EHX Hot Tubes - Analysis?

[fryingpan]

I've done some reading and I've come to the conclusion that a preamp with many cascaded CMOS stages would probably result, even after filtering, in probably too much mush and noise for a preamp as opposed to a bespoke effect. Sunn apparently cascaded three CMOS stages in a single feedback loop, followed by another single CMOS stage, and the Beta amp was somewhat capable of clean, not congested sounding tones (whereas the Hot Tubes is always compressed sounding, not that it's a bad sound per se). What are the benefits of cascading CMOS stages in a single FB loop, soundwise? Does every single stage distort or do they function as a whole? The single stages do have a FB resistor, by the way, so it looks like some sort of hybrid solution. Apparently cascaded stages in a single feedback loop improve the open loop gain, thus allowing a better behaviour by the "fake opamp" circuit. Furthermore, Teemu Impala Kyttälä did suggest using CMOS chips as a possible gain stage, and actually suggested operating them at higher voltage (15V) due to their softer Vin-Vout curve, but most designs I've seen, the Beta amp included, operate the chips at 8-9V (or lower still), which linearises (counterintuitively) the operation of the chip somewhat and provides greater gain. Is there a reason? Most "complex" designs feature opamps or other amplifiers anyway so one could rely on the CMOS stage only as a low-gain wave shaper (maybe even just a single CMOS stage to decrease IMD - of course having a harmonically complex signal input in a decidedly non-linear device is going to make things far too distorted).

[PRR]

> Does every single stage distort

Each stage has gain of 5-100.

In cascade, only the last stage has "large" levels. Below gross clipping, the earlier stages run clean.

Yes, at some gross-overdrive point the intermediate stages also clip. The action here is too complicated for simple analysis. Deriving the theoretical result does not tell you what it "sounds" like.

What do these parts cost? A lot? Half-buck for a chip, a dime per resistor. Total less than a large french-fry. Stick it together and try it.

[teemuk]

What are the benefits of cascading CMOS stages in a single FB loop, soundwise? Does every single stage distort or do they function as a whole?

They basically "function as a whole".

When you cascade them inside a single global negative feedback loop the total open loop gain naturally increases, and when you enclose the loop you have more open loop gain to "correct" inherent distortion of the CMOS stage(s).

A single linear CMOS stage can't "cleanly" swing very close to rails because it has that very large non-linear area of operation, which provides all that "soft clipping". A single stage also has very low-ish open loop gain (especially compared to traditional opamp) so even when loop is closed there isn't much to reduce distortion.

When you cascade them inside a single NFB loop there's much more open loop gain to reduce distortion when loop is closed. The stage enclosed by loop will therefore operate more linearly, it can swing the output signal closer to rails (than a single stage), but it will - as a natural side effect - also clip proportionally harder than a single CMOS stage. That additional linearity in operation still has to come from somewhere, and it comes from turning those "soft" distortion characteristics more abrupt.

...Just like in any negative feedback system.

So, cascading stages linearizes their operation, increases headroom, and turns clipping characteristics harder.

It is an often exploited characteristics because a single CMOS stage is terribly non-linear and all that distortion it creates can easily turn tone into something people tend to describe as "congested" or "undefined".

---

Correct me if I'm wrong... But I seem to recall an application note stating that if you drive a linear CMOS stage with an opamp "input" stage, and wrap the whole thing inside a (global) negative feedback loop you essentially create a "rail-to-rail" opamp circuit. The MOSFET can swing very close to rails, much more than BJT output of an opamp, but that poor linearity naturally has to be fixed first... with plenty of open loop gain provided by that opamp.

[teemuk]

Oh, forgot to mention, when the open loop gain is increased (cascading multiplies open loop gains of each stage), the closed loop characteristics naturally become more predictable. The circuit more accurately does what feedback loop is trying to force it to do. Gain ratios, implemented filters, etc. They will behave more predictably. So the operation more and more starts to resemble that of a generic OpAmp.

[anotherjim]

I tried 3 inverters in series with a single feedback loop a while ago - it did not work. Maybe it was down to too much leakage/capacitive coupling on a solderless breadboard upsetting the connection between inverters?

If each inverter was given a very large feedback resistor (purely to bias without reducing gain of that stage) and cap coupled between stages, then an overall feedback resistor could be used as expected.

[fryingpan]

I tried 3 inverters in series with a single feedback loop a while ago - it did not work. Maybe it was down to too much leakage/capacitive coupling on a solderless breadboard upsetting the connection between inverters?

If each inverter was given a very large feedback resistor (purely to bias without reducing gain of that stage) and cap coupled between stages, then an overall feedback resistor could be used as expected.

Fairchild's application note does suggest cascading CMOS stages in series though (without employing any coupling or individual feedback). I wonder if simulations (eg. LTSpice) can be useful.

[fryingpan]

A single linear CMOS stage can't "cleanly" swing very close to rails because it has that very large non-linear area of operation, which provides all that "soft clipping". A single stage also has very low-ish open loop gain (especially compared to traditional opamp) so even when loop is closed there isn't much to reduce distortion.

When you cascade them inside a single NFB loop there's much more open loop gain to reduce distortion when loop is closed. The stage enclosed by loop will therefore operate more linearly, it can swing the output signal closer to rails (than a single stage), but it will - as a natural side effect - also clip proportionally harder than a single CMOS stage. That additional linearity in operation still has to come from somewhere, and it comes from turning those "soft" distortion characteristics more abrupt.

...Just like in any negative feedback system.

