Who makes


Who makes solid state amplifiers based on the "Power Paradigm", not "Voltage Paradigm".

How do you know if a cone speaker is designed to work better under the "Power Paradigm" better than "Voltage Paradigm"?
cdc
Cdc, IME and based on my readings, your questions are counter-intuitive and contradictory. I'll take the second question first.

IMO, based **solely** from an electrical compatibility perspective, a "perfect" Power Paradigm amp friendly speaker is one which has a totally flat impedance curve (say 8 ohms or higher) and a zero phase angle as a function of frequency. Such a speaker would be easy on a SS amp too, but the higher the impedance, the less current and correlatively the less power the SS amp could deliver.

As many of our knowledgeable techie members have said, one can call the manufacturer to ask whether the speaker in question was voiced to be driven by a solid state or tube amp. Some manufacturers (e.g., Revel) disclose the best amp to use for driving their speakers. Another clue is knowing whether the manufacturer used a SS or tube amp to showcase their speakers at audio shows.

Perhaps other members can weigh in on your first question, but I am not aware of a SS amp that functions like a Power Paradigm (tube) amp. OTOH, some tube amps can perform somewhat like a SS amp. Such tube amps have "low'ish" output impedances, "tight'ish" output voltage regulation, and moderate damping factors. However, some members might comment that tube amps that operate in the foregoing way use negative feedback which can degrade the sonics if used in excessive amounts and/or inappropriate ways.

I have exhausted these issues before. I suggest you look through some of my posts that discuss the topic. I raised questions similar to those asked in your OP and several of our tech savvy "EE-types" have provided comprehensive responses.

Happy Holidays,

Bruce
I've been around the industry and an avid audiophile since 71 or so. It's really as simple as listening. I've heard a lot of speakers with tubes that were voiced' with SS. If you speak with a lot of the speaker designers, they'll tell you that they don't even 'voice' their speakers. I know one who told me a couple of weeks ago that the first time he hears his designs can be after they are in production. I know how that sounds, but his speakers are considered some of the best ever made and are one of the biggest names ever in high end audio.

I've heard this guys amps with SS as well as tubes. They sound great with both. Personally I'm a tube guy, but I just got an Ayre and it's the best SS I've heard to date.

I think too many of us get caught up in tech specs etc.. Heck, I have MIT MH 770 CVT speaker cables I"m about to sell off. They were made for tube gear and it's with their highest speaker cables. I used them with Quicksilver pre/silver mono's (selling them off ;) ). They sounded awesome compared to every cable I tried with the amps. Now I'm running an Ayre integrated as I am moving over to a remote control system. The cables sound awesome. I'm changing them to AQ since the Vandy's I"m going to eventually purchase were made with the AQ cables in mind. That said, I have listened to the various cables I'm looking at. Trust in the person who's shop you buy at as they are with these products daily and listen to systems not just components.

Not taking anything away from the question I hope as I find it interesting to say the least. I had this same conversation when I got my Proacs with Quicksilvers as I hated the Krell stuff with them (other than the Krell DAC I got), but I listened to them with both SS as well as AR and Quicksilvers it was tubes all day for me. That said, I know someone who got the same speakers with Levinson gear and the bass was unreal and made me want more. The amps offered different sounds and both would appeal to different listeners.
Bifwynee/Bruce, good reply. Atleast I appreciate that you have taken the time to get a deeper understanding of the amp-speaker electrical interface. It's a complicated affair there - more complicated than meets the eye once one delves into the details. I'm sure that it's made you a better audio consumer & you can better make the trade-offs when you go out next to purchase audio gear. Like the SYMS clothing company once said in their TV ads "an educated consumer is a better consumer".

To Cdc:
before answering your question, let's take a step back & find out what is really meant by a "voltage paradigm". In a voltage paradigm amplifier, the output power doubles each time the speaker impedance halves (let us assume for the sake of simplicity that the power amplifier output has infinite current source/sink capacity. Such an amplifier is not available practically but it makes the discussion easier). The output power doubles because the output current capacity doubles; not because the output voltage capacity doubles.
For example:
300W into 8 Ohms. P=V^/R implies V = 49V approx.
600W into 4 Ohms. P=V^2/R implies V = 49V again!
1200W into 2 Ohms. P=V^2/R implies V = 49V once again!
So, as you can see, as impedance halves, output power doubles, the output voltage remains the same.
OTOH,
300W into 8 Ohms. P=I^2*R implies I = 6.12Amps
600W into 4 Ohms. P=I^2*R implies I = 12.24Amps. Output current doubled...
1200W into 2 Ohms. P=I^2*R implies I=24.49Amps. Output current doubled yet again!
So, output power is doubling as impedance is halving because output current is doubling.

Now that you understand this, a tube amp cannot double its output current as speaker impedance halves because tubes are output voltage devices & have large output impedance. The output transformer makes things much better to drive a speaker load but the ratio of amp output impedance to speaker impedance is quite high making it hard for the tube amp to output large amounts of current into a low speaker impedance.

Solid-state amps have output impedances that are sub-1Ohm (because the output stage of a s.s. amp is almost always the BJT emitter or a MOSFET source of a JFET source, which has very low output impedance & several semiconductor devices are paralleled to make the net output impedance even lower). So, even if the speaker impedance drops 8 --> 4 --> 2 & even 1 Ohms, the s.s. amp output impedance is still an order of magnitude (ie. 10X) lower than the speaker impedance. By the physics of this, a s.s. amp is able to output progressively more output current into a lower speaker impedance *while maintaining its output voltage* (as shown above).

A "power paradigm" amplifier cannot maintain its output voltage constant as speaker impedance varies over the audio band. This is the key difference between the voltage paradigm & power paradigm.

One would have to make a very high output impedance s.s. amp such that this s.s. amp cannot deliver large output current into a lower speaker impedance. As Bruce has pointed out "your questions are counter-intuitive and contradictory" because the very nature of s.s. amplifier design ensures very low output impedance: paralleling output devices decreases output impedance, negative feedback (local or global) reduces output impedance, increase in temperature reduces output impedance, etc. You have to go the extra mile to make the output impedance high in a s.s amp. IOW, s.s. are naturally voltage paradigm amplifiers.

Now I am stating & asking the forum at large: could McIntosh's philosophy of using output auto-formers be one technique to increase the output impedance of a s.s. amp (I believe that McIntosh makes several s.s. amps w/ autoformers, no?) such that these s.s. amps show some/a lot of the characteristics of tube amplifiers?

