What is "amp-like distortion" anyway?

Started by Fancy Lime, May 16, 2019, 03:54:02 PM

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amptramp

A big part of amp-like distortion is the addition of even harmonics which add a pleasant even-order harmonic distortion.  In the amp schematic shown above:

https://4.bp.blogspot.com/-VMofNzunqMQ/WhwIGL0br3I/AAAAAAAAE7w/j0QHv1mpyqomaC5g0C1sUmJJQDWaWB0DgCLcBGAs/s1600/Sunn%2BModel%2BT%2B2nd%2BGen_ed.GIF

we see the top part of the inverter driving R27, an 82 K resistor while the bottom part is driving R28, a 120 K resistor.  A differential amplifier based on a long-tailed pair like this should not have R27 = R28 because the top stage is a common cathode amplifier and the bottom stage is a common grid amplifier with a different gain equation but there are some amplifiers that have a balance control so you can tune for equal drive from both the top and bottom stages.  Any deviation from the desired values leads to even-order harmonic addition and this is the most important characteristic of tube sound, so it is deliberately added in some amplifiers.

There is tube-like distortion that does not depend on clipping and the imbalance in drive gives the extra harmonic content we associate with tubes.

teemuk

QuoteA big part of amp-like distortion is the addition of even harmonics which add a pleasant even-order harmonic distortion.

This is nothing but a myth.

Harmonics are largely related to circuit architecture:
Push-pull, differential and cascode -types of circuits tend to produce odd order harmonics because of their nature to cancel even order ones. In fact, build any circuit - solid-state or vacuum tube - with symmetric distortion characteristics and the distortion produces dominantly odd order harmonics.
Single-ended circuit architectures - whether solid-state or tube - tend to produce even order harmonic distortion. In fact, build any kind of circuit that introduces asymmetric distortion and it will introduce even order harmonic distortion IN ADDITION to odd order distortion.

Your generalisation is basically claiming that single-ended circuits are more "tubey" than push-pull types. I find such generalisations totally pointless.
By the way, amp designers like Jim Kelley and Alexander Dumble - to name a few - were largely aiming to produce odd order distortion in their tube amps.

This with sine waves. Factor in intermodulation distortion that occurs with ALL complex signals (anything other but single frequency) and the intermodulation will also produce sum and difference frequencies related to all frequencies within the signal. Math will tell you that most will be anything but harmonically related (which would be simply integer multiples). As asymmetric clipping produces largely BOTH even and odd order harmonics you can be sure that its contribution to overall IMD is that overall more distortion and harmonics will be produced when complex signals are being distorted. This is one of those things that doesn't jive too well with e.g. "high gain" design. There is a reason why many high gain amps produce more symmetric-type of clipping than asymmetric type.

What certain tube circuits feature is kind of "dynamic interaction" of harmonics created by distortion. In interaction with overall envelope of the signal the distortion may shift from prominently asymmetric to prominently symmetric, or vice versa. As this changes the "timbre" of distorted tone it adds a sense of "touch sensitivity" or "feel" to the behavior of the circuit as well as kind of a "swirly" effect. The distortion kinda "responds" to ones playing.
This is an effect that can be achieved with solid-state circuitry as easily as with vacuum tube circuitry, though. However, it mostly requires one to cascade two circuits with dissimilar distorting characteristics. So, a single diode clipping stage (whether symmetric or asymmetric) does not introduce such characteristic, nor do two cascaded diode clipping stages that are both symmetric. They just introduce the same pattern of harmonic distortion regardless of envelope. If you think about this for a moment you realize that this clause actually covers A LOT of simple distortion effects introduced prior to 1980's.
However, cascade an asymmetrically clipping stage to a symmetrically clipping stage (or vice versa) and you get that interaction of shifting harmonics. Vice versa, you can asymmetrically clip, invert signal, and asymmetrically clip again and you most likely get that kind of interaction. If you think about this for a moment you realize that these scheme covers A LOT of tube amps and likewise circuits.

That's one one effect typically associated with "tubeyness". Then again, designers like Jim Kelley purposefully introduced symmetric distortion characteristics throughout the whole amp circuitry because that was what glorified "tube power amp" clipping is all about, at least with push-pull amps. Push-pull power amps, practically all PPIMV schemes, differential stages (e.g. LTP) and alike also introduce prominently symmetric distortion.