So it's actually better to operate CMOS stages at, say, 10V or even lower (eg. 5V)? The transfer curve is much softer at 15V than at lower voltages (where it is quite linear at the centre of the curve), yet you suggest using CMOS inverters at higher voltages in your book. Do you intend this as a specific effect (very fuzzy distortion) or are there any advantages in your view to doing so? I mean, if linearity is the aim, a single CMOS stage at 5V is much more linear than, I suspect, any chain of series CMOS stages at 15V.

[teemuk]

The difference in clipping characteristics probably isn't that striking, at least audibly. Whether the linear CMOS stage is powered by 5 volt supply or by 15 volt supply the transfer characteristics is pretty much a "S" function, meaning there's very narrow linear operating area surrounded by broad non-linear gain-reducing area of operation. They will all "soft clip", the higher supply rail slightly softer, but even such characteristic can be easily swamped by significant headroom difference in overall input sensitivity. The lower supply voltage operates the chip cooler so it's "safer".

Anyway, there's no "rights or wrongs" in this issue since we are talking about an "effect" circuit, and preference how that effect should sound like is very subjective.

Designers generally choose to employ linear CMOS amps because of their highly non-linear characteristics overall (which provide that extremely "soft" clipping), so if any great linearity is a design goal then these circuits hardly even come to discussion. Linear CMOS inverter amps are – in distortion circuits - exploited due to their gradual non-linearity, which's side effect is ruining great linearity.

No, they are not "operational amps": The circuit is basically a complementary class-A "push-pull" common source amp and bears no similarity to circuit architecture of a traditional opamp. The area of "linear" class-A operation is also extremely small, and during "overdrive" the complementary devices behave like "class-B" amps and start to produce abrupt "clipping" of current draw. The differential behaviour of the "push-pull" circuit, however, reduces this distortion by producing an output signal, which is an intermediate of "clean" and "clipped" currents. Yes, like many circuits, feedback is exploited and is establishing certain operating conditions. In this case it largely biases the DC potential to supply voltage's "center". The open loop gain of the circuit, however, is far too low to produce predictable effects of feedback loop operation or even decent linearity of output.

Now all that soft clipping can be very nice and "subtle", assuming it's not introduced in cascades. If it is the IMD products will multiply like bacteria: The first clipping stage introduces IMD products of each harmonic frequency within the complex signal, and harmonics of the clipping. The second stage will add IMD products of all signal frequencies, all IMD frequencies, and all clipping products, and so on and so on. It doesn't take much to turn signal into complete undefined "mud". Generally this kind of tone is "out of comfort zone" for most but if it's the goal then one has a pretty good "circuit tool" to achieve it.

Such side effect can be reduced by actually clipping "harder" because linear operating area is proportionally larger and the stage operates less at non-linear areas of operation at similar input signal levels. Harder clipping is also going to have a more "aggressive" tone to it, which is in some cases a preferable characteristic over extreme "softness".

So you can likely encounter two different "schools" of how CMOS distortion circuits are utilized:
1) Exploit their great non-linearity but without "overdoing" the effect. This practically means that the signal is probably clipped only in 1 – 2 "soft" stages in maximum. The supply voltage characteristics likely aren't that big of an issue because overall magnitude of clipping is controlled in great extent by input signal's sensitivity.
2) Exploit less non-linearity to produce harder clipping characteristics and relatively less "mushier" tone. In practice this means employment of the "cascade" circuit with global feedback. Yes, there are other solutions to "hard clip" as well, but one CMOS inverter chip usually packs so much potential "stages" that it would be kind a shame to waste them... Look at MXR Envelope Filter effect's design for some enjoyment. Yes, hard clipping can be overdone too but it's usually more "forgiving" for retaining signal integrity at lower signal levels and lighter picking dynamics.

...And having two design schools doesn't mean they couldn't be combined.

Speaking of symmetric versus asymmetric characteristics of conventional CMOS linear amps, yes: The characteristics technically aren't "purely" symmetrical. The "N" and "P" devices, in practice, are not entirely "complementary" so they do have slight differences in their characteristics curves. Still, the circuit is kind of a complementary "push-pull" stage and as such – assuming proper DC offset bias - does inherently produce far more "symmetric" characteristics than, say, a traditional single-ended MOS amp, which has very, very different characteristics to "cut off" and to "saturate". (You can try this with certain CMOS inverter chips that allow "discrete" access to some of the integrated MOS transistors). So in a sense one can expect modestly "symmetric" performance from the generic linear CMOS amp circuit. One handy trick to alter this characteristics (to one extreme or another) is deliberately manipulating of DC offset.
...And if you are worried about producing too "asymmetric" characteristics with a generic CMOS stage then you can operate two stages in "push-pull" and amplify their output with a differential amp. Now the stages will correct their inherent asymmetry.

[fryingpan]

One last question (I swear! EDIT: actually, no. See below. ). What's the purpose of local feedback (input and output of each CMOS inverter connected through a high-value resistor, maybe AC coupled with caps between them) when (usually three) cascaded inverters are globally fed back? Is it to stabilise their behaviour by ensuring that the input is roughly at Vdd/2?

...And if you are worried about producing too "asymmetric" characteristics with a generic CMOS stage then you can operate two stages in "push-pull" and amplify their output with a differential amp. Now the stages will correct their inherent asymmetry.

Wouldn't two parallel CMOS inverters fed into differential input amplify the error signal between them?

[tubesimmer]

A bit late to the conversation, but this will shed some light on the inner workings:

http://pedalprojects.blogspot.com/2013/04/how-does-red-llama-work.html