Another devislish way to make a s.s. amplifier behave in a power paradigm manner would be to use it with a very low impedance speaker such as using a s.s. amp to drive an Apogee Full Range speaker where the midrange is driven directly by the amp & has a speaker impedance of 0.14 Ohms (I did not make a mistake here!!). Now, the s.s. amp will see a speaker load that is in the same ball-park as its own output impedance & current will be limited (just like a tube amplifier seeing a 4-Ohm speaker load when its own output impedance is in the 4 Ohm region). Such an amplifier's life could be very short-lived if not chosen correctly. Devilish, as I wrote! ;-) Also, how many such speakers exist today? Almost zero. so, this scenario is not realistic.

I don't know of any other s.s. manuf that makes their s.s. amps power paradigm but memory & experience could be failing me.....
It would be great to hear from other far more knowledgeable members. Thanks.
Double tap. ;-)
Just a reminder that Bob Carver's Sunfire amp had both "voltage source" and "current source" outputs. The current source output had a 1 ohm power resistor in series with the output. See the pictures here:
http://www.hometheaterhifi.com/volume_2_1/productr.html
Excellent responses by Bruce and Bombaywalla.

Bob R. adds a good point also. During the 1980s and 1990s Bob Carver designed some Carver Corporation and later Sunfire Corporation solid state amplifiers that were intended to emulate tube amplifier characteristics to some approximation. That was accomplished in part by putting a resistor in series with the output, as Bob mentioned.

One of Carver's earlier such attempts, during the 1980s, involved configuring an amplifier such that its "transfer function" (the relation between its output and its input) approximately matched that of a well regarded high end tube amp, at least when driving a specific speaker load. As demonstrated by electronically "subtracting" the output of one amp from the output of the other, with both amps receiving identical inputs, and measuring and listening to the residue. That ended up provoking a good deal of controversy, of course.

I can't recall any other solid state amps that can be said to approximate power paradigm characteristics. I recall reading that Nelson Pass, and perhaps some others, have created some designs that essentially act as current sources, having VERY high output impedances (e.g., 25 ohms). But those would not maintain an approximation of constant power delivery as a function of load impedance either, because their output voltage would vary dramatically as load impedance varies. (Power = voltage times current, oversimplifying slightly).

Regarding the McIntosh solid state amps that use autoformers at their outputs, those have very solid state-like output impedances (e.g., 0.2 ohms or less). The autoformers appear to be used to make life easier on the output devices when faced with low impedance loads, by making those loads appear to the output devices as higher impedances. Thereby reducing distortion, and probably also increasing power capability into low impedances relative to what it would otherwise be.

Best regards,
-- Al
Ctsooner, I'm not really looking to start another lengthy discussion about tube vs SS amps. I'll leave it this way. It is plausible that a speaker designer, a dealer sales rep and/or a customer could be indifferent to plugging a tube amp or a SS amp into a speaker if either (x) the speaker has extremely benign impedance and phase angle characteristics, or (y) the tube amp has very low output impedance.

As Al and Ralph Karsten (Atmasphere) have said on numerous occasions, a speaker's ultimate acoustic presentation will be affected to the extent an amp has a high'ish output impedance and the speaker was voiced (intentionally or not) to be driven by an amp that has a low output impedance. This is not my opinion -- it Ohm's Law.

It is my experience that when I drive my speakers off the 8 ohm taps of my amp, the speakers sound bright and detailed, maybe too much so at times. In contrast, when driving the speakers off the 4 ohm taps, bass is more extended and tighter, imaging less forward. Admittedly, I am conflicted about which acoustic presentation sounds better to my ears. It just depends.

This is no coincidence. The output impedance of my amp off the 4 ohm taps is about .55 ohms in the lower frequency bands; and about 1.1 ohms off the 8 ohms taps. It is similarly notable that the impedance curve of my speakers is roughly 4 ohms between 70 Hz and 700 Hz, rising sharply and peaking at 21-22 ohms at the 2.2K Hz crossover point, dropping again to about 5 or 6 ohms as frequency increases.

Let's put a sonic face (sic, an oxymoron) on what I just said. John Atkinson's bench test report of my amp states that output voltage regulation is +/- .4 db off the 4 ohm tap and about +/- .8 db off the 8 ohm tap. What this means in plain English is that my speakers should be about 1.6 db louder at the midrange highpoint of about 2.2K Hz as compared to the bass saddle of 70 to 700 Hz -- IF I use the 8 ohm taps. In contrast, the SPL delta off the 4 ohm taps should be about .8 ohms. Those stats cogently explain what I hear.

Oh ... the damping factor of my amp is also affected. Theoretically, about 7 ohms off the 8 ohm taps and about 14 ohms off the 4 ohm taps. Although with my speakers, those stats should be halved because my speaker's impedance is about 4 ohms in the critical parts of the bass frequencies. But those stats explain why I perceive bass to be more extended and tighter off the 4 ohm taps.

This is Ohm's Law, not my opinion. So, unless a dealer's sales rep explains in plain English what I just said above, he's either ignorant or scamming the customer. Of course, he could be honest and say even though a tube amp may be causing certain acoustic colorations, they sound good, in his/her opinion. Then it's on the customer to decide.

Al or Ralph, if you can simplify or clarify what I just said, I'm sure I and the other readers would appreciate your edits.

Regards,

Bruce
Bifwynne, thanks. I was just going by what I was reading atmasphere.
I think Al hit on one company, Pass Labs, that made the solid state amp act like a current driven amp. And The Carver amp that Bob mentioned looks interesting too.
Just one last thought. The OP doesn't ask about a speaker's phase angle characteristics. Definitely off topic.

Suffice to say that a speaker with highly negative (i.e., capacitive) phase angle and low impedance characteristics in the power spectrum (say 30 to 400 Hz ??) can really give a tube amp, even a SS amp, a bad day. That in part makes for a tough to drive speaker that calls for a "current" beast like a Bryston or Krell SS amp.

In my case, my tube amp has a large'ish power supply of 1040 joules. I surmise my amp's power supply reserve helps it to muscle its was through some pretty tough negative phase angles in the speaker's bass region.

Bruce
Cdc, I believe that Pass amps are SS amps that use very low, or no, negative feedback. Even still, as a SS amp, I would expect it to be a constant voltage source.
If it can't be driven with tubes, I am not interested.

And since going with high efficiency speakers, I might also add that if it can't be driven with low power tubes, I'm also out.

Shakey
Shakey deal, your last comment is based on a very shaky foundation. LOL :)
I ran a high power/low current Carver m4.0t transfer function amp for years.

