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.
bifwynne
When I have had tube amps with various impedance taps I simply tried the speaker on each tap. I then went with the tap that sounded best to me. It really varied from speaker tot speaker. If I had two speakers rated at 8 ohms one might be best on the 8 ohm tap while the other was better on the 4 ohm tap. I don't think you can figure out by the specs which tap will be better
Alan
Alan, note that Bruce's question, as summarized in the last paragraph of his post before the P.S., is not about predicting which tap will be best. The question is if a generally applicable guideline can be defined for the maximum amount of variation of speaker impedance as a function of frequency that can be tolerated before it becomes likely that no tap can be chosen which will allow many tube amplifiers to perform at their best.

The question basically relates to speaker selection, given that the intention is to use a tube-based amplifier having an output transformer.

I don't have a good enough quantitative feel for the variables that are involved to suggest an answer, and it might be that too many variables are involved for a useful answer to be defined. But hopefully Ralph, Duke, etc. will shed some further light on the question.

Regards,
-- Al
Correct Al. Btw, just for fun, I pulled the Stereophile article which listed 2013 recommeded componenents -- speakers in particular. I drilled into the Class A speaker list write-ups and read John Atkinson's bench test reports, focusing on the impedance and phase angle charts. I needed dramamine after looking at some speakers' wacko impedance/phase angle charts. Need I say more?

So the point is, even if one's tube amp has relatively low output impedance and tight output voltage regulation, if the intended speaker has goofy impedance and phase angle dips, peaks and curves, will the impedance values (which change as a function of frequency) presented to the output tubes via the primary windings of the output transformer result in the output tubes operating outside of their sweet spots.

If so, as Al crisply said, "it becomes likely that no tap can be chosen which will allow many tube amplifiers to perform at their best," just at their least worst.
Interesting question. IMO, there is more to it than being in the output tubes sweet spot. If speakers were purely resistive than the answer to your question would be very use full. Unfortunately speakers are typically far from it as the amp has to deal with other factors such as inductance and reactance.

IME, you have to try all of the taps to find which is in the sweet spot of the amp, not just the tubes. I have found that with one brand of tube amp, when used with an 8 ohm nominal speaker, it was the 4 ohm tap that sounded best. With a different tube amp on the same speakers the 8 ohm tap sounded better.
Folks, I'd like to keep this OP open for a while. I've sent some private messages to a few of our fellow tech members. If Al (Almarg), one of our most tech-wise members, is scratching his head a bit, I think clarity and insight would be helpful and much appreciated.

To underscore the point, copied below is the web page that links to Stereophile's list of 2013 recommended loudspeakers. Interested members should drill a click or two into the article to read John Atkinson's bench test measurements for each speaker on the Class A list - Graph 1 in particular. You'll need drammamine when studying the impedance and phase graphs. The B&W 800 D is literally off the chart.

http://www.stereophile.com/content/2013-recommended-components-loudspeakers

Regards,

Bruce
Good luck with your eye recovery, it doesn't seem to have negatively impacted your insight too much.
Thanks Unsound. I assume y

No doubt that having good vision is a blessing. Ditto with good hearing.

And how to better enjoy the blessing of good hearing than to listen to beautiful music, even if certain frequencies may not be amplified within the optimal sweet spot of my amp's output tubes. LOL. Right now I am listening to a superb CD recording of Fandango.

Very nice. Very nice indeed.
Thanks Unsound. I assume your reference to "insight" is a pun. If so, very clever. :-')

No doubt that having good vision is a blessing. Ditto with good hearing.

And how to better enjoy the blessing of good hearing than to listen to beautiful music, even if certain frequencies may not be amplified within the optimal sweet spot of my amp's output tubes. LOL. Right now I am listening to a superb CD recording of Fandango.

Very nice. Very nice indeed.
For the technically interested:

Came across this article written by Thomas Mayer, "Speaker Impedance and Amplifier Output Taps: at this web site:

http://vinylsavor.blogspot.com/2011/08/speaker-impedance-and-amplifier-output.html

To head off anyone actually interested in trying the ideas mentioned in the Mayer article, please note Mr. Mayer's DISCLAIMER:

"Vacuum tube circuits work with dangerously high voltages. Do not attempt to build circuits presented on this site if you do not have the required experience and skills to work with such voltages. I assume no responsibility whatsoever for any damage caused by the usage of my circuits."

And that goes to mixing and matching output taps too!