There have been designs from Peavey and Behringer that allow user to alternate between symmetric or asymmetric distortiopn characteristics. So far I haven't heard anyone claim that one is "tubier" than the other. They just sound a slight bit different and its nice to have versatility.

Distortion is just one part of the equation. A complete amplifier will also have certain type of "voicing". This voicing is also consisting of multiple parts with certain interaction.

A classic Fender tube amp voicing, for example, is kinda "broad bandwidth" which is almost "level" except for the "gull wing" -type of response introduced in the preamp section. i.e. Notch at midrange frequencies. This "voicing" also voices the power amp distortion (which is typical distortion mechanic of old Fender tube amps) as those attenuated mid-range frequencies will generate overall less IMD while the larger bandwidth (especially towards low end) also contributes to type of IMD.
The distorted signal will be subject to another frequency response "mutilation", largely by "damping" characteristics of the power amp and overall response of the loudspeaker system that starts to roll off high frequencies around 5 kHz. This is basically post-distortion tone enhancement.

A classic "Marshall" type of voicing, on the other hand, has very "bright" response and the low frequecies are attenuated heavily in the preamp section. The dip at mid-range is also less prominent than in Fender amps. This provides its own unique IMD pattern, which may be, or may not be, also interacting with distortion characteristics of the power amp. Marshall power amps are generally more "damped" than Fender power amps so their frequency response is more "level". Once again, in a complete amp the loudspaker system adds its own response, prominently attenuation of frequencies above 5kHz.

These things weren't that well reseached before late 1970's and there was a clear distinction between "effects" and "amps". After extensive research there have been several designs, e.g. Scholz R&D Rockman products, FMIC solid-state Fender amps, SansAmps series of products, which concentrate not only on certain type of clipping but replicating that entire "amp like" voicing within the design. Rockman and FMIC SS Fender, for example, introduce "preamp like" voicing before distorting stage(s) and a "cabinet simulator" -type of voicing post distortion. Classic Boss HM-2 effect also incorporated a "preamp like" voicing before distortion and a "cab sim" (disguised as tone controls) post distortion.
Yes, there is a sort of generic pattern...

But "amp like" is a factor of many characteristics in practice and then we need to remember that there are hundreds of different types of amps, which all sound kinda different. However, you can find some generic "patterns" from those too. Classic Fender (and higher gain derivatives like Dumble or Mesa Mark series amps) are based on certain type of circuit architecture, and certain type of voicing methodology. Research enough and you will start to see a pattern. Classic Marshall -types of designs and higher gain derivatives (e.g. Soldano, Mesa Rectifier series amps, Peavey 5150, etc.) are largely following certain type of design architecture and overall similar voicing methods. If you research enough you once again will start to see a a generic pattern.

Rob Strand

QuoteThis is nothing but a myth.
Harmonics are largely related to circuit architecture:
Push-pull, differential and cascode -types of circuits tend to produce odd order harmonics because of their nature to cancel even order ones. In fact, build any circuit - solid-state or vacuum tube - with symmetric distortion characteristics and the distortion produces dominantly odd order harmonics.
Single-ended circuit architectures - whether solid-state or tube - tend to produce even order harmonic distortion. In fact, build any kind of circuit that introduces asymmetric distortion and it will introduce even order harmonic distortion IN ADDITION to odd order distortion.
Some time back I got off the even harmonics thing.   If you look at this type of configuration is has *no* even harmonics.   However it retains the general characters of the distorting part.



I've started to think that the compressive sound more to do with the "duty cycle", for example a stage with even harmonics starts to make a sine-wave narrow on one polarity and wider in another.   That effect can get emphasized by bias shifts when the grids conduct.   When you push such behaviour through the above circuit you end-up with ideas similar to those discussed in the Peavey's patents.
Send:     . .- .-. - .... / - --- / --. --- .-. -
According to the water analogy of electricity, transistor leakage is caused by holes.

teemuk

#23
^ Above is essentially the conceptual scheme depicting a typical push-pull tube power amp.

Let's add that basically each of those "parallel" stages can, and typically will, clip asymmetrically and even fairly "hard". The differential output of their output signals, on the other hand, is symmetrically distorted signal with moderately soft clipping.

