OK, mental exercise: have 20,000 amplifiers with those distortion characteristics, each one is fed a separate pure sine wave of the group that makes that complex waveform, and then combine their outputs, appropriately attenuated, in a "perfect" summing device. And alternatively, have a single such amp fed with the complex waveform made up of 20,000 sine waves; compare the output of that with the summing device. Will they match?
Frank
Before jumping to the 20000 number, why don’t you start this mental exercise with a two tone signal, two amplifiers and a two input perfect summer, then may be go to a three tone signal, three amplifiers…
By progressing this way, one at least has the chance to figure a pattern emerging
George
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Moved the goalposts, I saw what you did there.
It had two tone capability as was the norm for IM testers. Like I said, not as flexible or versatile as modern instruments, but certainly multitone.
Big "if" in the presence of 19,999 other full scale tones. Strikes me that using a musical signal where you feel there's a difference (or mirable dictu, actually demonstrated audibility of a difference) and nulling it against the input might give a clue?
If you want to get a frequency resolution narrow enough to let you look at all of the space between the 20,000 tones, the measurement time would be rather long.
Let me try:
You have 20k amplifiers each having a transfer characteristic 'A', each being fed a signal S1....S20k. Each amp output is thus A*S1....A*S20k. After the perfect summer you have A*(S1+S2+...S20k).
Now take a single 'A' amp and feed it (S1+S2...S20k). Output will be A*(S1+S2...S20k).
Looks like a match to me. Of course, we could have skipped all of this by just invoking the superposition principle
jan
Okay, let's go back to the original premise: "accumulated harmonics of many simultaneous tones from reaching an audible threshold". Let's try for infinity (and beyond!): what happens when the number of tones increases a magnitude, for each trial: by Richard's assertion, at each tenfold increase in number of tones the overall level of distortion will increase by at least some amount. So the limit as the number of tones approaches infinity is that the signal becomes completely distortion, nothing but. So an input signal that is composed of a number of tones approaching infinity is also output totally as distortion. Hmmm, where's the hole here ... ?
Frank
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This is a blunder, I've had common mode effects on the brain lately; MM single-sided operation will be fine, especially given the cascoding, as long as the other side is grounded through a lot less than 100k. Thanks SG for pointing this out.
There's a simple counter example to this scenario: take an amplifier with extreme even harmonic distortion, positive excursions severely differ from negative excursions in wave shape. Take 2 perfect sine waves of matching frequency and amplitude, but opposite phase as input: output from summing device is the difference between the positive and negative wave shapes; but that from the combined signals fed into single amplifier will be a null.Let me try:
You have 20k amplifiers each having a transfer characteristic 'A', each being fed a signal S1....S20k. Each amp output is thus A*S1....A*S20k. After the perfect summer you have A*(S1+S2+...S20k).
Now take a single 'A' amp and feed it (S1+S2...S20k). Output will be A*(S1+S2...S20k).
Looks like a match to me. Of course, we could have skipped all of this by just invoking the superposition principle
jan
Frank
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Yes if you sum two perfect sinewaves that are 180 degr out of phase you get zero. Send that through an amp and the output is still zero.
Not sure what that proves?
jan.
In the other case, say your amp has a transfer function of 1*Vi + 0.5*Vi^2 (lots of 2nd harmonics as you postulated).
The 'pos' sine wave V gets an output of 1*V + 0.5*V^2.
The other is 180 degr out of phase so that amp gets an input of -V and the output is 1*-V + 0.5*-V^2. Add that after the two amps and again you get zero.
You'll have a hard time to prove the superposition principle wrong.
jan
The 'pos' sine wave V gets an output of 1*V + 0.5*V^2.
The other is 180 degr out of phase so that amp gets an input of -V and the output is 1*-V + 0.5*-V^2. Add that after the two amps and again you get zero.
You'll have a hard time to prove the superposition principle wrong.
jan
The superposition principle (it is actually a theorem) holds for linear systems only.
Yes I just found that out too. I thought it was valid for continuous systems as opposed to discrete time systems.
Another learning moment! Life is good
Edit: another give-away that I was wrong was, that if I was right, we wouldn't have the cancellation of harmonics in push-pull systems. Silly me.
jan
Another learning moment! Life is good
Edit: another give-away that I was wrong was, that if I was right, we wouldn't have the cancellation of harmonics in push-pull systems. Silly me.
jan