Regards,

BIF
Hi Bruce, If you want a general rule of thumb for hooking up a speaker to your amplifier taps, look at the impedance of the speaker in the woofer region. The majority of the amplifier power and distortion will be made in the bass region, so its best to get the match as good as you can in that area. Don't worry about impedance peaks that are part of the box resonance- that will work out as long as the speaker designer has done his homework.

This will be true as long as both the amplifier and the speaker operate in the same paradigm.

So if you are looking at a B&W 802, which is a Voltage Paradigm device, and using your amplifier, which is also Voltage Paradigm, you would use the 4-ohm tap rather than the 8-ohm tap, despite the fact that B&W rates the speaker as 'nominally 8 ohms'. This is because the two woofers are in parallel and present a 4-ohm load to the amplifier in the range where it will do the most work.

You are correct about this 'back impedance' thing BTW. The transformer transforms the speaker impedance into something that the power tubes can deal with- it is a two way street. So impedance peaks and dips of the speaker are transformed into impedance peaks and dips that the power tubes have to deal with. So if there is a 4-ohm load on the 8 ohm tap, it will cut the load impedance on the tubes by half- and they will make less power and more distortion as a result.
Thanks Ralph. Al (Almarg) and I were hoping you'd chime in. Did you get a chance to look at the Thomas Mayer article in the URL link above. Mayer presents an interesting option relating to hooking up an amp's output taps. The option really pertains to speakers that have two sets of terminals for bi-wiring or bi-amping like my Paradigm Sig. 8s. Any thoughts??

I'd like to turn around your observation that "if there is a 4-ohm load on the 8 ohm tap, it will cut the load impedance on the tubes by half- and they will make less power and more distortion as a result." What happens if I use the 4 ohm tap and the amp is driving speaker impedance loads in the upper frequencies ranging from 8 to 20 ohms?

Let me share my anecdotal reactions when trying the different taps of my Ref 150:

(1) When using the 16 ohm taps, the music is open and detailed, but bass is clearly thin. I'm not sure about this, but while the music is open and detailed, it seems like the high end is a little too light. Btw, the S8's impedance drops to about 5 or 6 ohms north of 5K Hz.

(2) When using the 4 ohm tap, bass is deeper and a little tighter, but the midrange and treble are darker. Detail and imaging is fair.

(3) The 8 ohm tap seems to be the best compromise. I use a subwoofer so I can supplement SPL below 50 Hz. Bass is not as tight as off the 4 ohm tap, but I get more detail and better imaging.

So Ralph, is picking a particular amplifier tap an exercise best described as choosing the tap which sounds best, or choosing a tap that sounds the least worst.

Last point -- take a look at the Stereophile 2013 list of Class A recommended speakers. As an example, JA measured the B&W 800 D impedance as literally off the chart at certain frequencies. A couple of negative phase angle saddles at -67 degrees too. I suspect, not a very tube friendly speaker.

The URL link is here:

http://www.stereophile.com/content/bampw-800-diamond-loudspeaker-measurements

Thanks for the insights.

Bruce
THis is a fun question that seems to me to be one of those questions that can only be partially addressed by any answer based on theory. Aren't most questions that way usually as it turns out?

Like AL said, too many variables likely to be able to predict what is best in each case, even if comprehensive relevant measurements (beyond just published specs) were available.

Being aware of the theoretical issues and interactions likely helps predict general patterns to expect, but ya gotta test out the options to really determine or confirm what is either "best" or equivalently "least worst" in each case. The answer is often based as much on subjective reactions to what is heard as it is on anything quantitative that can be measured or specified.
Mapman, I can't disagree ....., but I'm wondering out loud here if the Thomas Mayer article presents an option or two for those whose speakers permit bi-amping/bi-wiring. In such cases, there may be a way to use the 4 ohm tap for the bass and the 8 or 16 ohm tap for the mid/tweet.

My woofer/mid x-over is about 230 Hz. Might be interesting if I can use the 4 ohm tap for the woofers and then use a higher rated tap for everything north of 230 Hz. Just asking ... that's all.

Hoping Ralph comes back with some thoughts. If so, what looks like an academic OP may have some practical utility. Was hoping I'd hear back from ARC, but so far nada.
+1 Mapman, or as Albert Einstein is rumored to have said:

"In theory, theory and practice are the same. In practice, they are not."

and the always appropriate in audiophilia:

"Not all that counts can be counted, and not all that can be counted, counts."
Swampwalker, there may be a practical answer here. I'm hoping to hear back from Ralph.

