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Re: Harmonic adjustment, PDFs and other weird science

Naz,

Interesting questions, huh?

I think your parallel smaller tubes analogy for analyzing a single tube is spot on. Consider a “thought” example: Imagine a DHT tube with a straight filament (and cylindrical grid and plate structures to match), for simplicity. We can mentally break up that line filament along with nearby sections of the grid and plate into small pieces, each of which is a smaller tube in parallel with other pieces, together comprising the whole tube. Let’s say this imaginary tube uses a 10 volt AC filament supply. Let’s look at two points in time:

1.) When the AC heater supply crosses through zero volts, all points on the cathode/filament are at the same potential (let’s say that potential is ground - with a negatively biased grid). The filament is already hot and stays hot despite the zero volts across it, since the thermal time constant is far longer than a period of the AC heater supply at 60 Hz or 50 Hz. So this is not a thermal discussion, but a voltage discussion. Since there are equal voltages on each of our “mini-tube” segments, each tube equally shares in total plate current, gm, rp, etc. Simple, right?

2.) When the AC heater supply hits a peak at a point in time 4.16mS (or 5ms) later, there will be 10*1.414 = 14.14 volts difference from one end of the cathode to the other. Only the center point will be at zero volts, as in case #1. Remember that the temperature hasn’t changed anywhere on the filament from case #1 above. But the voltages are now radically differently distributed across the filament. One side is 7.07 volts above ground; the other is 7.07 volts below ground. Thinking again of each little segment as being part of a string of parallel tubes, we need to ask what would happen to any little tube segment when we raise or lower its cathode voltage by +/- 7 volts (thereby changing the local Vgk by +/-7 volts) while keeping its plate voltage the same as its mates. To the first approximation everything will average out to case #1 above, as you say. But, that only applies to the extent that the tube is linear. Since the tube cannot be perfectly linear, the outer segment which is at 7.07 volts above ground will drop its current BY LESS than the increase in current from the segment at 7.07 volts below ground (you can look at plate curves and see this non-linear effect). So total plate current will increase a tiny bit compared to case #1, during the AC peak. Likewise the reduction in gm on one end segment is less than the gain in gm on the other end, so average gm increases just slightly at the AC peak compared to case #1. Then, after another 8.3mS (or 10ms), the AC peak reverses and the end segments trade their effects, but the summation at the plate is the same as it was on the reverse peak. So both plate current and gm are modulated by 120 Hz or 100 Hz. Averaging all the small tube segments does not return us exactly to the situation of case #1, due to non-linearity. This means that the signal is subjected both to an ADDITIVE 120 Hz noise, and it is also MULTIPLIED by 120 Hz due to gm changes (intermodulation). We can actually see 120 Hz sidebands on either side of all pure tones on a close-in spectrum analyzer shot of a DHT output. We might be able to tweak a hum pot to remove, by cancellation, much of the 120 Hz additive noise part, but the intermodulating part is left to do some damage. Not enough to keep us from using DHTs, but enough for serious tube-heads to consider for ultimate designs.

Your deliberate ARC bias unbalancing was a static test – the plate current and gm effects were fixed once you set the bias controls, and they were not varying at 120 Hz.

I agree that the original designers of DHT tubes knew about these effects and did what they could to minimize them. I don’t see how offsetting the spacing of one side of the cathode could have helped. For most purposes over the decades efforts to minimize DHT heater modulation effects were “good enough”. But today we are demanding new levels of performance out of tube circuits. Our speakers and sources offer higher levels of resolution than what was available in the Thirties. Maybe greater DHT heater supply sophistication is worth some additional work, just as we are also taking B+ power supply regulation to high levels or as we are elevating current source technology to new levels.

…Thanks for the discussion.

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