There are several manufacturers exploiting this concept. Earliest ones including Intersound (IVP preamp) and Hartley-Thompson, which simply employed transformer coupled push-pull BJT or FET stages for creating distortion. Jim Kelley ("Line Amp") and Sound City ("SMF") featured similar low current, transformer coupled -push-pull "tube power amp emulations" but they were realized using vacuum tubes. These early "emulations" were rather crude circuits and did not try to model other tube power amp -related characteristics such as DC bias shifting, sag and effects of low damping factor.
Basically, what they did could have simply been achieved by using a pair of anti-parallel clipping diodes as well.

Earliest Korg/Vox "Valvereactor" power amp employed the same idea of transformer coupling a low current push-pull voltage amplifier stage (buffered by SS power amp) but later incarnations omitted the transformer coupling replacing it with an OpAmp differential amplifier, which achieves the very same end result. They took the differential scheme from the Vox "Brian May" amp, which was actually a Samick design. It featured a low current BJT push-pull stage with differential amp output and that actually emulated, not a tube power amp, but power amp of a vintage transistorized radio. The differential scheme is even older and there are triangle-to-sinewave converters that have basically identical circuit architectures.
There was also a hybrid Hughes-Kettner bass amp ("Quantum 600" IIRC), which's power amp operated on pretty much the same principle as well. Tube-push-pull stage driving a differential, driving a SS "Buffer" for power amplification.

Earliest Valvereactor circuits, BTW, are very ingenious design because they also exploit "trans-impedance" architecture to reflect the reactive loudspeaker load to the (low current tube) voltage amp stage, but in suitable, higher impedance. In addition they model lower damping of tube amps with current feedback.

Behringer holds a patent for push-pull tube stage coupled to differential amp output, but it has a user adjustment to adjust balance of differential's input (even vs. odd harmonics). The circuitry is featured in various sound processor units. They also employ similar circuit realized with FETs in their guitar amps and sans the symmetry adjustment.
"Texture" control of Peavey's Valveking amps (IIRC) adjusts balance of signals from the power amp's phase splitter stage, once again to vary amplitude of odd vs. even harmonic distortion.

Trace-Elliot, and before them GMT (Gallien-Krueger), exploited the transformer coupling idea but implemented it straight to power amp architecture with high power output transformers. Trace-Elliot also modeled the low damping factor of tube amps with current feedback. GMT amps featured a "current limiter" to starve the differential input stage of the power amp (for reduced headroom and "power amp distortion" at lower volume levels) - similarly to some tube amps (e.g. Carslbro). For a 1970's design this was damn impressive feature. Tube guitar amps mostly started to exploit such circuitry decades later.

Quilter amps (of the late 1970's and early 1980's) exploited "diode steering" and "bi-polarity" of semiconductors for similar "push-pull" effect, the aforementioned Peavey T-Dynamics goes to same category as well as later circuit designs from Line 6 and Quilter (again).
Pritchard amps again use push-pull -type of circuit architecture for low current voltage amplification of their power amps. In addition they model sag and damping. T-Dynamics is one of the few designs that tries to model the dynamic DC bias shifting and resulting "crossover" distortion. Pritchard, for example, regards is an unfavourable characteristic. Tastes vary.

Roland's analog "TubeLogic" circuits, and some Peavey TransTube -related circuits use low current push-pull amps that exploit complementary semiconductors. These also feature the dynamic bias shifting + crossover distortion characteristic under heavier overdrive.

I probably missed a lot of related examples.

ElectricDruid

#24
Quote from: teemuk on May 24, 2019, 10:08:04 AM
The differential scheme is even older and there are triangle-to-sinewave converters that have basically identical circuit architectures.

I've been experimenting with exactly this recently. I've used this circuit as a soft overdrive for an electric organ:

https://electricdruid.net/wp-content/uploads/2017/06/SineSubOsc.jpghttps://electricdruid.net/wp-content/uploads/2017/06/SineSubOsc.jpg


Obviously for this job you don't need the ramp-to-triangle convertor on the top row, and you can tweak the bottom row. I think it makes an excellent sound. It's got a nice soft approach to clipping, so it's quite responsive (you can dig in or back off) and you can tweak the symmetry with the trim provided. I haven't tried it on a guitar yet, but it sounds great on organ - nice and growly, without getting too filthy.

