# The dark side of constant power amplifiers (and similar schemes)

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#### Elvee

In a recent thread (that turned sour), the subject of "constant power amplifiers" (load invariant) was raised.

The usefulness or desirability or such a scheme is debatable, but there are more fundamental questions about the consequences of including such a "feature" in an amplifier.

In the thread in question (that I don't want to revive for obvious reasons), I said that this class of non-linear circuits was suitable for industrial control or processing, but not for audio.

Here is what I mean by that.

The first pic below is such a device in its spice-idealized, canonical form. It is easily visible by simple inspection of the equation that the circuit does indeed perform the task.
Rv (R virtual) is an internal constant required for scaling and dimensional consistency. Here, everything is unitary as the circuit is simply meant for theoretical analysis.

We see that apparently, in this perfect form, the circuit performs perfectly: the THD is LTspice's floor for these settings.

Everything perfect then?

Not really. The sim shows the situation for a purely passive, resistive load. An amplifier is supposed to drive a speaker, which is far from this ideal: amongst other things, it generates back emf after it has been excited.

Let's see the behavior of the amplifier's output when it is subjected to a back emf.
The instantaneous input voltage/power is set at some level, 0.5/0.25 times the maximum for example, and the stimulus source is placed in series with the output load.

The situation has changed completely: the circuit now shows its non-linear nature: to keep the power constant, it needs to alter its output impedance, leading to severe distortion of the current into the load.
These results are general, and not linked to this particular implementation of the scheme (which is canonical anyway): this behavior is required to achieve the constant (instantaneous) power constant.

This means that such an amplifier will necessarily have an output impedance having the following attributes:
-Finite
-Variable
-Non-linear

That is a killer combination, even if the hardware does its job perfectly.

A good reason to stay clear of this kind of "improvement"

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#### JMFahey

In a recent thread (that turned sour),

Indeed, that thread was closed by moderation, why are you reviving it here?

#### Bigun

Paid Member
Indeed, that thread was closed by moderation, why are you reviving it here?

He isn't and he clearly states that. I think if you look over some of his posts in other threads you will see that Elvee contributes a lot of very good things to the forum.

#### Elvee

Indeed, that thread was closed by moderation, why are you reviving it here?
Constant power amplifiers were not the subject of that thread. The amplifier that was the subject happened to be (supposed to be) constant power, and the debate drifted off limits.
This lame duck of vintage amplifier can rest in peace, but I think it is useful to put the record straight on the subject: such load-invariant amplifiers are not a good idea, for very fundamental and theoretical reasons.

BTW, the thread was not closed by the moderation, but I think that it would have been had the discussion continued

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#### godfrey

FWIW, you can get fairly constant power over a fairly wide range of load impedance just by using a linear amplifier with a modest damping factor.

Indeed. Hopefully this one won't be derailed by people responding to the voices in their head, rather than what's actually been posted.

I always find your input interesting and thought provoking, even though (or perhaps because) it tends to make my head hurt.

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#### Elvee

FWIW, you can get fairly constant power over a fairly wide range of load impedance just by using a linear amplifier with a modest damping factor.
Indeed. But I am not sure sacrificing the damping factor is worth the result.

It would be possible to make a "proper" constant power amp by using a modified AGC rather than real time instantaneous computation, but I am not sure it is worth the trouble: you will have to dimension the voltage aspect of the amp in function of the highest resistance load it is supposed to drive, and the current aspect for the minimum one. All considered, very disadvantageous tradeoffs.

Once a stinker.

#### godfrey

It would be possible to make a "proper" constant power amp by using a modified AGC...
That wouldn't really work with a multi-tone signal (e.g. music) and a load like a speaker whose impedance varies with frequency. I agree none of this is worth pursuing except as an intellectual curiosity.

#### Fast Eddie D

This is a nice summary of "constant current/constant power" amplifiers. Thank you Elvee.

The whole audio/ "hi-fi" industry is geared towards high damping factor voltage amplifiers and reltively low Q speakers. It is a convention that provides a "one size fits all" (not really ) approach to mixing and matching components.

Hi fi wasn't always this way. Speakers of yesteryear were typically high Q, high resonance, relatively efficient units. They did not require high damping from the amplifier or a sealed box to work properly. Look at the first speaker released by Wharfedale in the 1930s - it set the bar for speakers for 25 years or so, yet it is an oddity by today's standards. Furthermore, it might be difficult to drive it properly with a modern amplifier.

I looked at some of the modern "current source" amplifiers here and quickly realised that they might be useful for specific applications. I don't think you could build a "one size fits all" current amplifier; it might be optimised for one speaker that benefits from an optimised current amplifier but be disasterous with any other speaker.

Hi-fis of yesteryear were often fully integrated units like the "console" hi-fi of the 50s. In a design like this, the designer has control over everything from source to amplifier to speaker and isn't constrained to high damping factor or whatever parameter is required to fit the "one size fits all" convention of today.

#### matze

In a recent thread (that turned sour), the subject of "constant power amplifiers" (load invariant) was raised.

The usefulness or desirability or such a scheme is debatable, but there are more fundamental questions about the consequences of including such a "feature" in an amplifier.

In the thread in question (that I don't want to revive for obvious reasons), I said that this class of non-linear circuits was suitable for industrial control or processing, but not for audio.

Here is what I mean by that.

The first pic below is such a device in its spice-idealized, canonical form. It is easily visible by simple inspection of the equation that the circuit does indeed perform the task.
Rv (R virtual) is an internal constant required for scaling and dimensional consistency. Here, everything is unitary as the circuit is simply meant for theoretical analysis.

