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^^ 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.

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.

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.

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.

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.

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 :)

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.

There really isn't a 'witch's brew' unless the designer of the amp really doesn't know what he's doing :)

To the latter question, because of the confusion that exists in the industry, you still have to try things out.

Al, it sounds to me like you got what I was trying to convey. I am wondering if there can be a better term than 'output impedance'...