Take a look at the Thomas Mayer link in my earlier post. It may be possible to creatively use all the taps on my amp to better match impedance because my speakers can be bi-wired. If Ralph thinks so, please award me a +1.

If not, then I deserve a demerit of -1. I promise to accept my lashing with grace and dignity. :0(
Bruce, I'd imagine there would be some situations in which doing that would provide results that are subjectively preferable. But keep in mind that as indicated in the article the output voltage of the 8 ohm tap is higher than the output voltage of the 4 ohm tap, by up to about 3 db depending on the impedances that are involved, and the output voltage of the 16 ohm tap is higher than the output voltage of the 8 ohm tap by a similar amount.

It's safe to assume that commercially made integrated speakers are not designed to be driven that way, and so doing that would result in an unintended brighter tonal balance.

It's a good question, however, so no lashes are warranted :-)

Best regards,
-- Al
Bruce, I have set up systems plenty of times where we did something like that.

For example we had a set Sound Lab Dynastats about 20 years ago where the amps played the woofer just fine, but were rolled off on the ESL panel. So we installed an autoformer similar to the ZEROs to step up the speaker impedance, but only on the ESL panel- the woofer remained direct. It worked very well.

Similarly, you can do the same thing with the taps on the output transformer of the amplifier if the loudspeaker can be biwired. As you have surmised, quite often (certainly true of B&W, which are not tube-friendly speakers generally speaking) no one tap will be satisfied at all frequencies with some speakers.

You will of course need more than one speaker cable, and also some care should be exercised as you might expect!
Thanks Ralph. What's that old adage, "curiosity killed the cat." I hope that's not me. I e-mailed ARC with my inquiry and asked whether they would be willing to advise on how I might try this little experiment. I hope the ARC audio-cops don't confiscate my gear because, like Richard Fader of Fort Lee, NJ (SNL fame, circa 1975, courtesy of Gilda Radner/Rosanna Rosannadanna), I ask too many questions. :-(

Thanks again,

Bruce

P.S. If the idea has legs, it's kinda' a cool tweak that others may want to look into.

P.S.S. - Duke LeJeune (Audiokinesis) called me about the Q. He said he was quite interested in the issue and wanted to do more reading on the subject. He promised to get back to me after he digs himself out from under the pile of paperwork that accumulated while he was at RMAF.
Here is the response from ARC:

Hello Bruce,

Yes, this is possible if you can bi-wire your speakers.

You can hook one part of the speaker to the zero to 4 ohm tap and the other part of the speaker to the zero to 8 ohm tap. Check with speaker manufacturer for help to determine which part of the speaker works best at 4 and which part works best at 8 ohms. Only problem with this solution is you may not have the ability to balance the sound level between taps.

If you want to get creative, you could also try bi wiring using the set up in the attached file. It may give you better results. Have fun!

Best Regards,

Kalvin Dahl
Customer Support

P.S. -- I couldn't send along ARC's drawing, but it illustrates hooking the speaker's low end terminal up to the 0 (-) and 4 (+) ohm taps; and the high end terminal to the 4 (-) and 16 (+) Ohm taps.
I couldn't send along ARC's drawing, but it illustrates hooking the speaker's low end terminal up to the 0 (-) and 4 (+) ohm taps; and the high end terminal to the 4 (-) and 16 (+) Ohm taps.
Hi Bruce,

That suggestion is actually the same as in the first figure of the Vinylsavor paper you had linked to earlier. See that figure and the two paragraphs of the paper which are just above it. That arrangement should function well, and will provide proper phasing and level matching. In terms of impedance matching and output levels, from the perspective of the output tubes and from the perspective of the speaker it would be similar to connecting both sections of the speaker to the 4 ohm tap. I don't know whether or not it would be likely to provide any benefit in terms of the performance of the transformer itself.

Best regards,
-- Al
Thanks Al. I hope to hear back from the Paradigm tech folks re the creative hook up idea. If they respond, I'll post it here if it's useful.

On reflection, I find this issue quite interesting, but also a bit troubling. Folks tout the benefits of tube amps over SS amps. Yet, at the same time, I am not reading about application limitations, e.g., Voltage vs Power Paradigm characteristics and back impedance matching issues.

Al ... in the end, it seems like the issue of speaker/amp compatibility has gone full circle. Even if an amp can be a de facto constant voltage source and thereby behave "SS-like," the issue of back impedance remains.

