I was reading the article by Aaron Nadell (sorry, lost the online link to it), and have a question regarding its practical use. To illustrate my question, I have attached two potential schematics to compare, A and B.
Most of what I see uses a configuration like B, with the capacitor connected directly to the common cathodes. I have seen very few recent schematics, either at DIYAudio or otherwise, who use a scheme like A.
The A scheme is the one presented in the article, where R1 is 60 ohms in this particular application, and is a critical value. To quote the article, "At any other value the third harmonics generated in the output tubes would either be too weak to cancel the original distortion entirely, or so strong as to more than balance it and thus introduce distortion themselves."
I also recall some statements identifying this resistor at Lynn Olson's site, but notice this resistor in none of his Karna-Amity schematics.
So, what's the recommendation? Hook up a spectrum analyzer and tweak R1 for lowest odd order distortion, or just leave it out?
Most of what I see uses a configuration like B, with the capacitor connected directly to the common cathodes. I have seen very few recent schematics, either at DIYAudio or otherwise, who use a scheme like A.
The A scheme is the one presented in the article, where R1 is 60 ohms in this particular application, and is a critical value. To quote the article, "At any other value the third harmonics generated in the output tubes would either be too weak to cancel the original distortion entirely, or so strong as to more than balance it and thus introduce distortion themselves."
I also recall some statements identifying this resistor at Lynn Olson's site, but notice this resistor in none of his Karna-Amity schematics.
So, what's the recommendation? Hook up a spectrum analyzer and tweak R1 for lowest odd order distortion, or just leave it out?
They're really the same thing... or rather, B is a special case of A where R1=0.
In B, usually R2 is set by what you want the cathode bias to be, unless you're also applying grid bias.
In my experiments, I set the resistance R1+R2 to be what I wanted for cathode bias, then "moved the tap" to optimize distortion. At least with the tubes I was using, I don't think the optimum was ever with R1=0.
Does that make any sense at all?
Pete
In B, usually R2 is set by what you want the cathode bias to be, unless you're also applying grid bias.
In my experiments, I set the resistance R1+R2 to be what I wanted for cathode bias, then "moved the tap" to optimize distortion. At least with the tubes I was using, I don't think the optimum was ever with R1=0.
Does that make any sense at all?
Pete
Sure, makes complete sense. You are the first one, however, that seems to actually set R1 to something other than 0. Hence my question.
What equipment do you use, and what is the test procedure? In the case where you have multiple stages, do you repeat this process for each stage?
Thanks.
What equipment do you use, and what is the test procedure? In the case where you have multiple stages, do you repeat this process for each stage?
Thanks.
I've only tried it with one stage... multiple stages might get a little more complex, unless you look at them one at a time.
I tweaked by having a distortion analyzer (HP 8903B) running, and watching the distortion residual on a scope while also watching the THD number.
You can get a pretty good sense of what an FFT will look like by looking at the residual - for example, you can easily tell when 2nd or 3rd is dominant.
Pete
I tweaked by having a distortion analyzer (HP 8903B) running, and watching the distortion residual on a scope while also watching the THD number.
You can get a pretty good sense of what an FFT will look like by looking at the residual - for example, you can easily tell when 2nd or 3rd is dominant.
Pete
Bringing this thread back from the dead. Has everyone seen Steve Bench's take on this concept?
Steve's WE HEQ
I am still trying to get my head around this a bit, but actually going back to the original simplified schematic above in this thread helped.
Steve's WE HEQ
I am still trying to get my head around this a bit, but actually going back to the original simplified schematic above in this thread helped.
The usual explanations of the WE Harmonic Equalizer in the freq. domain are somewhat obtuse and hard to understand. It actually is fairly simple in principle. Notice that the gm of a tube increases with current, non-linearly, and so therefore does the gain of a stage. (for a simple 3/2 power law tube model: gm = K I ^ 1/3) By monitoring the B+ or cathode current of a class A P-P stage, one gets a non-linearly coded (gm1 + gm2 = K I1 ^1/3 + K I2 ^ 1/3) indication of the stage gain. Ideally, one would want to hold gm1+gm2 constant for a constant P-P stage gain. (as the current falls in one tube it rises in the other P-P tube)
A constant current CCS on the cathodes does not quite get it right for constant gain because of the sum of 1/3 power terms is not linear. (leading to odd harmonics at large signal amplitude with a CCS tail) So any correction scheme (altering stage bias for example) must take into account the differential audio signal and the non-linear sum. One could also use a modulated CCS in the tail of the corrected stage to alter gms.
WE tried to do this in a single stage. Steve has done this in a separate LTP like control stage. (Steve ended up doing pre-distortion of the final stage based on the input signal to it) Clearly, a differential correction stage with similar non-linearity to the corrected stage is needed when done separately, in order to accurately take into account the 1/3 power variation of gms with audio signal over large signal variation.
Other approaches use a split tail under the corrected (or corrector) stage to vary tail current slightly versus differential audio signal. Another approach monitors the current of the outut stage and uses that to oppositely control the tail current or bias in a driver stage. (inline correction, gain of driver predistorts to the complement of the output stage gain)
No doubt other possibilities remain. For example, one could inject a constant low amplitude HF carrier into an amplifier's input and monitor the HF signal gain at the output, then use that to control a tail current in the amp. Might fit nicely with the idea of HF bias for the OT to eliminate core hysteresis.
Don
A constant current CCS on the cathodes does not quite get it right for constant gain because of the sum of 1/3 power terms is not linear. (leading to odd harmonics at large signal amplitude with a CCS tail) So any correction scheme (altering stage bias for example) must take into account the differential audio signal and the non-linear sum. One could also use a modulated CCS in the tail of the corrected stage to alter gms.
WE tried to do this in a single stage. Steve has done this in a separate LTP like control stage. (Steve ended up doing pre-distortion of the final stage based on the input signal to it) Clearly, a differential correction stage with similar non-linearity to the corrected stage is needed when done separately, in order to accurately take into account the 1/3 power variation of gms with audio signal over large signal variation.
Other approaches use a split tail under the corrected (or corrector) stage to vary tail current slightly versus differential audio signal. Another approach monitors the current of the outut stage and uses that to oppositely control the tail current or bias in a driver stage. (inline correction, gain of driver predistorts to the complement of the output stage gain)
No doubt other possibilities remain. For example, one could inject a constant low amplitude HF carrier into an amplifier's input and monitor the HF signal gain at the output, then use that to control a tail current in the amp. Might fit nicely with the idea of HF bias for the OT to eliminate core hysteresis.
Don
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Such a trick is used in modern opamps, to linearize diffpairs, but an additional emitter follower is used, for common-mode feedback by current.
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