It did in fact work best and quite well overall with more "power paradigm" friendly speakers I owned concurrently, specifically Magnepan and Triangle. Though at 360 w/ch it went plenty loud, it left a lot to be desired especially in the bass region with others I also owned concurrently, like OHM, B&W and Dynaudio.
The way to get a conventional solid state amplifier to operate in the Power Paradigm would be to add some current feedback, but not so much that it acts like a 'current source' device.

To my knowledge, no such products exist - for now. If you want to take advantage of Power Paradigm principles, you will, for the time being, have to use a tube amplifier.
The Nelson Pass amps I referred to earlier that act essentially as current sources and therefore have very high output impedance are listed at his "First Watt" site here. (His amps that are marketed under the Pass Labs name are of course voltage paradigm amps, as Bruce indicated). The ones I was referring to, which I suppose could be called "current paradigm" amps, are the F1, F1J, F2, and F2J, which are indicated as no longer being produced. The literature provided at the site indicates that they are of course only suitable for use with a limited number of speakers, primarily those using just one driver and providing high efficiency.

What may be more interesting, though, are the currently produced SIT-1 and SIT-2 models, which I hadn't been aware of previously. Based on a quick look at their descriptions, specs, and manuals, those would appear to be true solid state power paradigm designs, although their power ratings are limited to SET territory at 10 watts.

Best regards,
-- Al
12-02-13: Bifwynne
Al or Ralph, if you can simplify or clarify what I just said, I'm sure I and the other readers would appreciate your edits.
You said it all clearly and well as far as I am concerned, Bruce, aside from a minor miswording that I suspect was inadvertent: As you probably realize, damping factor is not measured in ohms. Since it is the ratio of two impedances, it has no units.

Best regards,
-- Al
Hi Bifwynne,
It doesn't seem that Shakeydeal was making a proclamation but rather just
stating an opinion about his preferences. I know this is of course pure
subjectivity but I understand his rationale for feeling that way.
Charles,
12-02-13: Bifwynne
Suffice to say that a speaker with highly negative (i.e., capacitive) phase angle and low impedance characteristics in the power spectrum (say 30 to 400 Hz ??) can really give a tube amp, even a SS amp, a bad day. That in part makes for a tough to drive speaker that calls for a "current" beast like a Bryston or Krell SS amp.
That is another good point. Is the current output more important than the voltage as that is what gives the speaker its dynamic range? What is voltage good for? It seems like a cheap way make the amp appear to be powerful when reading the specs.
Thanks all. I will have to give this some thought. Previously, I had the simplified idea that if a speaker is over 8 ohm, and especially 16 ohm like those back in the 60's, you need tubes because you just won't get any power out of a reasonable sized ss amp.
"What is voltage good for? It seems like a cheap way make the amp appear to be powerful when reading the specs."

Obviously, there can be no power without voltage, but with home hifi, not all watts are created equally. True powerhouse amps are either large and heavy and use beefy power transformers and in most cases with typical less efficient Class A or even Class A/B amps will also require extensive heat sinks to dissipate the heat created by wasted power.

The exceptions are amps designed to be more efficient, like Class G amps that have been around for many years or more significantly these days, Class D amps, that achieve new frontiers in power amp efficiency and sound quality not possible prior/otherwise.

One of the most unique advantages of a tube amp in regards to how far teh watts go is soft clipping. Tube amps soft clip by nature, which means sonic artifacts of amp clipping is more acceptable to our ears than is the case with most hard clipping SS amps.

Best to avoid clipping altogether IMHO, which in the past was quite hard to avoid in many cases using traditional Class A/B technology. No longer the case with new higher efficiency and more practical (for many compared to a traditional Class A/B monster sized power amp) high power Class D amps.
^^ Cdc, its actually simple math. All speakers are driven by power and if the amp can make the power into the speaker the voltage and current will be exactly the same regardless of the amplifier.

Obviously there is more to it than that- what is going on here is how the amplifier responds to different impedances that will be present in any speaker at various frequencies.

The idea behind the Voltage Paradigm was essentially to deal with box resonance, which is represented by a large impedance peak in the bass region, usually just above the cutoff frequency of the woofer in the box. If you drive that peak with the same power as other frequencies, you will get a one-note bass boom. To control this effect and other issues associated with peaks and dips in the driver response and also due to the crossover, the Voltage Paradigm was created as a sort of standard for driving loudspeakers. You know how a transistor amp can double power as impedance is cut in half? The converse is true too- if you double impedance, the *power* is cut in half. that works nicely for controlling output when dealing with a resonance.

(In the Power Paradigm, the resonance is set up ideally to allow the amplifier to put out the power, but at a frequency that should result in extension of the bottom octave of the speaker's response. This allows a speaker of similar size to go deeper than a speaker designed for the Voltage Paradigm. In both cases, we are looking for flat frequency response, and it is possible that the Voltage Paradigm approach will result in flatter response in some cases. However, the brain has a tipping point wherein distortion will overshadow frequency response errors in its perception of coloration- IOW, a system that has flat frequency response may well sound more colored due to the types of distortion generated. This is why two amps might measure with identical frequency response, yet one might sound bright while the other does not. The Power Paradigm seeks to use this fact to audiophile's advantage while the Voltage Paradigm ignores it.)

Unfortunately, in 99 44/100 percent of all amplifiers, this means that they have to run negative feedback either to create linearity, to create a low enough output impedance or both in the amplifier.

Now that I think of it though, it seems to me that what you are interested in doing is getting a solid state amp that otherwise has the character usually found in tube amps- greater linearity, such that feedback is not required. There are a couple of amps you might look at. The first has been mentioned- Pass Labs. I *think* they may be offering zero feedback amplifiers with a little more power, that otherwise are considered Voltage Paradigm devices. The other amp is the Ayre.

It is not easy to build a reliable solid state amplifier that does not use feedback, which is why most designers don't bother. But Nelson and Charlie did- so you might want to give their amps a listen. That way you can use a Voltage Paradigm speaker and see what you think.

One reason why tubes have increased linearity over solid state has to do with the non-linear capacitive aspects that exist within the layers of almost any solid state output device (which tubes don't have). This non-linear aspect is magnified by current. This is why all solid state amps will have lower distortion and will sound better when driving higher impedance loudspeakers. Yes- they won't make as much power, but they will have more musical finesse. This is also why tubes are still very much in evidence half a century after being declared obsolete.

So you might consider a higher impedance speaker to go with the amplifiers I suggested. That will be giving you a good chance for the better sound within the constraints of solid state technology.
Cdc,

The specs on the full range speakers you use indicate response down to only 125hz.