So, in the context of matching tube friendly speakers with tube amps having low output impedance and tight output voltage regulation characteristics, one should STILL try to pick a speaker with as flat an impedance curve as possible.

Problem is, as illustrated by drilling into the bench measurements of Stereophile's 2013 list of Class A speakers, most of the listed speakers have flaky impedance and phase angle characteristics that are not very tube amp friendly.

I guess it's back to the drawing board for me. Either I find a speaker that is a top performer and has tube friendly impedance and phase angle characteristics, or I try out high-end SS amps.

I have another thread running that speaks to how one can meaningfully audition speakers in the current environment. Unfortunately, with the demise of B&M hi-end audio stores, it's very hit and miss.
^Without touching upon the specific technical issues you brought up in this particular thread, I've been saying things along these lines for some time now here, much to the disagreement of quite a few. And furthermore, that it might be more likely to find speakers with a steadier low impedance than a steadier high impedance, which might provide ss amps with some advantages in that regard too.
Which comes first, the speakers or the amp? :^)

Guess which way amp makers tend to lean?

And those who make speakers?

The rest of us are more "moderate" and less
extreme in our leanings I suppose.

I am more in the "speakers" first camp. Just make
sure the speakers you hear and like are being driven to
their max, and the specific amp to do it is easier to choose
from tehre.

But it'll work the other way also if done right, choose your
amp and then your speakers. But the speakers you'd really
like to have in that room may not be the right ones for you
then.

Just don't do either in a vacuum (no pun intended).
Well said, Bruce. And it seems to me to be safe to assume that the reason a lot of audiophiles find themselves on an amplifier merry-go-round at times is not that there is anything inferior about the amplifiers they've tried, it's just that the impedance characteristics of the speakers make amplifier selection excessively critical.

But hey, there are exceptions. My Daedalus Ulysses, for example, would be suitable matches for just about any amplifier known to mankind, except for the really flea-powered types. They are something like 6 +/- 1 ohm at all frequencies above 100 Hz, with a gradual rise to around 10 ohms at 20 Hz. And with benign phase angles, high efficiency, and high power handling capability. The 6 ohm nominal impedance, also, happens to be a perfect match for one of my amp's three output taps, which is indicated as being for 4 to 8 ohm loads.

And as I indicated in your thread about auditioning speakers, Daedalus provides 30-day return privileges, less two-way shipping and $300.

Best,
-- Al
One review I read indicated Daedulus were champs in the "tonality" dept. at RMAF. Probably not a coincidence...

Speakers are kind of like wind socks and amps like the wind. The wind has to deliver enough air to keep the thing properly inflated. Really big balloons may take a lot of air, and some amps may not be able to deliver enough juice with some speakers to do the job properly. Amp technology is becoming more efficient than ever these days (green in a sense) so there are possibilities now with high efficiency amps that did not exist before, so the utility of high efficiency easy to drive speakers is reduced somewhat overall, but as long as the shoe fits, you should be good.
Right questions Mapman, but wrong focus. I surmise that most speakers are voiced to be driven by SS amps. If my surmise is valid, the bias is that one should buy speakers first and then match the best SS amp, unless the speaker can do double duty.

I suggest you look at the specs on Stereophile's 2013 Class A speakers. Most are not very tube amp friendly. Don't misunderstand me ... I am very pleased with my ARC Ref 150. What's frustrating is that I have no idea how good my ARC Ref 150 really sounds because, as Al said above, the impedance varies so much as a function of frequency, it's difficult to know when it's functioning within the sweet spot range of its output section.

Oh well, another expensive lesson learned.
Back again. Tom Tutay rigged up a set of temporary speakers cables to let me use all 3 taps of my amp. As a reminder, my speakers can be bi-wired/bi-amped. I believe the lower terminals (LT) feed the woofers/mid range. The upper terminals (UT) feed the tweeter.

Here's what I'm trying. LT: The zero tap goes to the neg. terminal and the 4 ohm tap feeds the hot. If I've got that right, the amp's output impedance with the LT configuration is 4 ohms, which matches the LT woofer and lower midrange impedance, which is about 4 ohms from 50 Hz to 700 Hz; impedance then rises to about 21 ohms at the 2.2K Hz tweeter/midrange cross-over point.

UT: The 4 ohm tap is split wire, so I'm using the other head of the 4 ohm bi-wire to feed the negative terminal. Then, I'm running Tom's single cable off the 16 ohm tap to the hot. If I've got this right, the amp's output impedance on the UT configuration is 8 ohms. Not a perfect impedance match with the speakers, but better. The UT tweeter impedance ranges from 21 ohms at the 2.2K cross-over point and then falls to about 5 or 6 ohms at 4K or 5K Hz.

