This contribution is the result of discussion on the email group. It started when I said (in my sometimes pedantic manner) that there is no such thing as a "Watt RMS". Although this term is incorrect, it is in regular use in the Hi-Fi industry. I confirmed my memory of this by checking recognised engineering textbooks, but did not find any reference to Watts RMS. If you must enlarge on plain ordinary Watts, the correct term is "Watts Average" for A.C. power. It can be legitimately called "Effective", "Sinewave", or "Continuous". It is certainly most easily derived from RMS voltage and/or current. and it is exactly half of the peak power. (Ref: Electric Circuits - Morris/Senior P450, Radiotron Designers Handbook P134, et al).

For a diluted history of power, consider the humble 240V/60W light globe. In a D.C circuit of 240V, it will draw 0.25A, so the product of V and I will give 60W. When installed into domestic 240V A.C. it will still draw 0.25A, (both stated in RMS), power is still 60W, and if a description is essential, it is "average". Why average you may ask? The A.C voltage waveform is swinging between +/- 340V (240V x 1.414). If instantaneous powers are calculated, a peak of 120W occurs at 90 and 270 degrees of the cycle, and zero at 0, 180 and 360 degrees. When a very large number of number of instantaneous powers are calculated over a full cycle, their AVERAGE is 60W. Note that RMS values of voltage or current were not used in this method of determining average power. My recollection of student days, was that the concept of RMS was introduced AFTER the explanation of Average power. The constant, 1.414 is the square root of 2 (Peak/RMS), and 0.707 is it's inverse (RMS/Peak). RMS is a value assigned to an alternating voltage or current, and it means "Root of the Mean of the Square". It has the same average heating effect into a given load, as D.C of the same value. RMS is assumed unless otherwise stated. (e.g. 240V house supply, or the fridge draws 8A. As Watts RMS don't seem to appear in any serious text-book, where then did they come from? The background goes something like this, as I remember. Amplifiers of the 1950s and 1960s (Yes, I was around then), may be rated thus:- Power Output 10 Watts (20 Watts U.S) at 0.1% distortion (Americans prefer Peak ratings). No mention of Watts RMS yet. These amplifiers were fitted with well-regulated power supplies (2 capacitors and a choke). Along comes solid-state, and it was found that a single large capacitor was OK as the PS filter for a stereo pair. It was not as well regulated, but a lot simpler, smaller and cheaper. The voltage rail sagged considerably when driven continuously at high power. Enter the marketing people, who think "We can make use of this". As an example, take a SS equivalent to the above. If we only draw power from the amplifier for a very short period of time, we will get a lot more, as the PS will "hold up".

In an extreme case it may even give 20 Watts (40 Watts peak). Since there is a stereo pair on the one chassis, we can add them together and call it a 80W "Peak Music Power" amplifier, and make more money. This happened in the 1970s, and was the subject of a few critical articles and letters in the better electronic magazines of the time. Some reviewers, and test labs wanted better than this, and tested amps for continuous rating. "No-name" Watts, or average Watts, sounded a bit "ordinary", after "Peak Music Power Watts", especially to the non-technical majority. "Watts RMS" was born, and there is nothing more scientific about it than this. (Some of this article is a little generalised for the benefit of nontechnical members). I am sure the techo 10% won' t mind.

RMS Examples

The process of calculating the RMS value of something can be applied to anything - voltage values, the height measurements of trees, any sequence of numbers (e.g. Tattslotto numbers), including a sequence of power values. The issue is whether the result of performing the RMS-process actually means anything. In the case of power, it does not mean anything particular, since squaring power values before averaging them isn’t useful. In contrast though, it is well known that power is proportional to voltage-squared (P = V2/R), so to determine power by measuring voltage, it is necessary to first square all the individual voltage values in a sine-wave.

As Doug states in his article, RMS stands for the square-Root, of the Mean-value, of the Squared values. Here's a sample RMS calculation that might assist in a further understanding:

Four voltage values: 1, 2, -1, -2
Squared values: 1, 4, 1, 4
Mean of Squared values: (1+4+1+4)/4 = 2.5
square-Root of the Mean Squared Values: 1.581 Volts RMS

Note that in the case of voltages where the values are negative, the RMS process has the effect of making the contribution from the negative numbers turn positive, due to the fact that squaring a negative number makes it positive. If this is not done, then the averaging process would cancel out the positive values and negative values, giving a mean value of zero for symmetric wave forms.

If one actually cares to calculate the RMS value of a sequence of power values, then the result is different from what is obtained by multiplying the RMS volts by the RMS current. For example, if we have a sine wave source, with 2 Volts peak output (1.414 Volts RMS), and a current of 1 Amp peak (0.7071 Amp RMS), then the power is 1 Watt average. To calculate the RMS-power requires sampling the power-waveform at regular intervals, and then doing the same process as above on the resulting sequence of numbers. It turns out that the RMS value of the power is then 1.22 Watts RMS (I have a spreadsheet to show this for anyone interested).

Doug T