## Amplifier power

Let’s first review how to calculate power. We shall consider resistive loads.

E = voltage in volts (V)
I = current in amperes (A)
R = resistance in ohms (Ω)  The peak value of an alternating voltage or current whose waveform is a sine wave is 1.414 the r.m.s. value. Conversely, the r.m.s. value of the peak is 0.707 of the peak.

With aid of graphs I show the power developed in 8 ohms when an amplifier, driven with a sine wave, applies 20Vr.m.s. across it.

If you are confused (most people are) about when to use upper or lower case letters, read this The graphs shows, in black, the applied voltage with its value indicated on the left hand vertical axis, and the resultant power, in red, with its value indicated on the right hand vertical axis.

The applied voltage is 20, the square of which is 400. 400 divided by 8 (the resistance) is 50. The power in the resistance, with 20Vr.m.s. across it, is therefore 50W.
50W is indicated on the graph and is the continuous average power.

You will have noticed (won't you?) that during each cycle of the voltage the power will reach a peak twice.  One power peak coinciding with the positive peak of the voltage waveform, the other power peak coinciding with the negative peak of the voltage waveform.

It is worth repeating that I am talking now about the power which the amplifier can supply continuously when driven with a sine wave.  No clippping.  No lies.

The peak voltage is 28.28, the square of which is 800. It follows that the peak power is 100W. That is the continuously rated peak power, and is twice the average power.
The ‘peak power’ often quoted by manufacturers is usually a different matter entirely, see below.

You can see quite plainly that the power graph is symmetrical about the 50W line, and that 50W is the average.

You can also see quite plainly how the voltage peak corresponds to the power peak and how the r.m.s. value of the voltage coresponds to the average value of the power.

And, you can now see that trying to apply "peak = 1.4r.m.s." or "r.m.s. = 0.7peak" to power doesn't work and is patently nonsense.

Some manufacturers will quote a peak power figure which is higher than twice the average (although no mention will be made of that). What they don’t tell you is that it is the peak instantaneous non-repetitive power, sometimes called "peak music power output", and usually given unwarranted upper-case status of P.M.P.O.

And what is the “peak instantaneous non-repetitive power”?

We need to briefly consider an amplifier’s power supply. The following is a simple explanation and it isn’t necessary to remember that most amplifiers will have both a positive and a negative supply rail.
The supply, at least for the output stage, will be unregulated. This means that there will be a rectifier, I shall assume full-wave, to produce raw d.c. from the mains transformer’s secondary, and a smoothing, or reservoir, capacitor.
When the supply is lightly loaded, i.e. the amplifier is idling (not producing an output), the capacitor will charge to the peak value of the transformer’s output voltage.
When the amplifier is called upon to produce power, the charge in the capacitor is reduced as current is drawn from it. The voltage across it will, between peaks, fall slightly. The more current which is drawn form the supply, the more the voltage across the capacitor drops.

In a well designed supply, one with a very large value of capacitance, the voltage drop will be small.

A poorer design will exhibit a significant change in power supply voltage as the amplifier’s output power is increased – either due to the volume control being advanced or peaks in the music.
So, at low volumes the supply voltage is relatively high and the peak power can also be, for a very brief moment, relatively high.
But this brief pulse of high power rapidly discharges the power supply’s capacitor and its voltage is suddenly much lower than its previous value. If another similar peak of music arrives there isn’t enough voltage across the capacitor, which won’t have had time to recharge, to produce it correctly – the peak power now is much less.

Remember that power is proportional to the square of voltage.

This means that, in practice, you will encounter amplifiers which can produce, say, 80W continuous power (160W peak), but will be quoted as producing an instantaneous non-repetitive peak of many watts more.

Since there is no agreed method or procedure by which the instantaneous peak power is measured, it is impossible to compare amplifiers power capability using this figure.

The only meaningful way is to compare the continuous average power, calculated from the r.m.s. value of the applied voltage, when driven by a sine wave.

The curves below show the first 90 degrees of a voltage sinewave and the corresponding power in a resistive load.  Both amplitudes are normalised to 1 to make scaling easier.

They were drawn with Bezier curves and are a good fit to a sine function. 