signal described at Guitar Pickup Signal. The input stage has 280V B+, a 68k stopper, 1Meg leak, 100k plate, 2.7k cathode and a .68µF bypass cap. Again gain is about 60 in the bypassed frequencies, about 30 for the non-bypassed ones, this time with bias somewhere around -1.75V (which agrees with the schematic). 12dB more than -1.75V should be 7V D3 is 146.8hz. Judging by the frequency response graph on Merlin's spreadsheet, gain at that frequency would be somewhere between 30 and 32 dB, I'm gonna guess 31.5dB judging by where the line sits, or 37.6 gain.

Not forgetting the voltage divider formed by the grid stopper and grid leak resistors, at the onset of the signal we get .562Vp at the grid. At a gain of 37.6, output voltage is 21.131Vp. After a second we're getting .202 in and 7.595Vp out. 4 seconds later we're now getting .042Vp in and 1.579Vp out. This doesn't over drive the 1st stage, much less approach 12dB of it.

Moving on to the 2nd stage we still have 280V B+, 100k at the plate, and 1Meg for grid leak (I'm assuming the 1Meg gain pot is dimed). However, now we have 470k for a grid stopper, 10k on the cathode, and it's unbypassed, giving us a gain of 8.5. I'm gonna guess a bias of about -2.75V, and a cutoff voltage of about -3.75V looking at the graph on Merlin's spreadsheet. >1Vp is all that's needed to overdrive this stage on the negative swing, and 12dB then would be a driving signal of 4Vp.

Again, not neglecting the voltage divider formed by the grid leak and stopper resistors, at the start of the signal we're getting 14.375Vp of signal, definitely overdriving it, giving us 23.2dB of overdrive. After a a second we're down to 5.167 to the grid, still getting overdrive, but only 14.3dB of it. 4 seconds later we're down to 1.079 to the grid, barely overdriving, if at all.

I was gonna do the numbers for the 3rd stage, but realized that the wave form is no longer anything close to symmetrical on its voltage peaks, and would involve more math to calculate how much overdrive is had on the positive and negative peaks. Still, am I on the right track here with the example above, or have I gone off into the weeds somewhere?

[jmaf]

IMHO you are on the right track about the theory.

The input impedance of 12ax7's is several megohms, so the voltage divider formed by the grid leak and the grid stopper doesn't have too big an influence at audio frequency, the grid stopper end is for all purposes an open circuit at DC.

What guitarists are normally looking for is to overdrive the plates, getting natural tube clipping from the plate and not clipping from positive grids. To drive the plates hard you must bias each stage accordingly so you don't overdrive the grid, but do overdrive the plates.

When you said "12dB more than -1.75V should be 7V D3 is 146.8hz." I hope that doesn't mean -7 VDC bias because I think that'll shut off most 12ax7's.

Rule of thumb gain is approximately Rp / Rk. So 100k plate, 1.5k cathode is about 60something. 220k plate 1k cathode is very high gain(47dB) and is limited by the 12ax7 maximum gain of 40dB... Good luck.

[kg]

Okay, then let me apply this to a hypothetical case to see if I understand.

Let's take a 12AX7 gain stage. 300V B+, 68k grid stopper, 1Meg grid leak, 100k plate, 1.5k cathode, 22µF bypass cap (fully bypassed). Plugging those values into Merlin's load line spreadsheet says gain should be about 60, and bias should settle to about -1.5 at the grid. Thus it would take an input signal of 1.5Vp (or thereabouts) to bring about the onset of distortion. If I have the math correct, 12dB would be a ratio of 4:1, so to keep the overdrive of this particular stage at or below 12dB, we wouldn't want more than 6Vp at the grid. Am I on the right track here?

Another example, let's take the Marshall 2203 preamp, and the pickup signal described at Guitar Pickup Signal. The input stage has 280V B+, a 68k stopper, 1Meg leak, 100k plate, 2.7k cathode and a .68µF bypass cap. Again gain is about 60 in the bypassed frequencies, about 30 for the non-bypassed ones, this time with bias somewhere around -1.75V (which agrees with the schematic). 12dB more than -1.75V should be 7V D3 is 146.8hz. Judging by the frequency response graph on Merlin's spreadsheet, gain at that frequency would be somewhere between 30 and 32 dB, I'm gonna guess 31.5dB judging by where the line sits, or 37.6 gain.

Not forgetting the voltage divider formed by the grid stopper and grid leak resistors, at the onset of the signal we get .562Vp at the grid. At a gain of 37.6, output voltage is 21.131Vp. After a second we're getting .202 in and 7.595Vp out. 4 seconds later we're now getting .042Vp in and 1.579Vp out. This doesn't over drive the 1st stage, much less approach 12dB of it.

