The Truth About Amplifier Power Ratings

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. Perhaps on this basis, they should be referred to as power rantings :)

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 Millennium (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. These new terms are soundly (no pun intended) based on the science of marketing, having nothing to do with actual science or physics. PMPO is mathematically expressed as:

PMPO = P_REAL * k

where P_REAL is the real power as 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 randomly selected value of between 20 and 75 should be used.

An alternative (and equally useless) way to measure PMPO is to multiply the supply voltage by the instantaneous short-circuit current from the amplifier - the amplifier does not have to survive this test, and the current only has to exist for around 1us to obtain a satisfactory rating ...

PMPO = V_supply * I_peak

where V_supply is the total supply voltage and I_peak is the instantaneous (and possibly destructive) short-circuit current. Given that a 12V plugpack (wall wart) supply may be capable of perhaps 30A for a microsecond or two, this is perfectly acceptable, and gives a PMPO of ...

PMPO = 12 * 30 = 360W

This is a perfectly acceptable figure, and may be used with gay abandon (in the hope that someone will actually believe it).

Thus (using the first equation) 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

P_real = V_RMS * I_RMS

Since 8V across an 8 ohm load provides 1 Ampere of current, we obtain

P_real = 8 * 1 = 8 Watts

or, using the power formula

P_real = V² / R (Voltage squared, divided by impedance in ohms)

thus

P_real = 8² / 8 = 64 / 8 = 8 Watts

PMPO may now readily be calculated, using a median value of 45 which results in a totally satisfactory advertising power (P_a) of

P_a = 8 * 45 = 360W PMPO

You will notice that by fiddling with the figures to suit my goal, I have been able to make the PMPO figure the same, using two completely different 'test methods' and 'formulae'. Therefore, the figures must be correct, and the result must therefore be genuine :)
.

What ? You think I'm lying ? Well spotted gentle reader - the whole process is unadulterated horse-feathers.

It goes without saying that using the complete formula, the final P_a 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 (legitimate) 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 Boom Box 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 think i may have 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 approaches above. This method is just as invalid as the more technical methods described, but is not as much fun.

Warning

There are sites on the net where the author(s) seems to think that there is some logic (however perverse) in the PMPO rating. For example it has been claimed that PMPO is calculated as the maximum instantaneous power an amplifier can deliver, albeit under unrealistic conditions. Such claims are as false and misleading as PMPO - there is absolutely zero logic or science involved in making up a PMPO figure, as demonstrated by the following simple exercise.

Let's assume that an amplifier has a supply voltage of 14.8V DC. A little under 15V (unloaded) is not uncommon for so-called 12V plug-pack supplies. For the sake of the exercise, we shall further assume that the manufacturer used a 3,300uF filter cap (this is probably unrealistically high, but will do for the time being). The energy storage of the cap is measured in Joules (Watt/seconds). One Joule is 1W delivered for 1 second. For our 3,300uF cap, charged to 14.8V, we get ...

E = ½ C * V² = ½ 3,300^E-6 * 14.8² = ½ = 0.361 Joule (0.36W/s)

This number is obviously of no use as is, but if we assume that the cap is discharged in 1ms, that gives an instantaneous figure of 360W PMPO, which is much more satisfactory. Goodness me, I seem to have used yet another (almost completely) bogus formula to arrive at the number I first thought of :)

Note: The formula for energy in Joules is correct, as is the conversion from seconds to milliseconds. The bogus part is the simple fiddling with numbers to arrive at the answer I wanted.

It pretty much goes without saying that I can think of several other equally meaningless equations that will also give the figure of 360W, but there is absolutely no point in doing so. Just remember that if you see PMPO 'power' listed for an amplifier, the figure is false, and has no meaning at all. Before purchase, try to locate something on the package or in the instruction page that specifies the power in RMS or DIN. Failing that, obtain written assurance from the sales person that the claimed power is real, test it when you get home, then return the product next day. Explain that you were assured that the amplifier was indeed 1kW, but you were unable to obtain more than 5W from it - therefore, the product must be faulty.

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 (or trousers) 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 the same value of voltage and impedance as above (namely 8V RMS, 8Ω load), one can calculate the P_A70 (Advertising Power, as used in the 1970's) to a high degree of uselessness, thus

P_A70 (Peak Music Power) = (8 * 1.414)² / 8 Ohms = 16W

Or ...

P_A70 (P-P Music Power) = 16 * 1.414)² / 8 Ohms = 64W

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 (or at least close to it) 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 ....

Many thanks to Rod Elliot for granting us permission to post this useful article on amplifier power ratings. 

For more articles from Rod, please visit his website at:  http://sound.westhost.com/