Audio Engineering

Audio Principles 25

1.11 Root Mean Square Measurements ...........................................................................

Figure 1.20(a) shows that, according to Ohm’s law, the power dissipated in a resistance
is proportional to the square of the applied voltage. This causes no diffi culty with direct
current (DC), but with alternating signals such as audio it is harder to calculate the power.
Consequently, a unit of voltage for alternating signals was devised. Figure 1.20(b) shows
that the average power delivered during a cycle must be proportional to the mean of
the square of the applied voltage. Since power is proportional to the square of applied



 





Figure 1.20 : (a) Ohm’s law: the power developed in a resistor is proportional to the

square of the voltage. Consequently, 1 mW in 600 Ω requires 0.775 V. With a sinusoidal

alternating input (b), the power is a sine-squared function, which can be averaged over one

cycle. A DC voltage that delivers the same power has a value that is the square root of the

mean of the square of the sinusoidal input to be measured and the reference. The Bel is

too large so the decibel (dB) is used in practice. (b) As the dB is defi ned as a power ratio,

voltage ratios have to be squared. This is conveniently done by doubling the logs so that the

ratio is now multiplied by 20.