I suspect most any good quality amp should be able to do a good job with those.

The biggest, clearest challenges where power paradigm comes into play is generally at frequencies lower than 125hz. That's because power requirements increase exponentially with lower frequency for flat response. With bass extension down to only 125hz, and with a very small 3" driver alone, there is likely much less room for amps to differentiate themselves based on power paradigm alone. Not to say they will all sound the same, but the differences may be much less in the case of your specific speakers.

So, its always a good idea to understand the technology involved, but I am just wondering how much practically power paradigm matters really in the case of the OPs current 3" full range speakers specifically.

If a speaker change/upgrade is in the plans at some point, even more reason to clearly understand the options as best as possible before pulling the trigger.
Is the current output more important than the voltage as that is what gives the speaker its dynamic range? What is voltage good for? It seems like a cheap way make the amp appear to be powerful when reading the specs.
voltage & current are duals of each other - where you will find voltage, you'll find current flow. The converse is also true - Where you'll find current, you'll find voltage. Voltage & current cannot exist without each other.
Think of voltage as electric pressure (old engineering texts had voltage as E) similar to water pressure. Current flows from higher electric pressure to lower electric pressure.
When an amp is delivering power into a speaker it's a combination of voltage & current. The voltage impressed (by the amp) at the speaker terminals causes current to flow in the passive x-over components. Depending on the various values of R, C, L in the x-over components, these respective components develop a voltage across them proportional to the music signal. This gets xferred to the speaker drivers. It's the voltage signal that causes pistonic movement in the speaker drivers & that produces sound. No voltage, no sound. So, voltage is good for a whole lot of things. How much current can be output from the power amp depends on how robust its power supply is. So, as Mapman suggested, not all watts are created equal in the sense that 2 100W amps might have vastly different power supplies. in such a case, the power amp with a more robust power supply will be able to drive a more difficult speaker load because it will be able to output more current into the difficult load to create a proportional-to-music-signal voltage for the speaker drivers.
Amps with a weaker power supply cannot drive difficult loads (yet it will still be a 100W/ch amp).
Thanks Bombaywalla,
This also explains why certain amplifiers rated at say for example 40 watts/channel can out drive another amp that's rated at 100 watt/channel . Power supply quality matters.
YEs, and most modern high quality speakers that are not large and use porting and other methods to deliver extended low end bass response out of a smaller package, as is popular with most these days, ARE difficult loads, even quality small monitor style speakers with top notch low end extension for their size.

COmbine that with a lot of the popular and low cost commercial amplification devices out there that also tend to emphasize many features in a small package that most can handle easily that use relatively small and inexpensive power supplies to deliver their watts as well and you have 90% of the reason why so many systems you hear normally have such mediocre sound, even if the speakers are in fact capable of much more.

Its like connecting a fire hose to a house spigot and expecting to be able to put out a house fire as well as the one hooked up to the high pressure (voltage), high volume (current) fire hydrant down the street.
where you will find voltage, you'll find current flow. Voltage & current cannot exist without each other.
Is that really true? I thought voltage is a measure of electric potential. A perfect battery has electric potential, but there is no current flow until a circuit is completed across its terminals.
Yes, you are correct, Bob. Here we are talking about power amps & power amps driving speakers so in both cases there is an electrical circuit completed around the voltage source (the amp) which will cause current flow.
I assumed this due to nature of the question from the OP.
The Zamp puts out 12 amperes at 45 watts. It still seems to me that current capacity, along with slew rate, would increase dynamic headroom before clipping. Because 12 amps x 120 volts = 1,440 watts, not 45 watts.
Atmasphere makes a convincing argument for tubes and I can see how his amps could better a ss amp in the right setup. What I don't get is do you want the power of a tube amp at the impedance peak to lower the FR or the reduced power of a ss amp to control resonances? Is this where the whole voltage / power paradigm relates to which is better for which speaker? Because for the rest of the frequency range, this would not matter. Other than nominal speaker impedance.
Is it easier to make a ss amp that can drive a 2 ohm load than a tube amp?
A vented speaker benefits from the control of a ss amp? Would a sealed box benefit from the deeper extension of a tube amp as there is no impedance peak from a vented port? Just that of the driver itself.
The best amp is the one that matches best to the best speakers.

In the end, that's really all that matters, no matter how it is accomplished in any particular case.

Figuring out what will work best with what is the tricky part. The rest is largely subjective.

I've heard all shapes and sizes sound equally excellent, though probably never exactly the same. Pretty close though. The key was always someone who knew how to put the right pieces together and make it all work. That and good (but rarely ever close to perfect) source material to work with.

Only tube amps will ever have that really cool looking retro glow going on to boot though.
Cdc, FWIW, the example you cited of the Zamp cannot be correct at least not into any known speaker load.

The power formula is P= Voltage X Current

When related to Ohm's Law the power formula can all be shown be P=Current squared x Resistance

The lower the impedance of the speaker, the more current will be present for a given amount of power. So if we have a one ohm load, to do 45 watts the current will be the square root of 45, or 6.07 amps.

Usually that high current spec is the amount of current that will be present when the power supply of the amplifier is shorted out for 10 milliseconds. FWIW, we make tube amps with greater amounts of current by *that* measure...

Also, it usually is easier to build a transistor amp than it is a tube amp. Traditionally tube power is more expensive than solid state.
So if we have a one ohm load, to do 45 watts the current will be the square root of 45, or 6.07 amps.
Thanks Atmasphere. I think you are talking about speaker impedance and how it requires a certain amount of power to drive it? But what about musical dynamic peaks? That's what I'm, mistakenly(?) trying to get at. If you play a song at 90 dB with 110dB musical peaks like rim shots, don't you need the current to give that dynamic range for the 10 milliseconds?
the power supply of the amplifier is shorted out for 10 milliseconds. FWIW, we make tube amps with greater amounts of current by *that* measure...
So tube amps have more current on tap than ss?
If you play a song at 90 dB with 110dB musical peaks like rim shots, don't you need the current to give that dynamic range for the 10 milliseconds?
yes, you do. this sudden burst of current comes from the power supply capacitors. like you wrote, the rim shots (your example) are extremely quick & fleeting events. By the time the bridge rectifier reacts to this quick event, the event itself has passed. The power supply itself cannot react fast enough to quick events & that is by design - it's supposed to be a DC power supply that remains steady no matter what (given the amp is being driven within its limits). SO, it's the capacitor bank of the power supply that reacts to these quick events. That's why many amp manuf boast about how much power supply cap they have + you'll find many other amp manuf to have bypass caps in parallel w/ the power supply main cap. These bypass caps are much smaller (10,000uF) with very low ESR such that they can react very quickly to rim shot events.
So tube amps have more current on tap than ss?
Not as a general rule; more often than not the opposite would be true. It goes without saying that generalizations are not likely to be meaningful if drawn based on a comparison between a $349 amplifier and amplifiers that are in a VASTLY different league in terms of performance, quality, and price.
... what about musical dynamic peaks? That's what I'm, mistakenly(?) trying to get at. If you play a song at 90 dB with 110dB musical peaks like rim shots, don't you need the current to give that dynamic range for the 10 milliseconds?
Good response by Bombaywalla, of course, to which I'll add some further specifics.

