# Simple Circuit Measures the RMS Value of an AC Power Line

The rms value of an ac signal compares the heating value of an unknown ac signal to that of a known dc signal across identical loads and is equal to the amount of dc required to produce an identical amount of heat in the load. When the power dissipated in the loads is equal, the known dc voltage equals the rms value of the unknown ac signal. For example, if we applied 1 V ac rms to a resistive heating element, it would produce exactly the same amount of heat as if we had applied 1 V dc.

Mathematically, the rms value of a voltage is defined as This formula represents the standard deviation of a zero-average statistical signal.

Simpler relationships include the following:   In general, measuring the rms value requires an rms-to-dc converter, which provides a dc output equal to the rms value of any input waveform. Unfortunately, the range of ac signals to be measured can be very large, while the input range of typical rms-to-dc converters is only a few volts. To be useful for rms-to-dc converters, the large input voltages must, thus, be scaled down. Measuring the rms value of a home power line, for example, requires addtional circuitry that attenuates the ac signal to a suitable value that accomodates the input range of the rms-to-dc converter. This application solves the problem of rms measurements for large ac signals such as those from the electric power line.

In Figure 1, the AD628 programmable-gain difference amplifier, configured for a gain of 1/25, scales the power line signal before applying it to the AD8436 rms-to-dc converter, which can only accept voltages within 0.7 V of either supply. The difference amplifier has a ±120-V common-mode input and differential-mode range, making it well suited for dividing down the high-voltage power line. The precise dc equivalent of the rms value of the ac waveform is provided at RMS OUT. Figure 2 shows the 330-V ac p-p, 60-Hz home power line, the scaled output from the difference amplifier, and the dc output of the rms-to-dc converter.