Tube DIY Asylum: Re: Partial slew rate distortion by Lynn Olson

... "as the current swings drawn by the load are increased, the beautifully flat horizontal AC loadline of the tube and CCS alone gets tilted more and more vertically, venturing down into the curved portions of the curves and adding THD" ...

Actually, it's worse than the load-line getting slanted down from the horizontal (no current fluctuation, tube is looking into an infinite impedance). A slanted load-line simply represents a finite resistive load for the tube, usually expressed as a ratio to Rp (dynamic plate impedance).

(Minor Digression: Traditionally, 3.5~5 times Rp was considered a pretty easy load for the tube, keeping in mind that removing the cathode-bypass cap also multiplies the Rp, thus both generating local feedback (good) but also degrading the load/Rp ratio (not good at all). When the load/Rp ratio is unfavorable (1:1 or worse) local feedback can't correct the descent of the load-line into the ugly low-current region, where abundant upper harmonics are generated. Local or global feedback will reduce distortion in direct proportion to the reduction in gain, but has no effect on the proportion of harmonics. So whether or not local feedback, or degeneration as it is sometimes called, is used, it can't change the behavior of the load-line, which in turn controls the proportion of upper harmonics. The relation of the load-line to the grid-lines creates the tube's distortion "signature".)

The proportion of upper to lower harmonics is critical to the sound of electronics. In the late Fifties, there were serious proposals by Norman Crowhurst, D.E.L. Shorter of the BBC, and other engineers to weight the harmonics by the square, or preferably, the cube of the order in order to better correlate with the subjective impression. This was never taken up, partly due to marketing reasons, and partly due to the extra complexity of measuring each harmonic at least out to the 10th and calculating it's impact (this was back in the day of the slide rule, remember). But what they said then still applies now, especially when you consider the devastating impact of high-order terms on IM distortion. D.E.L. Shorter mathematically demonstrated in a series of "Wireless World" articles that when you have 3 dominant tones of roughly equal magnitude, IM sum-and-difference terms start to outnumber THD harmonics. When you have 4 dominant tones, then IM distortion greatly dominates.

In other words, the more spectrally complex the source material is, the more IM sum-and-difference tones you get ... and this goes up as the *square* of the number of tones present in the original source. So with complex material, you're not really hearing THD, but thousands of sum-and-difference IM distortion components. This is much worse when you start with high-order THD ... the primary benefit of low-order (2nd and 3rd) harmonics is they generated fewer IM sidebands, thus giving a cleaner spectrum overall. The reason a massed chorus becomes a roaring haze of distortion, for example, is the very dense spectrum generates thousands of sidetones that were never present in the live, unamplified performance, and ear instantly detects the fraud. That's why you can tell "PA" sound at such a great distance.

Returning our old friend the load-line, yes, a resistive load creates a slope, and we have to watch out as the load-line approach the low-current region. But a *reactance* - either inductive or capacitive - creates an ellipse, and ultimately, a full circle when the load is 100% reactive with no resistive component. (A circular load-line is what blows out bipolar transistors when the circle momentarily exceeds the Safe Operating Area of the transistor current/voltage curve. It only takes a few milliseconds of exceeding SOA to melt down the tiny gold wires going to the chip and destroy the device. This is why you see fast-acting current-sensing protection circuits in bipolar-transistor amplifiers.)

Fortunately in the tube world, we don't need to worry about a circular or elliptical load-line destroying the device. It takes a prolonged thermal overload to wreck the plate structure, and even voltage flash-over can be tolerated occasionally. So outright destruction is not an immediate concern.

But an elliptical load-line *does* edge us closer to that troublesome low-current region, and also spells big trouble for pentodes that like to see a defined resistive load for lowest distortion. (Pentodes give lowest distortion not into an infinite load, but a specified resistive load. If you really want to see pentode distortion skyrocket, just add a little capacitance to that ideal resistive load. Look at the wavy plate curves, and the reason becomes obvious.)

In the output stage, of course, we are in a worst-case situation, driving a messy mechanical motor-drive chock-full of resonances. We get not just the expected resonances at driver resonance (Fs), but lots of other resonances thanks to cone standing waves, internal cabinet standing waves, spider resonances (no relation to the movie), dust-cap resonances, standing-waves between the horn-mouth and the reflective phase plug/waveguide, etc. etc. etc. Not only that, but our favorite speakers, the ones with the lowest IM distortion (horns and electrostats), are the worst behaved from the viewpoint of internal resonances that are reflected back to the amplifier (also known as Back-EMF). Direct-radiators are pretty ill-behaved too, thanks to lots of stored energy in cabinets and standing-waves on the cone itself.

All this trash gets sent right back to the amplifier output stage, which has to play music right through these harmonically unrelated back-EMF resonances. In the real-world amplifiers we can buy, though, the amplifier does interact with the back-EMF resonances, exaggerating the audibility of what might otherwise be a fairly minor speaker coloration.

So we care about behavior with reactive loads, no matter whether it's in an output stage or in an intermediate stage. It's probably not as important in an input or preamp stage, simply because the voltage/current swings are so much less and the loads are well-known and well-defined.

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