I took a look at the specs of the Zamp, and it appears that what Ralph (Atmasphere) surmised about the 12 amp current spec is correct -- it most likely represents how much current the amplifier can supply into a short circuit (zero ohms) for a miniscule amount of time. Also, I would infer that the reference to 12 amps "peak" probably means "peak" not only in the sense of maximum, but also in the sense of being distinguished from RMS, which is the form in which the voltages and currents corresponding to maximum continuous power ratings are defined. For the sinusoidal waveforms upon which these numbers are based, RMS current equals peak current divided by the square root of 2, so on an RMS basis the maximum current rating is only about 8.5 amps.

In any event, what is important to realize is that the specified peak current is unlikely to ever be available to a real world speaker load, because for a reasonable load impedance the amplifier will not be able to supply the voltage corresponding to that current times that impedance, and it will not be able to supply the power corresponding to that current squared times that impedance.

What I think you are really asking about in this question is what is referred to as dynamic headroom, meaning the ability of the amplifier to deliver greater amounts of power to a speaker for brief amounts of time than its specified continuous maximum rating.

Dynamic headroom is often unspecified, and when it is specified there is often no indication of the amount of time the power increase can be sustained for, so comparing that spec for different amplifiers is usually not very meaningful. Also, having more dynamic headroom is not necessarily a positive attribute. It can be looked at in two ways: The amplifier is ABLE to deliver more power for a short time than it can deliver continuously, or it is UNABLE to continuously deliver an amount of power that is close to what it can deliver for a short period of time. Some of the world's best amplifiers have essentially zero dynamic headroom.

My impression is that typical dynamic headroom numbers range from zero to a few db, and rarely if ever exceed or even reach perhaps 6 db. 6 db corresponds to a four-fold increase in power, and would raise the sound pressure level heard by the listener by no more than 6 db, and perhaps somewhat less due to "thermal compression" in the speaker.

A number that generally says more about the robustness of a solid state (but not tube) amplifier than all of the foregoing is how closely its 4 ohm continuous power rating approaches being double its 8 ohm rating. The two ratings for the Zamp are 45 and 60 watts, which may be a better ratio than most other amplifiers in its price class have (many of which do not even have a 4 ohm rating), but does not approach the factor of 2 that many multi-kilobuck solid state amplifiers can achieve.

Regards,
-- Al
"A number that generally says more about the robustness of a solid state (but not tube) amplifier than all of the foregoing is how closely its 4 ohm continuous power rating approaches being double its 8 ohm rating."

That's the most common spec out there to use to help gauge ability to handle a "difficult" load.

Not perfect or 100% reliable always (numbers are meaningful but no single number can tell the whole story) but is generally a useful benchmark to help weed out pretenders.

If a similar rating is even provided into 2 ohm, that is usually a good omen as well that shows the maker really cares about these things.

Even more bankable than the specs is when reviewers like Stereophile actually perform measurements with 8 4 and 2 ohms when bench testing a product as part of the review.
Mapman, I agree with your comments buy you might be missing something: how the use of negative feedback affects this.

As you probably know, most transistor amps (especially ones that can double power nicely even to 2 ohms) employ negative feedback. **All** inexpensive solid state amplifiers do as well.

Now if the speaker is only going down to 4 ohms, the fact that the amp can't double power into that impedance does not mean that it is not a voltage source. This is due to the fact that the feedback of the amplifier will make it act like a voltage source independently of the amp's ability to double power. If you have heard of the Wolcott tube amplifier, this amp employed enough negative feedback to also act as a voltage source, and it was completely unable to double its power into lower impedances.

Its right about here that I see where a lot of designers get into a little bit of trouble in understanding the effect of output impedance on how the amplifier responds to load. The thing that clears the air is something called Kirchoff's Law- the law of energy conservation.

Now its understood that adding negative feedback to an amplifier reduces its output impedance, right? But right here we see that this really is not the case at all. If a circuit really has a lower output impedance, it can therefore drive lower impedance loads without loss of performance. So if negative feedback really did reduce output impedance, you could make any amplifier drive 2 ohms without losses just by adding more feedback!

Obviously that does not happen- if you really want to drive lower impedances you need things like more power tubes/transistors, bigger output transformers/heatsinks, etc. IOW Kirchoff's Law stands in your way. IOW adding negative feedback to an amplifier does not affect its actual output impedance at all, only its voltage response.

(Kirchoff's Law BTW is a basic law that says that the energy in an electrical circuit cannot be more or less than the amount of energy put into it. Its one of the first things you learn in electrical engineering.)

From this we can see that the term 'output impedance' as used by the Voltage Paradigm does not in fact refer to the actual output impedance of the amplifier at all! Instead, it refers to the how the amplifier *reacts* to its load impedance with its voltage response. That is something quite different.