An important point is that the amp's voltage gain off the 4 ohm taps is about 2.5 db less than off the 8 ohm taps. As a result, the speakers may be a tad bright.

I'll try this set up for a while and see how I like it. Be back. ;-)
Is the UT impedance really 8 ohms? Would it not be 12 - the difference between 16 and 4 ohm taps?? If so, the gain may even be higher than 2.5 dB
Fla, I get your question, but that's what ARC told me. I don't know why.

In any case, last night, I switched everything around. I'm using the zero ohm tap for both UT and LT (negative) terminals and separately wiring the 4 ohm hot lead to the LT (hot) and the the 8 ohm tap to the UT (hot). As I suspected, the speakers are a tad bright, but the bass is better. I'll play around with it for a while and see what sounds best.

Valuable lessons here for those interested in tube amps. Lesson One -- be mindful of the impedances off the amp's output taps. The lower, the tighter the voltage regulatons and the "SS-like" the amp will operate (i.e., constant voltage source).

Lesson Two -- notwithstanding Lesson One -- keep in mind the the output trannies work both ways to the match voltage and the IMPEDANCE of the amp's output section to the speakers.

The trannies step down voltage and impedance to match the speakers via the secondary windings. At the same time, the trannies step up the speaker impedance via the primary windings to match the sweet spot of the output tubes.

My humble non-techie advice: if your set on using a tube amp that uses output trannies, try to match it with speakers that have the flattest possible impedance curve. My non-techie reaction is that most of the speakers on the 2013 Stereophile Class A list have some pretty wicked impedance and phase angle graphs, suggesting non-optimal tube amp matches. Just me musing. ;>')
Final report: I played around with pretty much every variation and permutation of the amp taps and speaker terminals I could think up. I just couldn't find an overall better combo that bested using the amp's 8 ohm taps on both the LT and UT terminals. I lose some bass tightness and extension, but not enough to justify using the amp's 4 ohm taps or all of the taps in the various configurations mentioned above.

Well my back-impedance experiment is over. I've got great electronics and very good speakers. Gonna just enjoy the music and turn up the juice until my wife screams. ;-)
...most of the speakers on the 2013 Stereophile Class A list have some pretty wicked impedance and phase angle graphs, suggesting non-optimal tube amp matches.

Stereophile does not recognize anything other than the Voltage Paradigm. So loudspeakers that might work a lot better with tubes probably won't get the same rating as they likely won't measure as well.

One take-away from this is that if you have sorted out that you like what tubes do, then the thing to do is find a loudspeaker that works best with tubes. Overall you will get better sound for your investment dollar in the tube amp. I think this is true regardless of whether the tube amp is capable of true voltage-source response or not! There is a good reason why some loudspeakers have a reputation for being 'hard to drive'. You want to pay attention to that, because a hard to drive speaker is less likely to perform as well **because** it makes the amp work harder: that is true regardless of the amplifier technology.
"However, SS amps produce less current and correlatively less power as impedance increases."
Very interesting post. I'm enjoying the interactions. However one clarification. Your statement in quotes above is really not correct. For well designed solid state amplifiers with well designed power supplies, this statement is not accurate. Not starting a tube vs solid state conversation, just a clarification.

enjoy
Bruce, enjoy!

I have several minor corrections and clarifications to most of the recent posts, though (excluding Ralph's, of course!).
10-30-13: Bifwynne
LT: The zero tap goes to the neg. terminal and the 4 ohm tap feeds the hot. If I've got that right, the amp's output impedance with the LT configuration is 4 ohms, which matches the LT woofer and lower midrange impedance ...
As I believe you realize, the output impedance of the 4 ohm tap of your amp (and that of most other tube amps, aside mainly from some OTL's and SETs) is much less than 4 ohms. It would be more correct to say that the load impedance that the tap is designed to drive or work into is 4 ohms.
UT: The 4 ohm tap is split wire, so I'm using the other head of the 4 ohm bi-wire to feed the negative terminal. Then, I'm running Tom's single cable off the 16 ohm tap to the hot. If I've got this right, the amp's output impedance on the UT configuration is 8 ohms.... An important point is that the amp's voltage gain off the 4 ohm taps is about 2.5 db less than off the 8 ohm taps. As a result, the speakers may be a tad bright.