Moving on to the 2nd stage we still have 280V B+, 100k at the plate, and 1Meg for grid leak (I'm assuming the 1Meg gain pot is dimed). However, now we have 470k for a grid stopper, 10k on the cathode, and it's unbypassed, giving us a gain of 8.5. I'm gonna guess a bias of about -2.75V, and a cutoff voltage of about -3.75V looking at the graph on Merlin's spreadsheet. >1Vp is all that's needed to overdrive this stage on the negative swing, and 12dB then would be a driving signal of 4Vp.

Again, not neglecting the voltage divider formed by the grid leak and stopper resistors, at the start of the signal we're getting 14.375Vp of signal, definitely overdriving it, giving us 23.2dB of overdrive. After a a second we're down to 5.167 to the grid, still getting overdrive, but only 14.3dB of it. 4 seconds later we're down to 1.079 to the grid, barely overdriving, if at all.

I was gonna do the numbers for the 3rd stage, but realized that the wave form is no longer anything close to symmetrical on its voltage peaks, and would involve more math to calculate how much overdrive is had on the positive and negative peaks. Still, am I on the right track here with the example above, or have I gone off into the weeds somewhere?

koreth, you're on the right track. however, as you correctly surmised, the analysis pretty much falls apart as overdrive (and distortion levels) become huge.

the POINT of the 12dB statement is that tubes have a "sweet spot" in terms of overdrive that maximize their gradual transition into higher order harmonic distortion. applying 50vac to a traditional 12ax7 isn't gonna make great sounding distortion; it's gonna sound like ass. that's why in all cascaded gain designs there are methods to reduce the drive at the subsequent grids.. usually by voltage dividers, or judicious bypass and coupling cap value selection.

amps typically described as highly "touch sensitive" have optimized their stages to the sweet spot. guitarists like them because they "clean up" with reduced input signal, but get dirty when the pick is dug in.

[TransLucid]

The choice of operating point also affects the type of distortion generated. Lower quiescent dc voltage on the grid makes the stage cutoff before grid conduction, while higher points do the opposite. The best amount of overdrive will depend on whether the operating point is centered or leans one way or the other...

[teemuk]

The "subtle amounts of overdrive in each stage" -theory sounds nice on paper but I've never seen too many amps follow it in practice.

[kg]

The "subtle amounts of overdrive in each stage" -theory sounds nice on paper but I've never seen too many amps follow it in practice.

i agree, and for really high gain designs, it just won't work.

anyone with an oscilloscope and some experience with tube guitar amps will likely agree with me that it is remarkable how much distortion appears to the eyes before it is even slightly perceptible to the ears.

[Koreth]

So then, even if you were to double the amount of overdrive permissible at each stage to 24dB, I wonder how many more stages you'd need to add to a modern high gain amp with 4 or 5 stages like a Recto or Mk IV to achieve the same amount of distortion.

[exclamationmark]

I had the same questions when I built my first pre-amp a couple months ago. Basically I asked 'How much signal is enough signal" in regards to clipping. In the end I found it was just easier to listen to the result and start tweaking it. Theory only got me so far, and it's not like you can mathematically calculate how good something will sound (within sensible limits...). Obviously you're not going to pass a something like 200v pk-pk into a 12ax7 stage and wonder why it sounds like a nest of angry bees. Dissect some high-gain amplifier schematics and in particular look for where the voltage dividers are placed.

When viewing my pre-amp on a scope, it actually surprised me that the output started to look like a square wave before I could hear any of what I would call 'distortion'.

[kg]

When viewing my pre-amp on a scope, it actually surprised me that the output started to look like a square wave before I could hear any of what I would call 'distortion'.

exactly!

[NorCalTuna]

Frankly, the first time I did that I thought I f'ed something up. Awesome experience!

[jmaf]

The "subtle amounts of overdrive in each stage" -theory sounds nice on paper but I've never seen too many amps follow it in practice.

Most Trainwrecks are notable for that fact. You can dial in clean to high distortion using the guitar volume alone.

[teemuk]

When viewing my pre-amp on a scope, it actually surprised me that the output started to look like a square wave before I could hear any of what I would call 'distortion'.

Ah, a statement from the "I like my cleans tones with a bit of dirt" -school, I assume. Once you know what to listen even that slight bit of distortion becomes fairly evident. Hence the popularity of "sterile" solid-state amps for some applications.