So in our example of the inexpensive solid state amp that cannot quite double its power into 4 ohms, it is still a voltage source as its feedback causes it to *limit* its output power into lower impedances, based on what it can linearly do into higher impedances. This can be a bit confusing! On the ground what this means is that the example amplifier probably will not ever put out 60 or 65 watts unless the loudspeaker has a very flat 4 ohm impedance curve.
Ralph,
Now if the speaker is only going down to 4 ohms, the fact that the amp can't double power into that impedance does not mean that it is not a voltage source. This is due to the fact that the feedback of the amplifier will make it act like a voltage source independently of the amp's ability to double power.
ok. feedback keeps the output impedance low such that the lower impedance of the speaker is still much higher than the amp output impedance & the amp acts like a voltage source.
Now its understood that adding negative feedback to an amplifier reduces its output impedance, right? But right here we see that this really is not the case at all.
i'm having a lot of trouble accepting this. There's a closed form equation that clearly shows that negative feedback reduces output impedance. output impedance is reduced by a factor of gain*feedback factor. Now, if gain of the amp falls off, then you can keep adding negative feedback & it will not reduce the output impedance much at all. Most power amps are AC-coupled amps so their response at the low end is a high-pass. is that why amp gain is rolling off at low freq & negative feedback is not having the desired effect.
If a circuit really has a lower output impedance, it can therefore drive lower impedance loads without loss of performance. So if negative feedback really did reduce output impedance, you could make any amplifier drive 2 ohms without losses just by adding more feedback!
I don't think so. ability to drive a lower speaker impedance will depend on the output stage (more output current needs to be shared by more output devices), how much current the power transformer can supply, heatsinking ability (all these points you've mentioned in your next sentence). You can keep adding negative feedback but If the amp is incapable of supplying the current, additional negative feedback does nothing.
From this we can see that the term 'output impedance' as used by the Voltage Paradigm does not in fact refer to the actual output impedance of the amplifier at all! Instead, it refers to the how the amplifier *reacts* to its load impedance with its voltage response. That is something quite different.
I have no idea what you've written here!
So in our example of the inexpensive solid state amp that cannot quite double its power into 4 ohms, it is still a voltage source as its feedback causes it to *limit* its output power into lower impedances, based on what it can linearly do into higher impedances.
i'm not sure that this making any sense. your statement seems to imply that this example power amp has intelligence in that it can figure out how much power it can output linearly into a higher impedance & store that in its memory & then restrict its output to that same power level when it encounters lower impedances. Nah, I don't think that happens. I believe that your example power amp will simply run out of ability to drive a lower impedance when it draws all the current it can based on its power output stage & its power transformer.
Will somebody out there please explain why I became a tax attorney when this EE stuff is just sooooo cool??? :) Ralph, if I went back to school to become a EE, would you hire me?
Tech guys -- let me put a face on the dynamic headroom discussion. My amp is a tube amp rated at 150 wpc, as measured off the 8 ohms taps into an 8 ohm load. The power supply is rated at 1040 joules. ARC couldn't fit another power supply cap into the chassis -- no more real estate. If relevant, the sensitivity rating of my speakers is 92 db. And yes, if I push the volume, I bleed out of ears. That is if my wife doesn't make me bleed from the top of my head with a rolling pin first. :)

So in plain English -- what does that mean? Is the 1040 joule stat even relevant?
Hi Bruce,

Kudos on your interest in the technical aspects of this stuff. Most people's eyes just glaze over :-)

Regarding the 1040 joule energy storage capacity of your amp's power supply (that number perhaps being particularly appropriate considering your occupation :-)): What would happen without adequate energy storage is that during musical passages requiring lots of energy, especially high volume bass transients, the amount of ripple on the DC output voltages of the power supply would increase significantly, and since it is that DC which powers the audio circuits, the result would probably be some degree of contamination of the audio signal.

Now, is 1040 joules overkill for a 150 watt amplifier, that presumably has well designed audio signal pathways? I don't know. Particularly in audio, it seems that the line demarcating good conservative design (i.e., design that provides comfortable margins relative to the expected needs) and overkill can be very blurry.

Perhaps Ralph or Bombaywalla will have some additional thoughts on your question, but that's the best I can do on it.

Best regards,
-- Al
Al has it right of course. If I can add something, those high Joule numbers mean that it will be harder for the output stage to modulate that power supply. This reduces IM distortion at higher output powers. Nice huh?

Bombaywalla, I think you have missed some things in my post and it may be because I did not write clearly enough. But before I restate anything, I want you to examine what you wrote below:

i'm having a lot of trouble accepting this. There's a closed form equation that clearly shows that negative feedback reduces output impedance.

VS.:

I don't think so. ability to drive a lower speaker impedance will depend on the output stage (more output current needs to be shared by more output devices), how much current the power transformer can supply, heatsinking ability (all these points you've mentioned in your next sentence). You can keep adding negative feedback but If the amp is incapable of supplying the current, additional negative feedback does nothing

These comments are actually contradictory- here's why (and please do not feel like I am in any way attacking you on this, I have seen very intelligent people struggle with this in the past until they looked at the math): On one hand, you have your formula, OTOH you acknowledge that you need more current ability to drive lower impedances as I had stated (which you also acknowledge). This is something to reconcile.

(I think the difficulty here is that the understanding of how this works is based entirely in the Voltage Paradigm. I have always been careful to use the word 'paradigm' for a reason. A paradigm is a platform of thought; quite often anything outside of that platform is regarded automatically as blasphemy. The take-away here is that life does not care about what we think- reality goes on doing its thing regardless.)

So here is the nub of it: we both agree that you need more current to drive a lower impedance. Now this is fairly simple, so if I were to ask you which of two circuits is lower impedance, the one that has more current, or the one without, what would you say? I am hoping the former rather than the latter!

Now with that established, we can see that it is a profound violation of Kirchoff's Law that by simply adding negative feedback, we can make a lessor amplifier somehow have more current! That isn't going to happen- all we can do is change its *voltage response* (which gives rise to the 'intelligence' of the amplifier).

To put an even finer point to it, let's start with an amplifier that has a high output impedance, such that to drive a 4 ohm load it makes less power than into 8 ohms. We can assume that this amplifier has a fairly high output impedance, right? So if we add feedback with the assumption that it reduces output impedance, it would then follow that we would see the 4 ohm output power increase. But it doesn't- the 4 ohm output power will be seen to stay *exactly the same*. So we can only conclude that the addition of feedback did not affect the output impedance.

The same logic also says that the formula to which you refer (which I assume is correct) is changing something else, which the Voltage Paradigm has identified (incorrectly, based on the above proof) as 'output impedance'. IOW, 'output impedance' is a charged term under the Voltage Paradigm vernacular, and does not actually refer to actual output impedance! Crazy huh? Now go back to my prior post, and reread that part where you said I was not seeming to make any sense. Negative feedback is all about voltage response, not output impedance. The term 'output impedance' really refers to a combination of the actual output impedance of the circuit, in tandem with the servo gain which results from the feedback.

Funny how we can easily use the word 'impedance' and everyone anywhere in the world of electronics understands its meaning, but when you precede it with the word 'output' *and* you are in the field of audio, suddenly the actual impedance of the circuit in question isn't so relevant :)

If this is still a problem for you, just say so and we can go through some math. Its not complex by any means.

This is one of the reasons that I feel the Voltage Paradigm has holes in its theory, and thus becomes a leading edge of how we can effect improvement in the art.
Ralph, thanks for the thorough explanations. I too was having some difficulty understanding some of this, but after reading your two posts on the subject a couple of times I think I follow what you are saying.