Edit: Is this "amp-like"? I dunno. Amp-like is in the ear of the beholder, I guess. "Does it do the job you want and make the sound you like?" seems like a better way to ask the question to me.

dschwartz

Ok ok ok..
The law of diminishing returns apply nicely when trying to mimic "exactly" what a tube amp does.
The sansamp gets the meat and bones of amplifier emulation and does not emulate bias shifting, grid conduction, power sag, speaker compression, power amp impedance vs speaker behavior, etc, and it is still one of the most used analog amp sim.
Mostly all of those fancy tube emulation ckts were fine, and surely a lot of R&D was invested to develop them, but they failed to succeed commecially (mostly) because they were overengineered and with the focus on imitating tubes and not sound quality.
Even Fractal had to modify their clipping algorithms because they were too close to tube clipping and had some buzzy decay (which happens in real tube amps)
----------------------------------------------------------
Tubes are overrated!!

http://www.simplifieramp.com

phasetrans

Quote from: teemuk on May 24, 2019, 10:08:04 AM
....

Earliest Korg/Vox "Valvereactor" power amp employed the same idea of transformer coupling a low current push-pull...

Roland's analog "TubeLogic" circuits, and some Peavey TransTube -related circuits use low current push-pull amps that exploit complementary semiconductors. These also feature the dynamic bias shifting + crossover distortion characteristic under heavier overdrive.

Is there a collected history of the DC bias shift techniques? I have sat down several times to put together a DC bias shift block for conventional diode clippers, and it always seems to get too complicated.
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teemuk

#27
I'm aware of few only few "techniques"...

First one would be simply asymmetrically clipping the signal and then AC coupling it. I wouldn't really regard this as a "technique" rather than an inherent characteristic of capacitive coupling forcing the asymmetric signal to "balance" itself to a new crossover point while trying to maintain equal amount of energy at both negative and positive lobes of the waveform. RC time constant of coupling will naturally affect dynamics of this behaviour.
As said, ALL circuits that asymmetrically clip and then capacitively couple the signal will do this in some extent. The shifting will naturally affect the (DC) bias point of the subsequent stage. (This sort of also applies to shifting bias points of P-P amps as well). Unless the signal is distorted again after shifting the effects of shifting (to distortion's harmonic "profile") are usually inaudible.
Carvin engineers discovered the phenomenon in early 1980's or late 1970's while developing their tube amplifiers. (If "discover" is the right word, everyone knowing the art must have been aware of this characteristic). Their head engineer John Murphy devised a simple plan to mimic the effect with solid-state circuitry: Clip asymmetrically, invert and AC couple, then (asymmetrically) clip again. Essentially this does not differ from what typical tube preamp stages do with their single-ended (asymmetrically clipping) and capacitively coupled gain stages. Murphy's experiments with this technique culminated in Carvin's "Quad X" preamp, where as much as 11 (!!!) triode gain stages were cascaded, not so much for acquiring very high gain, but for enhancing this "shifting" phenomenon.


In the 1990's Saint Louis Music, at the time manufacturer of Ampeg and Crate amps, patented another shifting technique. A diode is employed to rectify the output signal of gain stage and the rectifier's output charges a capacitor. The resultant DC signal is fed back to gain stage's input, causing DC shift. The scheme was first employed in Ampeg's "VH"-series of amps (VH=Varying Harmonics) and later in Crate "FlexWave" amps.
I'm not sure how valid the patent is because Dynacord had actually employed the very same scheme already in the early 1980's in their tube emulating power amp. They also had patented their circuitry. Someone who is familiar with patenting can perhaps tell if the very same invention can co-exist in a German patent and in an American patent without the two infringing each other. Either way, it must have been "prior art" when SLM decided to patent.
This shouldn't be a too complicated technique because it only requires about three or four additional components.


QuoteEven Fractal had to modify their clipping algorithms because they were too close to tube clipping and had some buzzy decay (which happens in real tube amps)
I rememeber that episode. People were complaining about "digital fizz" when it was actually dynamic crossover distortion, which exists in REAL tube push-pull power amps as well. I think there are several lessons to learn from that story, which relate to overall human nature.

PRR

> if the very same invention can co-exist in a German patent and in an American patent without the two infringing each other.