10-31-13: F1a
Is the UT impedance really 8 ohms? Would it not be 12 - the difference between 16 and 4 ohm taps?? If so, the gain may even be higher than 2.5 dB.
Both statements are not correct. The load impedance that from the perspective of the amplifier is optimal for connection between the 4 ohm and 16 ohm taps is 4 ohms. As indicated in the paper Bruce referenced earlier, when 4, 8, and 16 ohm taps are provided the 4 ohm tap will normally be the center tap of the secondary winding of the transformer, with an equal number of turns "above" and "below" that point. That follows from the fact that transformers transform impedances in proportion to the square of the turns ratio. Presumably the transformer is designed such that a 4 ohm load connected between the common (negative or black) terminal and the 4 ohm tap will present the same impedance to the output tubes as when a 16 ohm load is connected between the common terminal and the 16 ohm tap. Therefore the number of secondary windings between the common terminal and the 16 ohm tap will be twice the number of windings between the common terminal and the 4 ohm tap. Therefore the number of secondary windings between the 4 and 16 ohm taps will be the same as the number of windings between the common terminal and the 4 ohm tap.
11-01-13: Minorl
"However, SS amps produce less current and correlatively less power as impedance increases."
Very interesting post. I'm enjoying the interactions. However one clarification. Your statement in quotes above is really not correct. For well designed solid state amplifiers with well designed power supplies, this statement is not accurate. Not starting a tube vs solid state conversation, just a clarification.
I don't see anything wrong with Bruce's statement, Minorl. As I'm sure you realize, almost all solid state amps have output impedances that are close to zero (i.e., a very small fraction of 1 ohm). Therefore, as a consequence of Ohm's Law and assuming that the amp is operated within the limits of its voltage, current, power, and thermal capabilities, the higher the load impedance the less current and power it will deliver, while delivering essentially constant voltage as load impedance varies. Power supply robustness will increase the CAPABILITIES of the amp under demanding conditions (especially into LOW impedances, and difficult impedance phase angles), and hopefully improve its sonics under most conditions.

Best regards,
-- Al
Yes you're right Al. Often pro reviewers will claim that the 16 ohm tap sounds more transparent because "the secondary windings are minimal thus there's less wire corrupting the signal" when in fact the opposite is true. The lower the tap, the less of the secondary is involved... correct?
Thanks Al. I got lazy and wrote too quickly. Of course you're 100% correct. The exercise was an attempt to match the amp's 4 ohm tap configuration with the speaker's low end terminals which are dedicated to the woofers and midrange. And to match the amp's 8 ohm tap configuration with the tweeters, which cross over from the midrange at 2.2K Hz and where there is a 21 ohms impedance peak which drops to about 5 or 6 ohms at 4 or 5K Hz.

As you say, the amp's output impedance off the 4 ohm tap configuration is .55 or .6 ohms, which ARC determined was an optimal match for a purely resistive 4 ohm speaker load. Output voltage regulation is +/- .4 db, which is pretty tight.

The amp's output impedance off the 8 ohm tap configuration is .8 ohms, which again ARC determined was an optimal match for a purely resistive 8 ohm speaker load. Output voltage regulation is +/- .8 db, still respectable.

I suspect I didn't like the sound because the amp's taps only did rough justice in matching amp and speaker impedance, plus the 8 ohm tap configuration is about 2.5 db greater than the 4 ohm tap configuration.

Last point, even though my speakers have some rough phase angles, the power supply of my amp is pretty robust -- 150 wpc, plus a 1000 joule power supply. Presumably, that's muscle enough to do a good job with moderately difficult speaker loads.

Regards,

Bruce
An amp will deliver specified rated output if the output drivers/pre drivers and power supply is robust enough to support this. An over simplification but really good amps double their power output when the load impedance is reduced in half. I agree that many don't, but some well designed amps do. There are many compromises in amp design and this is a major one. This is why the biggest and "best" had huge regulated power supplies. Which is also the major factor in the cost of those amps. As I said, I'm not trying to divert this most interesting discussion, but for well designed amps with well designed capable power supplies, I simply don't agree.

enjoy
11-01-13: Minorl
... really good amps double their power output when the load impedance is reduced in half.
And conversely, those amps halve their power output when the load impedance is doubled. Please re-read Bruce's statement, which refers to load impedance INCREASING.

