Elliott Sound Products Amplifier Power Ratings

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Page Last Updated 18 Jan 2002

This article was originally fairly superficial and frivolous, but has been expanded (a little) to explain the matter better.  Amplifier power ratings are usually honest in Hi-Fi equipment, but become very silly when it comes to the "mass market" systems.

"Exceedingly silly" happens when you look at computer speakers and "boom boxes" - most of which boast power ratings that (if true) would do a fine job of amplification for a large hall or small stadium.  This is quite obviously not the case, as anyone who has used them is aware - well below the point of mild discomfort, it is obvious that distortion is abundant, and the sound (almost literally) falls to pieces.

I have a set of computer speakers that are rated at 480W PMPO (yes - four hundred and eighty Watts).  I have measured them at less than 5W each before clipping.  There is no rhyme or reason that can explain such a difference, except ....

Power Ratings In The New Millenium (and Beyond)

Much has been said - and will no doubt continue to be said - about amplifier power ratings. There has been a disturbing tendency over the last few years to revisit the bad old days where terms such as PMP (Peak Music Power) and PMPO (Peak Music Power Output) have once again raised their ugly heads.

Admittedly, these "new" power rating are not used by hi-fi manufacturers, other than in the low-end equipment, which possibly rates "fi" at best.

These new terms are soundly (no pun intended) based on the science of marketing, and PMPO is mathematically expressed as

where Actual_Power is calculated by the formula below, and k is a constant whose value is approximately equal to one's grandmother's age, divided by the square root of the distance from the office to the advertisement writer's normal place of abode - measured in millimetres, inches, furlongs, statute miles or pounds per square inch - as appropriate, to provide the number you first thought of.

In the unlikely event that the value of k cannot be calculated from the above formulae to provide a totally meaningless (but plausible-looking) final result, a value of between 20 and 50 shall be used.

Thus we can now compute the power of an amplifier which manages to impress a voltage (which need not be sinusoidal - an harmonic distortion of up to 400% is considered perfectly acceptable - albeit mathematically impossible) of 8V across a speaker of 8 ohms. Actual (real) power may be calculated by

Since 8V across an 8 ohm load provides 1 Ampere of current, we obtain or, using the power formula thus PMPO may now readily be calculated, using the standby value of 20 which results in a totally satisfactory advertising power (Pa) of It goes without saying that using the complete formula, the final Pa rating could be anything from 500uW (totally unacceptable from a marketing perspective) to several Mega-Watts. Although figures in this latter range have considerable merit, it is probable that even the most gullible of Boom-Box or computer speaker buyers will be a little suspicious, especially when the plug-pack power supply offered (as an option) announces that it provides a mere 1A at 12V (or 12 Watts DC power output - as much as 7 (legimate) Watts of audio may be obtained from such a supply).

True, this figure will not be comprehensible per se, but suspicions may be aroused when a friend's genuine 20W system completely drowns them out with sound. A 160 Watt rated unit's apparent lack of power by comparison is easily explained by the fact that "This tape/CD/FM radio station was recorded at really low level" or some similar self-delusion.

This is a little more difficult to shrug off nonchalantly if one's Ghetto-Blaster were to be rated at 1.6MW for example. Even those who pay more for their sneakers than others might spend on a tailored suit (I had one of those once :-), or a real Hi-Fi system, will be forced to wonder why their unit was not supplied with a small nuclear power station to achieve such power.

It is worth noting that it is possible to merely think of a "good" (i.e. impressive looking) number, call it Watts (PMPO), and use that instead of the potentially tedious mathematical approach above.  This method is just as invalid as the more technical method described, but is not as much fun.

Advertising, 1970's Style

In the above mentioned bad old days, there was still a modicum of perverse logic used to calculate "Power". Advertisers (after consulting - sorry, interfacing - with someone who could count to more than 10 with their shoes still on), would use the peak value of the RMS voltage (Volts * 1.414), or the more adventurous could even use peak-to-peak (double the peak value).

Using these values, one can calculate the Pa70 (Advertising Power, as used in the 1970's) to a high degree of uselessness, thus

Technology has certainly come a long way since then, as is now apparent.

But Seriously, Folks

If, from the above, you have deduced that I am less than favourably impressed by such deceptions, you are correct. Indeed, the term "RMS" power is just as grating to an engineer, since there is no such thing.

"RMS" Power
Power is simply the product of RMS Volts and RMS Amps, and the resulting figure is "power". Not "RMS Power" - or any of the insane derivatives described above - just "power".

The term RMS (Root Mean Squared) can only be applied to voltage or current. The RMS value is determined to be the Alternating Current (AC) equivalent of a Direct Current (DC) which creates the same amount of heat in a load.

For a sine wave, this is the peak value, divided by the square root of 2 - i.e. 1.414 (I shall not bore you with the exact reason for this, but it is a scientifically and mathematically accepted fact).

For a "perfect" square wave, it is the peak value alone, since if the positive and negative peaks were to be rectified (so as to be the same polarity), the result is DC.  This condition is quite common with guitar amps (the distortion is part of the sound), but should never occur in Hi-Fi, even briefly.

Power should only ever be measured with no clipping.  When an amp clips, there is more available power, but higher distortion.  It is not uncommon to see amplifier powers rated at 10% distortion.  This is quite unacceptable, as this indicates that there is severe clipping of the signal.  A good quality amplifier will have less than 0.1% distortion just before clipping, somewhat higher for push-pull valve amps, and a lot higher for single ended triode valves.

When I refer to power in any of my articles, common usage shall prevail, and I (like many others in audio) will reluctantly accept the term RMS Power to mean power.  All amplifier power ratings in the project pages (and elsewhere) are "RMS", unless otherwise stated.

Music Power
The music power of an amp is real, and is generally higher than the continuous power.  It is measured by using a tone-burst generator, and is the peak power than an amp can supply for (typically) about 10ms.  This is quite reasonable, but not terribly useful when it is examined carefully.  Since music is very dynamic, with the peak amplitude exceeding the average by 10 to 20dB (depending on the type of music), an amplifier is never called upon to provide full power all the time (at least if clipping is avoided, which should be all the time).

If the power supply is regulated or has considerable excess power capacity, the continuous and music power ratings will be almost identical.  The difference was (at one time) measured, and was called "dynamic headroom".  Few amps have a dynamic headroom of better than 1 or 2dB, and the greater the headroom, usually the cheaper the power supply for the rated power.

An amplifier with a much greater music power than its "RMS" power usually has a transformer and/or filter capacitor that is too small.  In most cases, a 90W (RMS) / 100W (music power) amp will not sound louder than a 90W amp with a regulated supply (so RMS and music power are the same).  The extra 10W represents a little under 0.5dB, which is barely audible in a comparative listening test.

C# - And on that note ....

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Note: Although the above is slightly toungue-in-cheek (SLIGHTLY??), it is meant to be taken seriously - this rubbish really happens - just look in the local papers, and on the cartons for computer speakers if you don't believe me!

This epistle is Copyright (c) 1999/2000/2002 Rod Elliott - All Rights Reserved (Yeah, like who else would want it? :-)