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Why there is no such thing as 'RMS watts' or 'watts RMS' and never has been

Most of what follows is an edited version of an email sent to me in April 2003 by the editor of Australian HI-FI. It was so well expressed I want to see it published, somewhere. So here it is.

Unfortunately the precise authorship has been lost due to rigorous cleaning of computer archives and trashed hard disks. I am told that much of it was probably from 'an electronics professor at Uni of NSW', originally written as a letter to The Guide, an insert into The Age newspaper. Should the lost electronics professor seek to claim authorship (or even banish his words from this site), I would plead with him or her to email me at scdawson (at) hifi-writer.com.

The section concerning history, however, was written by Greg Borrowman, the aforementioned editor, who is instituting a policy of 'banishing RMS watts (and variations) from Australian HI-FI'. I have rounded this out with some ruminations of my own.

The Complaint

I am writing to you to complain about frequently repeated false information provided to your readers about which I (and others) have been annoyed numerous times in the past. This solecism is the use of the technical term RMS in relation to (amplifier) power.

I have provided a technical explanation (attached) showing in considerable detail about why this use of RMS is wrong, but believe me, it is wrong, and invariably grates on anyone who knows anything at all about electronics.

A technically correct term for the measured power output of (and amplifier) would be 'long term almost undistorted sine wave average power into a resistive load', but this is commonly, and acceptably, shortened to just 'average power', or 'average sine wave power', since the other conditions in my longer description would be understood by technical people in this context.

I am always surprised that anyone claiming technical knowledge in this area would use the term RMS in relation to power output. Although it is a term used by advertisers and (some) specification writers, it has no place in any respectable publication, especially one pretending to impart technical expertise. I would strongly suggest that 'RMS power' be banned forever from any journal that wants any sort of technical respectability when it discusses technical matters.

Instead, I would advocate that the terms used should be just 'power', 'average power' or 'average sine wave power', all with the unit watt (abbreviated W). There could also perhaps be the occasional comment that it is sometimes erroneously referred to as 'RMS power'. Technical readers will understand, and others will at least not be mislead.

The Technical Details

Let us assume a sine wave input signal. The way the amplifier power is measured is to use a nominated load, and then to wind up the volume control until the output is just below the point at which it begins to distort significantly (according to some agreed and stated distortion measure, though this is not critical in practice). The average output power over many sine wave cycles is then measured. This is defined as the time integral of the instantaneous power over the measured time, divided by that time (which is always taken to be very large).

In simpler words, it is a straight average or mean of the output power, measured over a long time, and has a real technical significance (e.g. it measures the heating power of the amplifier).

By contrast, RMS (root mean square) power, would have to be defined as the square root of the time average of the square of the instantaneous power, since this is what 'RMS' means. This could be done, but it is not the power as measured, and furthermore, it would have no technical significance (e.g. it doesn't measure heating power).

The confusion in terminology comes because the nominated amplifier load for the measurement is nearly always purely resistive. For this case (only),the measured average power is proportional to the MS [mean square--ed] current or voltage (not RMS) or is (exactly) equal to RMS current times RMS voltage. But it is not the RMS power! There are several other power measures that are important with amplifiers (e.g. transient power measurements) but they shouldn't be used unless both writer and reader are clear about them.

The History Of How It All Went Awry

Almost every manufacturer, distributor, advertiser in the world involved in selling domestic audio equipment - and more than a few hi-fi magazines! - uses the term 'watts RMS' (incorrectly, as explained above). How did this go wrong?

What happened is that they started to use it as a short hand method of saying that the amplifier's output conformed with a now-defunct US amplifier standard known as IHF A202, which was introduced in 1978.

The idea was that the words 'watts RMS' would serve to show the continuous average power output of an amplifier had been measured correctly according to IHF A202. That is, using the correct test signal (a sine wave), the correct period of time for measurement (more than five minutes), a properly calibrated, true RMS-reading voltmeter with an accuracy of better than 1% of reading, without exceeding a specific level of distortion (0.1%) into a defined load (usually 8-ohms) with the amplifier first having been pre-conditioned by means of driving all channels simultaneously with a 1kHz sinusoidal signal to a nominal power output into the rated load equal to 33% of the rated power output for at least hour (or more if protective circuitry interfered with continuous operation).

This was misguided thinking even at the time, and it's now time to fix it!

Ruminations by Stephen Dawson

I agree entirely with the argument that RMS watts is meaningless. In fact, we use that term as an extreme shorthand for power in watts calculated from measuring the RMS voltage (RMS is validly used in this context).

Having said that, I strongly support continuing to measure and report upon 'average sine wave output power', where 'average' replaces RMS as the shorthand, measured in the traditional 'resistive load' way, despite its shortcomings in the real world.

My reason? It is a proxy measure of quality. It does not always track precisely with overall quality of course (what measure does?) But it still gives important information. For example, compare a Marantz 100 watt home theatre receiver with a Harman Kardon one. The Marantz will deliver something like 5 x 80 watts average sine wave ouput power, whereas the H/K will deliver somewhat more than 5 x 100 watts, because H/K's policy for specifications is to report with all five channels driven, whereas Marantz reports for two channels driven. In real world performance terms, this matters not at all on the face of it. But it does indicate that the H/K has a beefier power supply.

In a sense, using power measurements is a bit like reporting on how much an amplifier weighs. Weight has no direct influence on quality, but a high weight does tend to suggest more attention has been paid to quality issues. And, likewise, with power output.

© 2003 by Stephen Dawson