Also, it is important to distinguish between how an amplifier's MAXIMUM power capability varies as a function of load impedance, and how its power delivery varies as a function of load impedance when it is operated WITHIN its maximum capabilities, whatever they may be. It is the latter that is being discussed, NOT variation of MAXIMUM power capability as a function of load impedance.

For a given input signal level, ANY amplifier having near zero output impedance, such as most solid state amplifiers, WILL double power delivery into a halved load impedance, as long as it is operated within the limits of its voltage, current, power, and thermal capabilities. And conversely, its power delivery into a doubled load impedance will be cut in half. Those are simply consequences of Ohm's Law.

That is all consistent with Bruce's original statement, as well as with Ohm's Law. I'm surprised that you disagree. I suspect that you've misread what has been said.

Regards,
-- Al
That the impedance increases and consequently that the power output decreases with a ss amp becomes moot, as the speakers sensitivity typically increases with impedance as well. Ss amps will more often than not provide a more linear frequency response whether the impedance increases or decreases.
Unsound, I don't think that's quite the way it works.

As Al and Ralph Karsten have explained, SS amps are constant voltage sources -- Voltage Paradigm amps. As impedance increases, a SS amp - being a constant voltage source and typically ultra low output impedance -- will decrease current output and concurrently power delivered to the speaker. If the speaker was voiced (i.e., designed) to be driven by a SS amp, and as designed has a flat FR, that's just the way it was designed to function.

By contrast, tube amps with high output impedances are not considered constant voltage sources. Power output is less susceptible to changes in speaker impedance -- so called Power Paradigm amps. Therefore, if a Power Paradigm amp drives a speaker that was designed to be driven by a SS amp, it will deliver more power at high impedance peaks and therefore more SPL than the designer intended. Conversely, the amp will deliver less power than was intended at low impedances and therefore less SPL.

That's why if you read my posts about using NF in a tube amp, you will see such amps have lower output impedance and tighter output voltage regulation. Hence, the tube amp operates SS-like, similar to a Voltage Paradigm amp.

But that does not speak to the issue of this thread which is back-impedance. I've killed the issue as explained above. Too tired to write more. I'll let Al or Ralph fill in.
11-01-13: Unsound
Ss amps will more often than not provide a more linear frequency response whether the impedance increases or decreases.
True, fundamentally because the majority of speakers are designed with the expectation that they will be used with solid state amplifiers. Meaning that they conform to what Ralph refers to as voltage paradigm principles.

Best regards,
-- Al
Which all goes back to the OP with the very insightful follow up link.
F1a & Bruce, I concur with everything in your latest posts.

Best regards,
-- Al
^What you post is true, however: impedance affects sensitivity. The lower the numerical impedance the lower the sensitivity, and conversely the higher the numerical impedance the higher the sensitivity. So the issue of diminishing power output (so long as there is enough required power left, and dollar for dollar extra power is typically more readably available, and over a greater frequency range too) at higher impedances for ss amps, becomes moot. On the other hand as speakers' impedance changes so does it's sensitivity or demand for power change, something that typical tube amps can't adapt to, and ergo the linearity of the frequency response is compromised. Of course if the impedance is ruler flat it won't be an issue for either technology. But flatter impedance speakers seem to be easier to design with lower numerical impedances than higher numerical impedances, and ss amps tend to work better into lower impedance loads than tube amps.
When Ken Zelin worked for McIntosh, he prepared a graphic slide suggesting customers use the different taps on their Mac amps to adjust for room anomalies. You can find the graphic by googling Ken Zelin and output taps. It's available on the klipsch forums.
Unsound .... I'm not sure if we are saying the same thing, but just speaking past each other. Let me try it another way re sensitivity.

I surmise Ralph and Al might say that matching (1) a speaker with low sensitivity and that was designed to be driven by a high power SS amp, with (2) a low powered tube amp that functions "solid state like" (i.e., because it has low output impedance and tight output voltage regulation) might stress the tube amp. The result might be increased distortion, possible clipping and overall acoustic degradation.

So, if I had my druthers and wanted to match a tube amp that functioned solid state like with speakers that were voiced to be driven by a SS amp, I would try to match highly sensitive speakers (e.g., 90+ db) with a tube amp with a lots of wpc and a robust power supply. That's why I think my Paradigm S8 (v3) speakers (92 db sensitivity) work pretty ok with my ARC Ref 150 (150 wpc and 1000 joule power supply).

Optimally, I would really love it if my S8s had a flat 8 ohm impedance curve and zero phase angle function across the entire frequency range. Or, if the output section of my amp was indifferent to changes in back impedance off the primary windings of the output tranny.