What I'm still not quite seeing, though, is the SIGNIFICANCE, at the system level, of the distinction you are drawing between acting like a voltage source as a result of feedback and truly having low output impedance. Putting aside the effects that feedback may have on amplifier characteristics such as distortion, gain, and bandwidth, and PROVIDED that the amplifier is operated within the limits of its current, voltage, power, and thermal capabilities (whatever they may be), if we consider the amplifier to be a black box of unknown makeup, wouldn't it behave in the same manner with respect to its interaction with the speaker regardless of whether it achieved a given "output impedance" (as the term is commonly understood) with or without feedback?

And if so, isn't it reasonable to think of feedback as resulting in the amplifier having lower output impedance, as long as it is operated within the limits of its capabilities?

Best regards,
-- Al
Perhaps Ralph or Bombaywalla will have some additional thoughts on your question, but that's the best I can do on it.
Thanks, Al.
like Ralph & you, I was trying to understand what the strength of the ARC Ref150 power supply is when Bruce wrote 1040J. Tell me if I'm wrong:
150W/ch into 8 ohms - I calculate that the secondary is at 35VAC.
Energy = Voltage * Current * time
Then, 1040J/35VAC gives me a Current * time product = 29.71.
So, *supposing* the Ref150 power supply can provide 10Amps, then 29.71/10Amps = 2.971 secs. That's a long time to supply that much current.
How I read this is that with 1040J of storage energy, the Ref150 can supply 10Amps for 2.971 secs while maintaining 35VAC on the secondary.
With music program material no transient is going to last that long meaning that the Ref150 power is pretty darn robust....
Hi Al, the significance isn't. IOW, yes, to your first question. As to the second, no, simply because, well, the term is IMO mis-used.

To be clear here what I am saying is that the actual impedance of the circuit is not changed. IOW what is reasonable is that the amplifier using feedback and operating within its capabilities probably means that it is able to act as a voltage source. Now if the load is entirely resistive its probably not of much consequence. At any rate we are still talking about servo gain in the amplifier if it has feedback- and that servo gain does not actually affect its output impedance.

It is a lot easier to understand this when you look at the example of an amplifier trying to drive a lower output impedance, especially one that might be too low for the amplifier to do efficiently. Then its easy to see that feedback has no effect on output impedance.

Because of this I have really been of the opinion that a different term needs to be used, so that understanding of what is happening comes a little easier. Remember Bombaywalla asking me about intelligent amps? Because the feedback affects voltage response, it works out that it will cause the amp to make less power into higher impedances, which can work nicely if that higher impedance is a peak brought on by resonance.

The problem of course is that feedback also contributes to unnatural brightness in amplifiers, by adding trace amounts of odd-ordered harmonic distortion up to the 81st harmonic (see Crowhurst). Because our ears use these harmonics as loudness cues, we are very sensitive to them- so much so that amounts that are nearly impossible to measure with current equipment are not hard to hear.

So if we can be clear about what is happening, we will have an easier time charting our way to making the equipment do what music and our ears expect.

If we are confused about what the effects of various design considerations are on the behavior of the amp are, its guaranteed to be a muddle, and that is what the majority of the audio industry has been in for the last 40 years or so (by this I mean that the ideal in amplifiers under the Voltage Paradigm really has not changed all that much in that time- just look at how well an old Citation 12 can do against modern solid state).

I have no doubt that this is part of why tube amplifiers are still very much with us 50-60 years after being declared obsolete. Heck, tubes have been obsolete for longer than when they were the only game in town. Obviously, the use of that term is also mis-applied :)
12-06-13: Almarg
Ralph, thanks for the thorough explanations. I too was having some difficulty understanding some of this, but after reading your two posts on the subject a couple of times I think I follow what you are saying.
Thank you, Al, for this post. Good to know that I was not the only one having trouble interpreting what Ralph wrote. I know that if YOU are having trouble interpreting Ralph then I'm well within the right to be confused as well. ;-)

Ralph, thanks for your 2nd post - you have made things much clearer than what you wrote in your orig post on this matter. I think that I now follow what you are saying.

I like Al's question to you tho' as I was thinking along those lines as well. Please clarify further. Thank you.
This stuff is just soooo cool.

Tech guys, from a strictly intuitive and anecdotal perspective, I gather that the theory and formulas can take one just so far. That there's a "black box" aspect of synergy or a witch's brew of "X" factors going on in an amp that come together (or not) when driving a particular speaker.

To this point, I seem to recall that a while back Al may have posted something in another OP to the effect that the theory may help one identify a amp/speaker combo that MAY (??) work well and conversely MAY (??) not work well. But, and this is a big BUTT (sic), one will not know for sure until he/she tries out the particular amp/speaker combo of interest.

I recently posted an observation in the post running relating to amps and ESL speakers that speaks to the point made above. Based strictly on amp/speaker impedance matching theory, I surmise that my speakers should sound their best when driven off my amp's 4 ohms taps because voltage regulation is tighter, damping factor higher and output impedance lower.

But for some reason(s) that I can't explain, I keep coming back to the amp's 8 ohm taps. Maybe it's because the speaker's midrange band may be a little hotter (+ .8 db) and it works better in my furnished basement. Maybe it's because the 8 ohm taps punch out 2.5 db more gain that the 4 ohm taps. Maybe it's because there's a genie who lives in the output trannies. :) I just don't know. It just is -- to me.

So Ralph, what about hiring me if I go back to school to try my hand at becoming a EE??? ;-)

Best.

Bruce
Bombaywalla, your analysis of the 1040 joule number looks reasonable to me. Obviously the 10 amp number is just a rough guess, but even if it is off significantly the bottom line conclusion would undoubtedly still stand.

On the output impedance issue, I suspect that you didn't see Ralph's last post before submitting your last post, the two posts having appeared at around the same time. Given that clarification I think we are all on the same page technically, and what Ralph is essentially saying is that equating voltage source characteristics resulting from feedback with reduced output impedance, besides not being technically precise, reinforces lack of recognition of the tradeoffs that are involved. Given that interpretation, I see no issues.

Best regards,
-- Al
Thanks Al, Bombaywalla and Ralph. Obviously not being a EE tech, the only thing the joule power supply stat empirically and intuitively meant to me was that it helped the amp "muscle" its way through some tough speaker loads. But I didn't understand the current aspect.