We see that apparently, in this perfect form, the circuit performs perfectly: the THD is LTspice's floor for these settings.

Everything perfect then?

Not really. The sim shows the situation for a purely passive, resistive load. An amplifier is supposed to drive a speaker, which is far from this ideal: amongst other things, it generates back emf after it has been excited.

Let's see the behavior of the amplifier's output when it is subjected to a back emf.
The instantaneous input voltage/power is set at some level, 0.5/0.25 times the maximum for example, and the stimulus source is placed in series with the output load.

The situation has changed completely: the circuit now shows its non-linear nature: to keep the power constant, it needs to alter its output impedance, leading to severe distortion of the current into the load.
These results are general, and not linked to this particular implementation of the scheme (which is canonical anyway): this behavior is required to achieve the constant (instantaneous) power constant.

This means that such an amplifier will necessarily have an output impedance having the following attributes:
-Finite
-Variable
-Non-linear

That is a killer combination, even if the hardware does its job perfectly.

A good reason to stay clear of this kind of "improvement"

Hi Elvee,

if the circuit you are refering to is really *that* linear into a resitive load and if it has a differential input, it might be useful as front-end in a power amplifier. When using a non-inverting configuration together with not too high overall amplifier gain, the input stage may determine the overall performance due to common-mode input distortion.

Several ways to cope with that are known, e.g. the (common-mode controlled) cascode, a Cascomp or Edmond Stuart's nice idea of mudulating the front-end supply voltage (CMCL). Of course, using high supply voltages may solve the problem in most cases.

If one wants to circumvent high supply voltages, yet another candidate to tackle the common-mode problem would be interesting, even if it only performs well into a purely resistive load.
Could you please provide a reference to such a circuit? If you do not want to have it in the forum, could you please send me a private message?

Thanks and BR,
Matze

#### Elvee

That wouldn't really work with a multi-tone signal (e.g. music) and a load like a speaker whose impedance varies with frequency.
I can see at least two methods that would work in those conditions:

-Open loop: compute in real time the load impedance by calculating the I/V quotient, filter the result with an amplitude-dependent time constant (I don't remember the name of this piece of kit, it is also used in communication to lock a PLL on DSB-like signal to recreate the carrier), compute the square root and use it to control the gain

-Closed loop: compute the output power in real time by calculating the I*V product and servo it to the virtual input power (in real time too) with an AGC having preferably an adaptative time constant too.

Don't expect me to provide worked examples for the above...

The whole audio/ "hi-fi" industry is geared towards high damping factor voltage amplifiers and reltively low Q speakers. It is a convention that provides a "one size fits all" (not really ) approach to mixing and matching components.

Hi fi wasn't always this way. Speakers of yesteryear were typically high Q, high resonance, relatively efficient units. They did not require high damping from the amplifier or a sealed box to work properly. Look at the first speaker released by Wharfedale in the 1930s -

Agreed, but do you honestly think such a system could compare with a reasonably high-end present day system?
I have no doubt it would still sound good today, probably better than some cheap crap, but theory and technology have made serious advances in ~70 years

Hi Elvee,

if the circuit you are refering to is really *that* linear into a resitive load and if it has a differential input, it might be useful as front-end in a power amplifier.
See Jacco's appreciation of the circuit, it is a good summary....
Could you please provide a reference to such a circuit? If you do not want to have it in the forum, could you please send me a private message?
Make a search on my recent subjects, you'll find it easily.

#### Fast Eddie D

Agreed, but do you honestly think such a system could compare with a reasonably high-end present day system?

That is not the point that I am making at all. It could be used for specific applications, like maybe getting more bass extention out of a subwoofer that is in a smaller than optimal sealed enclosure.

I do not think it would work well with the vast majority of modern speaker designs.

I have no doubt it would still sound good today, probably better than some cheap crap, but theory and technology have made serious advances in ~70 years

Why of course. But the most relevant "advance" to this topic is the uniformity of modern hi-fi design. This is a big advantage, especially for a novice piecing together a system. You had to be an engineer to play hi-fi in the 1930s.

There are still tweakers that groove on the vintage equipment. You can make old speakers sound good with low electrical damping and quasi-current source amplifiers. It wouldn't work with most modern low Q speakers of course.

if this is true that constant power leads to no memory distortion = should sound well.
But if I remain correct Elvee has tin ears,
so who will build and listen to?

#### Elvee

if this is true that constant power leads to no memory distortion
You should explain and support this statement: reference or anything...?

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Sounds a bit flaky to me...
Anyway, a constant power amp should be very much worse in this respect, because of all the operations performed in the logarithmic domain

... and I was hot after read this
anyway constant power might be usable for input stage,
not as power output...
I do not understand this:
of all the operations performed in the logarithmic domain

#### Elvee

I do not understand this:
With semiconductor circuits, there is practically no other way to perform mathematical operations. In the example I gave, not only were the operations performed in logarithms, but there wasn't even a reverse conversion back into the arithmetic domain because only the relative magnitudes were of importance. I am not sure that's the kind of thing audiophiliacs fall in love with...

With semiconductor circuits, there is practically no other way to perform mathematical operations. In the example I gave, not only were the operations performed in logarithms, but there wasn't even a reverse conversion back into the arithmetic domain because only the relative magnitudes were of importance. I am not sure that's the kind of thing audiophiliacs fall in love with...

some nonaudiophile people in this forum reported better sound when using nomemdist topology but now I found only this http://www.diyaudio.com/forums/solid-state/31131-hafler-dh-200-220-mods-3.html#post395669

#### peufeu

really should I?
here it is: Memory Distortion Philosophies

really old stuff lol