Just my opinion.

Bruce
No argument here with that, other than perhaps that most tube amps don't function like ss amps with regard to adapting to impedance variations.
Unsound .... I'm not aware of any tube amp that functions "SS-like" and that can adapt to a speaker's impedance variations.

Not to say there isn't such a beast out there. Just don't know what the model is.

The closest analogy I can think of is the ARC HD 220, a hybrid tube/SS amp, which matches a tube based front end with a SS output stage.

Notwithstanding the foregoing variation, I wonder if there's a tube amp configuration that can do double as your inquiry posits??

But here's a EE question for the techies. New Sensor is coming out with a new audio power tube, the KT-150 which may be a drop in replacement for the KT-120 -- TBD??? ARC has advised me NOT to drop in the KT-150 yet because its engineering department is still studying it.

I wonder out loud if the "sweet spot impedance range" of an output tube changes if a tube model is changed, i.e., the KT-120 viz the KT-150? Or, is an output tube's sweet spot impedance range more dependent on the circuit topology???

Bruce
Clockmeister ... not sure exactly what Ken Zelin had in mind. If he noticed that the sound and timber of the system changed as a function of the amp's output tap used, and therefore suggested that one compensate by adjusting room acoustic characteristics, that kinda looked passed the underlying reason for the acoustic difference.

But a fix is a fix be it a Band-Aid of moving the furniture around or me trying to creatively use all the taps on my amp. Whatever works I suppose.
Unsound, you may be right. But here's a little exercise that might be of interest to you and/or others that responds to your last quip. I make several references to the 2013 Stereophile list of recommended components, which includes recommended tube amps.

Drill into the Stereophile reports for the Class A recommended tube amps, and in particular John Atkinson's bench test reports. He runs all the tubes amps through the pretty much the same bench tests. I think Graph 1 reports the results of the amp's voltage output across the full frequency spectrum when driving a simulated speaker load that presents varying impedances and phase angles. JA also measures the amp's output impedances off the various output taps.

What you will learn from the exercise is whether the tube amp in question will perform SS like with respect to varying speaker impedances - that is operate like a constant voltage source. As has been said numerous times, this is largely a function of the amp's output impedance. What you will NOT learn is anything about back impedance, other than the reviewer's subjective opinion about how well the amp sounds on the reference speakers used.

Here's an important caveat -- just because the tube amp being reviewed sounds great (or not) on the reviewer's reference speakers could be misinformation on how well the amp will sound on YOUR speakers. This is because the electrical characteristics of YOUR speaker may be very different that the reviewer's reference speakers. And I'm not even talking about the speakers' acoustic performance (i.e., design and build).

My advice to members who are interested in buying a tube amp is to try and grab a bench test report about the amp that will show the types of information disclosed in the JA reports. Look for a tube amp with low output impedance. Presumably, that type of amp will be able to adapt best to changing speaker impedances -- that is act like a constant voltage. Correlatively, the amp will have a DF that will not be in the sub-basement. This is not my subjective opinion -- it's Ohm's Law.

At the same time, try not to go overboard with a tube amp that uses tons of NF for the all reasons that Ralph Karsten, Al (Almarg) and other have already explained. Namely, TIM distortion and odd ordered harmonic distortion.

In addition, the amp should have robust power supply and wpc specs. That may help mitigate some of the problems associated with non-optimal amp and speaker impedance matching. AT the same time, I would try to match the amp with speakers having the flattest possible impedance and phase angle curves.

Finally, and most important -- listen carefully to what looks like might be a good match on paper. Actual results may not line up with projected results. And, as stated many times in this OP, one stat that could affect sound quality is how well the tube amp and speaker can match back impedance.

I sincerely hope this OP has been helpful to the members. I've learned a lot from our techie members and my amateur experiments. I realize that there are technical gaps that I simply cannot bridge because of the multitude of electrical variables in play. Nevertheless, I think one can avoid making highly probable bad matches if certain key electrical attributes that simply don't mesh well are avoided.

Best,

Bruce
What you post is true, however: impedance affects sensitivity.

Correct- but its important to understand that impedance has no effect on *efficiency* whatsoever. IOW, efficiency is the measure of *power* driving a speaker while sensitivity is the measure of the *voltage* involved and ignores the resulting power.

Audiophiles and speaker designers are both guilty of conflating the two terms as the same; the result can be confusion and people talking past each other.