You have to read, in detail, the I CLAIM at the end.

https://patents.google.com/patent/US5032796A/en
https://patentimages.storage.googleapis.com/5d/a3/b6/4d72c278c1166c/US5032796.pdf

Here: PDF page 10, column 8, new paragraph 1. There's 21 Claims, in increasingly excruciating detail. Small changes of claimed implementation and benefit can make two very-similar patents non-conflicting.

The patent has a long list of "citations", previous patents that this one acknowledges and builds-upon. Often a Patent Examiner (who does this all day long) will find others that the applicant didn't find and add them to the list.

I assume this Dynacord patent is https://patents.google.com/patent/DE3118042A1/en
The Google does not give full info on this one.
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phasetrans

Quote from: teemuk on May 26, 2019, 12:07:29 AM
This shouldn't be a too complicated technique because it only requires about three or four additional components.



Welp. Nothing new under the sun. I basically drew this at lunch on Friday and felt clever for something that wasn't as complicated. Back to reinventing the ancients...
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garcho

^ It's funny how much talk there is here of "new" distortion, overdrive, fuzz, etc., yet what will people do musically with this "new" sound, play a power chord? Do a minor pentatonic blues bend thingy? Play a one finger riff on the low E string? Always makes me chuckle. Youtube style pedal reviews are the same: "check out this awesome tone of me playing Led Zeppelin riffs poorly!" They have $10,000 of guitar/amp/FX and are doing a demo on their iPhone and someone else is listening to it on their laptop speakers, "the tone is amazing!". What happens when you get your perfect amp sim, you... play a D chord? I'm guessing there's no legion of Harry Partch fans here hiding in the shadows. I like building, tinkering, learning, for the sake of doing it, so I get it, not judging, just remarking.

I bet the OP could just make wtf he feels like and tell the dude "this is true amp-like distortion made from NOS unobtainium" and the guy will be like "whoa, it's perfect!". Then just mutter something about true bypass and capacitors and send him home with a smile on his face.
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"...and weird on top!"

phasetrans

Quote from: PRR on May 26, 2019, 12:48:40 AM
You have to read, in detail, the I CLAIM at the end.

https://patents.google.com/patent/US5032796A/en
https://patentimages.storage.googleapis.com/5d/a3/b6/4d72c278c1166c/US5032796.pdf

And, by coincidence of this threads timing, the patent in question expires on the very day (05/26/2019) that we are looking at it.

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Gus

Maybe off topic a little

I really think a part of the tube amp sound has a lot to do with the pentode(s) drive to a transformer to the speaker(s) and how they change with signal level.
Think about a 12 inch thin paper cone being driven by a set of 6V6s and transformer at about 17 to 20 watts and then how it changes when the guitar volume is reduced

Maybe part of "amp distortion" is paper cone distortion in the speaker(s) as well.

Rob Strand

QuoteMaybe off topic a little
Under clipping the output impedance of amp changes, which changes the frequency response.
The frequency response (or part of it) is determined from the "divider" formed from the output impedance of the amp and the speaker impedance. The pentodes also have a soft clipping when the plate swings below about 70 to 100V or so.

It's a combination of many subtle factors.  If it was one simple thing we'd have awesome tube amp emulators years ago.
Send:     . .- .-. - .... / - --- / --. --- .-. -
According to the water analogy of electricity, transistor leakage is caused by holes.

Gus

Quote from: Rob Strand on May 26, 2019, 10:27:11 PM
QuoteMaybe off topic a little
Under clipping the output impedance of amp changes, which changes the frequency response.
The frequency response (or part of it) is determined from the "divider" formed from the output impedance of the amp and the speaker impedance. The pentodes also have a soft clipping when the plate swings below about 70 to 100V or so.

It's a combination of many subtle factors.  If it was one simple thing we'd have awesome tube amp emulators years ago.

Rob I did not want to get to deep with my post. We could also add more detail about the inductance change with drive level and frequency.

Hybrid amps that have tube outputs and solid state preamps can sound different than tube preamps with solid state outputs.

There are the older MM amps that have opamp(with an interesting feedback network) preamps, opamp based output phase inverter driver that drives a BJT pentode cascode class B? stage into an output transformer.

IIRC Peavey and SG had hybrids with tube transformer out as well.

I do wonder how much of the speaker breakup and cabinet design is important? Examples like class D bass amps and high powered petal steel amps(high power defined as greater 100watts in guitar amps) going into more robust speakers. In the 90s I seem to remember solid state amps into cabs with nice 12" speakers being used.