My speakers present a 4 ohm impedance load and some highly capacitive phase angles in the bass region. Based on Bombaywalla's explanation, I gather that my amp not only performs "somewhat SS-like" because it has a somewhat "low'ish" output impedance, but the 10 amp and 2.92 second estimated stats (or perhaps less??) enables the amp to actually do what a real SS can do -- deliver some serious current into a speaker that presents a low impedance load and capacitive phase angles at low frequencies. Well ... at least to some degree. Cool!

Btw, ARC's new Ref 250 and Ref 750 mono amps have advertised power supplies of 900 and 1300 joules, respectively. And that's per channel.

Now I understand why it has been reported that a number of folks who own those amps are quoted as having cried out, "it's alive ... it's alive....," when cranking some serious volume. LOL :) Just kidding!

Best,

Bruce
Al, Ralph and Bombaywalla -- I'm still confused. Are you saying that a tube amp that uses negative feedback is able to adjust the amp's voltage output to compensate for impedance swings in such a way that power (i.e., watts, or volts x amps) approximates the amount of power (watts) a true constant voltage source SS amp would make at a given reference impedance and frequency, assuming that the SS amp was operating within its specs.

If that is correct, then how should I interpret John Atkinson's bench specs of the Ref 150 when he says that output (???) regulation is +/- .4 db off the 4 ohm taps (output impedance being .55 ohms) and +/- .8 db off the 8 ohm taps (output impedance being about 1.1 ohms)??? Is he speaking about output voltage or output watts?? Based on Ralph's explanation, if JA is referring to watts, then presumably voltage must be swinging all over the place to match the power output of a voltage source amp.

Presumably, current output may also change as a function of voltage change, but power (watts) is power (watts), i.e., V x A. I'll re-read the article again. Here's s the URL link to JA's Ref 150 report (Graph 1 in particular):

http://www.stereophile.com/content/audio-research-reference-150-power-amplifier-measurements

I also assume that an amp's output impedance number may have much to do with the number of turns on the output trannies' secondary windings. But here again, I assume negative feedback is also at play, further reducing measured output impedance. If I am tracking here, I surmise the "constant voltage source" paradigm breaks down with tube amps because in the end, as Ralph has said many times, a speaker's SPL is a function of the power (in watts) being pushed into the speaker circuits at a given frequency. So, the NF servo circuit is telling the amp to do "ramming speed" (ala Ben Hur) with **voltage** in those cases where speaker impedance is low, and the opposite when speaker impedance is higher.

I hate to even broach the subject of damping factor in light of this discussion.

Thanks for the clarifications.

BIF

P.S. If I am finally starting to get it, does that mean that not all SS amps are true constant voltage sources if power doesn't double down if impedance halves, and the opposite being the case if impedance doubles?? If so, then even saying a speaker was voiced to be driven by a SS amp is a bit of a misnomer. If the SS amp used as the reference source by the speaker designer wasn't a true constant voltage source, then one will never be certain of which SS amp to match up with the speaker of choice.

Guess one has to just go with what sounds good. Huh, ... we're back to where we started. If it sounds good (to you, or me), then it is good. LOL :)
Hi Bruce,

Starting with your last question first:
If I am finally starting to get it, does that mean that not all SS amps are true constant voltage sources if power doesn't double down if impedance halves, and the opposite being the case if impedance doubles??
An important distinction needs to be kept in mind between the amp's MAXIMUM power ratings doubling down, and the behavior it will have when operated within those maximum limits. All or nearly all solid state amps having feedback WILL double the amount of power delivered into a halved impedance as long as they are operated within those maximum power limits. (In saying that, I'm oversimplifying a bit by putting aside the effects of phase angle variations). Although, of course, in doing so their distortion performance may suffer.
Are you saying that a tube amp that uses negative feedback is able to adjust the amp's voltage output to compensate for impedance swings in such a way that power (i.e., watts, or volts x amps) approximates the amount of power (watts) a true constant voltage source SS amp would make at a given reference impedance and frequency, assuming that the SS amp was operating within its specs.
Feedback would cause the tube amp's output voltage to vary LESS as a function of load impedance variation than would otherwise be the case. In that respect, its behavior would come closer to the behavior of a solid state amp than would otherwise be the case.
If that is correct, then how should I interpret John Atkinson's bench specs of the Ref 150 when he says that output (???) regulation is +/- .4 db off the 4 ohm taps (output impedance being .55 ohms) and +/- .8 db off the 8 ohm taps (output impedance being about 1.1 ohms)??? Is he speaking about output voltage or output watts?? Based on Ralph's explanation, if JA is referring to watts, then presumably voltage must be swinging all over the place to match the power output of a voltage source amp.
As I see it the only conflict between Ralph's point and JA's statements would concern JA's use of the term "output impedance." Ralph's point is that that term is misleading with respect to what is really going on inside the amplifier, but, as Ralph indicated in his last response, when considering the amplifier/speaker interactions that result from varying speaker impedance there is no conflict.

The basic point is that the feedback that is designed into your amp REDUCES the amount by which the output voltage of your amp varies as a function of load impedance variation, thereby changing its behavior in the direction of being more solid state-like. An ideal voltage source would have regulation of +/- 0 db. An amp that is similar to yours but uses no feedback would have a regulation number that is significantly greater than +/- 0.8 db.
I also assume that an amp's output impedance number may have much to do with the number of turns on the output trannies' secondary windings. But here again, I assume negative feedback is also at play, further reducing measured output impedance.
True, if we define "output impedance" in the sense JA (and others) use that term.
I surmise the "constant voltage source" paradigm breaks down with tube amps because in the end, as Ralph has said many times, a speaker's SPL is a function of the power (in watts) being pushed into the speaker circuits at a given frequency. So, the NF servo circuit is telling the amp to do "ramming speed" (ala Ben Hur) with **voltage** in those cases where speaker impedance is low, and the opposite when speaker impedance is higher.
It doesn't break down, it's just that even with feedback your amp doesn't hold output voltage AS CONSTANT as nearly all solid state amps would (if operated within their limits), under the same conditions of load impedance variation. Therefore while your particular tube amp, operated within its limits, would increase power delivery as load impedance decreases, it would not do so to the same extent that a solid state amp would. It's a matter of degree.

Best,
-- Al
Thanks Al. So what is JA measuring in the first graph?? Is it volts or watts?
Hi Bruce,

I would think that he is measuring voltage, since it would be more practical to do that, and since the majority of speakers conform to the voltage paradigm.

BTW, this article may be of interest. It describes the standard simulated loudspeaker load he uses for those measurements.

Best,
-- Al