300b lovers

A good way to visualize the difference between even and odd-order distortion harmonics is to imagine a sine wave ... a perfect, happy little sine wave. That's the original signal.

* Now, use a single diode to clip one side of it ... say, the positive side. In addition to generating a DC offset, if you run a spectral analysis of it, you'll see a series of harmonics ... 2nd, 4th, 6th, etc. etc. If you look at the "transfer curve" ... a curve mapping the input/ratio at different levels ... you'll see a diagonal line that is perfectly straight (the linear portion) that also has a sharp bend in it at the top, with a flat-topped region beyond the bend. The transfer curve is actually the true distortion mechanism; the spectral analysis of it is an indirect indicator that is (relatively) easy to measure.

* Let's use two diodes to clip the top and bottom sides, both positive and negative. This is known as symmetric clipping. If the flat-topping is at exactly matched levels, there will no DC offset. Similarly, if the clipping is precisely symmetric, the spectral analysis now shows no even-order terms (2nd, 4th, 6th, etc) but only odd-order (3rd, 5th, 7th, etc.). The transfer curve now has TWO kinks in it, at matching plus and minus signal levels. If the levels precisely match, there will be no even-order terms, but odd-order terms are abundant.

The diodes create hard clipping. Vacuum tubes, properly biased, create a softer "knee" region, but rest assured distortion is still there, just not as much, and with less high-order content. The property of symmetric circuits is they cancel transfer curves that are precisely opposite in shape ... a "C" shape that is inverted in the other phase of the circuit. But that depends on symmetry and precise phasing that tracks as levels go up and down.

@curiousjim 

The speakers appear to be 8 ohm 90 dB from a stereophile review.  They dip to 3.2 ohms, which isn't bad.  The amps would drive them with no trouble in any reasonable sized room.  I cannot comment on pricing until Spatial Audio figures out all of their costs.  I would expect $15,000 - 20,000 per pair with premium tubes, but that might be off a bit.  There will be an announcement after the Seattle show in the spatial audio lab website once it is all figured out.

Hi, CuriousJim!

I am kind of dubious about any KEF speaker being really 91 dB/meter/watt. That’s almost 1% conversion efficiency, and believe it or not, that’s quite high for the mainstream market, and especially KEF. True efficiencies between 85 and 88 dB are much more common. Efficiencies in that range need 100 to 200 watt amplifiers, which is very large for tube amps. When people say XYZ speaker needs 200 watts to "come alive", they are not joking.

1% efficiency is 92 dB/meter/watt. 0.5% is 89 dB/meter/watt. 0.25% is 86 dB/meter/watt. This raises the question ... where does all that power go, if not making sound?

It heats the voice coil, which eventually radiates its heat to the magnet structure, which radiates its heat into the cabinet. Copper increases its resistance with temperature, which leads to a type of dynamic compression as the voice coil heats and cools. In addition, voice coil heating eventually damages the cylindrical former it is wound on, leading to driver failure over time. That’s why Nomex and other fire-resistant materials are commonly used for VC formers.

This is the charm of high efficiency speakers: for a given SPL, much less power is wasted in heating the voice coil. More is turned into sound, which is the goal.

P.S. I agree, it is somewhat annoying to realize that 99%, or more, of the expensive watts we buy do nothing more than heat a voice coil, but that’s what’s really happening. It’s kind of shocking: hundreds of watts from the AC wall socket end up as milliwatts of acoustic power. The rest ends up as heat, and not in a great place, either.

@atmasphere 

I have to admit that the conclusion about SE+PP leads to emphasis on 5th harmonic is a bit counter-intuitive to me from pure math perspective, but I haven’t read his paper and perhaps there are certain situations that contribute to that conclusion (?).

Many report excellent result using a tube pre with a solid state or push-pull tube power amp though. In many cases, such combination includes some SE stages with at least one PP stage. So, SE+PP is not necessarily bad empirically :-)

It is difficult to predict real-world distortion from idealized triode or pentode models. The models assume tubes with perfect physical assembly and ideal emission characteristics. In practice, grid windings are not evenly spaced, grids are tilted a little bit, coatings on the cathode are not perfectly uniform, and there is always just a bit of residual contamination. Tubes are not built by robots, but skilled technicians, and as a result, they are all a little different from each other. By looking at spectral distortion measurements, patterns that are unique to each manufacturer emerge, and none conform exactly to the tube model. (The map is not the territory.)

Successive stages multiply distortion terms as more and more kinks end up in the transfer curve. Of course, this applies to the entire transmission chain from microphone to loudspeaker, with everything in-between.

Models are useful for finding bias points and the expected high-frequency response, but predictions of high-order distortion can be way off from the tubes you can actually buy. Low-order terms like 2nd and 3rd harmonic distortion may conform to the model, but I wouldn’t trust it further than that, not with real tubes. Think of the models as first-order approximations.