A fun thing to show people was taking a 10 to 20 watt solid state practice amp(standard voltage feedback, mixed current and voltage should to be designed for the speaker used) and disconnecting the speaker and connecting it to a Mashall with greenbacks etc. type cab.

I have not heard this amp https://www.kemper-amps.com/

teemuk

#35
QuoteMM amps that have opamp (with an interesting feedback network) preamps
That particular circuit becames drastically "less interesting" when you figure out its just basically two back-to-back zener diodes in the feedback loop. Discrete zener diodes, but nevertheless just another iteration of diode clipping with increased voltage threshold.

Quoteopamp based output phase inverter driver that drives a BJT pentode cascode class B? stage into an output transformer.
Have you ever seen that output stage clipping in an oscilloscope? Its static, very hard clipping, similar to that generic solid-state power amps produce. Just because it's a tube design and has an output transformer doesn't mean it's "tubey" at all in typical sense. Peavey VTX series amplifiers used a similar output stage architecture and they added a (patented) tube power amp emulation circuitry to it. Imagine that, a tube power amp emulation circuit integrated to a tube power amp.  :icon_lol:

IMO, Music Man amps are great example of Leo Fender's ideal amp: Pristinely clean amps devoid of any distortion even at ear-obliterating volumes. However, they had to add a (preamp-based) distortion feature because at the time it was pretty much mandatory to have such thing in an amp. And their effort was really not all that great: Static diode clipping or that oddball grid leak bias + 470K grid impedance... ..."thing"... of the RD-series amps, which actually used a genuine 12AX7 triode to produce overdrive. Yet again a great example that "tube" is not an instant ticket to great tones, or to even producing those "tube tones" we're typically accustomed to.

Rob Strand

#36
QuoteHybrid amps that have tube outputs and solid state preamps can sound different than tube preamps with solid state outputs.

There are the older MM amps that have opamp(with an interesting feedback network) preamps, opamp based output phase inverter driver that drives a BJT pentode cascode class B? stage into an output transformer.

IIRC Peavey and SG had hybrids with tube transformer out as well.
I remember all of those.  Yes they do sound different.    The Peavey has the BJT diff-amp but the MM had that tricky cascode set-up.    The thing I remember about those amps is when you push the power amps they don't sound crappy like a SS amp they kept some character of the tubes.   So the tube output stage definitely contributes some "tubiness".   But the fact they sound different just means it's not the whole story.

QuoteI do wonder how much of the speaker breakup and cabinet design is important? Examples like class D bass amps and high powered petal steel amps(high power defined as greater 100watts in guitar amps) going into more robust speakers. In the 90s I seem to remember solid state amps into cabs with nice 12" speakers being used.

A fun thing to show people was taking a 10 to 20 watt solid state practice amp(standard voltage feedback, mixed current and voltage should to be designed for the speaker used) and disconnecting the speaker and connecting it to a Mashall with greenbacks etc. type cab.

IMHO the characteristic of 12" guitar speakers is a really important aspect of the tone.  That comes from both the frequency response and the impedance.   I'm always amazed how right the combination of 12" speakers + tube amps works for guitar.    The old 12" speaker designs are quite poor from a hifi perspective but they add a lot of goodness to guitars.    After 50 to 60 years of advances in technology we are still using the early designs as a reference.
Send:     . .- .-. - .... / - --- / --. --- .-. -
According to the water analogy of electricity, transistor leakage is caused by holes.

Ben N

Quote from: garcho on May 26, 2019, 02:40:08 PM
I bet the OP could just make wtf he feels like and tell the dude "this is true amp-like distortion made from NOS unobtainium" and the guy will be like "whoa, it's perfect!". Then just mutter something about true bypass and capacitors and send him home with a smile on his face.
See my post above. Great minds, etc.
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Ben N

That St. Louis Music patent circuit looks like it might be fun to breadboard.
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Rob Strand

QuoteThat St. Louis Music patent circuit looks like it might be fun to breadboard.
Jack Orman (AMZ) had some sound samples about 15 years ago and it sounded pretty good.
Go here and follow the AMZ link,
https://www.sabrotone.com/?p=2780
Send:     . .- .-. - .... / - --- / --. --- .-. -
According to the water analogy of electricity, transistor leakage is caused by holes.