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RMS

Abreviation for Root Mean Square. In electricity (including audio) this refers to the effective amount of power in an AC signal. Since AC power, by definition, is a periodic waveform with part of its period above and below “zero” it’s not as easy to know how much actual power is available over time as it is with DC, where the voltage and current are (relatively) steady. The Root Mean Square method is the commonly agreed upon method of computing what some people refer to as the “heating value” of the signal – the effective voltage that would generate the same heat as a DC (Direct Current) signal, over the same time. In a circuit whose impedance consists of a pure resistance, the RMS value of an AC wave is often called the effective value or DC-equivalent value. For example, if an AC source of 100 volts RMS is connected across a resistor, and the resulting current causes 50 watts of heat to be dissipated by the resistor, then 50 watts of heat will also be dissipated if a 100-volt DC source is connected to the resistor.

To determine RMS value, three mathematical operations are carried out on the function representing the AC waveform:

(1) The square of the waveform function (usually a sine wave) is determined.

(2) The function resulting from step (1) is averaged over time.

(3) The square root of the function resulting from step (2) is found.

Thus the term Root Mean Square (RMS). The RMS value of a complex signal must be read with an RMS meter to be accurate. Alternatively, the signal can be digitally sampled and the samples summed to yield the RMS value. As such, the RMS value of a complex signal can be thought of as the “area under the curve” of a signal as viewed in a wave editor software application.

For a sine wave, the RMS value is 0.707 times the peak value, or 0.354 times the peak-to-peak value. Household utility voltages are expressed in RMS terms. A so-called “117-volt” AC circuit carries about 165 volts peak, or 330 volts peak-to-peak.

Many speakers and amplifiers are rated in RMS value for similar reasons. We are most concerned with the amount of work to be done, which is why we use the unit of watt, but it’s also meaningful to differentiate between the peak and the RMS, because the RMS determines how much real, usable power is there to be converted into air movement.

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