Tube Amps and Friendly Speakers - Back Impedance

The issue of tube amp friendly speakers has been taken apart on the Forum. However, I have another tube amp/speaker compatibility question that I hope will attract the attention of our tech oriented members, especially those members who manufacture speakers or amps. As I will explain below, the question relates to what I call "back impedance." Although this OP is longer than I would have wanted, the subject is complicated. Please accept my apologies. In the end, I'm not sure there is a best answer or practical advice. But here goes.

First a warm-up. I think many tech oriented members, such as Ralph (Atmasphere), Duke (Audiokinesis) and Al (Almarg) to name a few, have written extensively about Voltage and Power Paradigm amps, and how these amps produce current and power when presented with varying speaker impedances that change as a function of frequency.

Very generally, Voltage Paradigm amp (i.e., usually SS amps) usually maintain constant voltage and as a result produce more current, and correlatively more power (i.e., watts), when speaker impedance drops. However, SS amps produce less current and correlatively less power as impedance increases. By contrast, Power Paradigm amps (i.e., usually tube amps) tend to produce constant power as speaker impedance changes. The Atmasphere White Paper on the so-called Voltage and Power Paradigms contains a much more cogent and comprehensive discussion of the highly simplified points in this paragraph.

Second, a tube amp twist. Our tech members have explained at great length that SS amps usually have very low output impedances. This characteristic goes hand-in-hand with high damping factors (DF) and the Voltage Paradigm attribute of SS amps being constant voltage sources.

Third, the tube amp twist is that some tube amps use negative feedback of various types which has the effect of lowering output impedance and raising DF. In short, this design attribute enables a tube amp to perform somewhat solid state-like. That is, this class of tube amps is able to produce output voltages that don't vary very much as speaker impedance changes as a function of frequency.

As a case in point, my tube amp, the ARC Ref 150, has 3 different output taps (4, 8 and 16 ohms), each of which has a different output impedance: 4 ohm tap -- +/- .4 db; 8 ohm tap -- +/- .8 db; and 16 ohm tap -- +/- 1.4 db. Take a look at John Atkinson's 2012 bench test measurements of the Ref 150 to get a better sense for how it performs when presented with a simulated speaker load -- Graph 1 in particular.

Now to the back impedance question. And let me caveat my question by saying that it applies to tube amps that use output transformers -- not OTL amps like Atmasphere amps. In addition, I am thinking about tube amps that have low output impedance.

As I mentioned above, this issue has been discussed before, but I'm not sure sufficiently so. I say this because without knowing more, I would have jumped to the conclusion that a tube amp that has a low output impedance tap like the Ref 150 should perform sufficiently "SS like" so that it could drive speakers that were voiced to be driven by solid state amps. In fact, if the 4 ohm tap produces the lowest output impedance, just use it regardless of the speaker's impedance characteristics (nominal or varying). Not so fast ...

As I also mentioned, the Ref 150, like many tube amps has 3 output taps (4, 8 and 16) that are intended to correspond to the nominal impedance of the speaker. The theory is that the amp and speakers will perform better if there's a good impedance match between the two components. Great! What the heck does that mean and how does it impact performance??

The explanations I read on some of the older Forum posts seems to go like this. One of the key functions of output transformers is to match the impedance load of the speakers to the optimal operating range of a tube amp's output tubes. So, in a crazy way that I still don't understand yet, an output tranny works two ways -- (1) it steps-down the output tubes' plate voltage and high impedance to match the speakers, and at the same time (2) it steps up the impedance loading presented to the output tubes through the interaction of the tranny's primary and secondary windings (or, back impedance). In the latter case, the impedance step-up relates to the speaker's impedance presented to the tranny's secondary windings.

So, if I got this halfway correct, the inference that one should always hook his/her speakers up to the 4 ohm tap just because it generally presents the lowest output impedance to the speakers is flawed. The fallacy is that blindly using the 4 ohm tap may not result in an optimal impedance match for the output tubes.

And I think our tech members mentioned that if the output tubes are presented with a stepped up impedance that is outside the optimal design range of the output tubes, the result could be higher distortion and/or loss of power delivery capability at a given frequency as a function of the speaker's impedance characteristics at that frequency. Perhaps that's why the sage advice of using the tap that sounds best keeps cropping up. There's a lot of variables in play that affect what's comes out of the business end of a speaker, e.g., DF, output voltage regulation, power delivery and distortion, all changing as a function of frequency.

Ok, so using a low impedance tap doesn't solve all the problems with varying speaker impedances. Then, is it practical to know how much variation in a particular speaker's impedance viz-a-viz the amp's output tap impedance can be tolerated to be assured that the back impedance presented to the output tubes is in the tubes' operating sweet spot. Stated differently, if one plugs a speaker having a nominal impedance of 8 ohms into the amp's 8 ohm tap, how much can the speaker's impedance vary, yet still maintain optimal back impedance presented to the output tubes by the output transformer. Plus or minus 2 ohms ??, 4 ohms ??, etc.

If the practical answer is not more than 4 ohms total variation (or -/+ 2 ohms), then that's one heck of a pretty flat speaker by any accounts. So, my hypothetical speaker's impedance should not be greater than 10 ohms or less than 6 ohms or else the amp's output tubes will be operating outside their sweet spot, possibly producing more distortion or less power than predicted, especially if driven hard (e.g., at high gain, especially in the bass region).

So, in summary: is it practical to know how much variation in a particular speaker's impedance viz-a-viz the amp's output tap impedance can be tolerated to be assured that the back impedance presented to the output tube is in the tube's sweet spot? And that is the question!

P.S. I apologize for any typos. Just had eye surgery and my vision is still coming back.