Red-faced Dr. Rich.

In my review of the NHT active speaker, the power rating of the power amplifiers was given in units of RMS (i.e., root mean square). I cannot tell you how many times I have taught my students in EE101 that power is not measured as an RMS quantity. Just to make sure they do not forget, I repeat a small derivation in almost every course I teach.

The output power of an amplifier is an average measurement. When a resistive load is driven by a sinusoidal voltage waveform or a sinusoidal current waveform, the average power dissipated by the load is calculated from an RMS voltage measurement. Typically, a voltmeter will express an AC voltage as an RMS quantity.

I will briefly explain what this RMS thing is about. If a DC voltage is applied across a resistor, the power thrown off by the resistor as heat can be measured. If the DC voltage is replaced with an AC sinusoidal voltage, and the AC sinusoid has a peak voltage equal to the DC voltage, then the resistor only throws off half as much heat because the instantaneous power across the load is not constant when a sign wave is applied. When the sine wave crosses zero, no power is supplied to the load; only when the sine wave is at its peak is the instantaneous power applied to the load equal to the DC power. For all other positions of the sine wave, the instantaneous power dissipated by the resistor is greater when driven by a DC source.

Circuit designers typically want a uniform average radiated power of a load whether it is driven by an AC source or subjected to a DC voltage. To do so, requires fiddling with the scale factor of the sinusoidal voltage. An RMS voltage is approximately 70% of the peak voltage. Thus, when the AC line voltage is measured with a meter, the meter registers 115 V RMS. On the oscilloscope, the peak voltage is 170 V Peak. Yes, the maximum voltage at your wall outlet is 170 V Peak but we are nonetheless familiar with the 115V number because that is the standard for calculating average power and most of the things we connect to outlets are rated in power.

In sum, RMS scaling factors for sinusoidal AC currents and voltages ensure that average power calculations using RMS values will yield the same constant power as if a DC voltage of the same value were applied to the load. It is all about calculating average power. RMS power has no meaning.