# Simple circuit measures RMS value of AC power line

The root-mean-square 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:

**Click on image to enlarge.**

This formula represents the standard deviation of a zero-average statistical signal.

Simple 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 accommodates 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.

**Figure 1: Simple circuit measures the RMS value of a 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.

**Figure 2: Input, intermediate, and output waveforms.**

The complete design draws only 2 mA, making it ideal for low-power applications. The external input resistor, 150 kΩ as shown, can be scaled up for use with signals larger than 400 V p-p. The input signal can exceed the power supply with no damage to the device, allowing the input signal to be present even in the absence of the supply voltage. In addition, the short-circuit protected system can operate on dual supplies up to ±18 V.

This circuit computes the true root-mean-square value of a complex AC (or AC plus DC) input signal and gives an equivalent dc output level. The true RMS value of a waveform is a more useful quantity than the average rectified value because it is a measure of the power in the signal. The RMS value of an AC-coupled signal is also its standard deviation.

**About the authors**

**David Karpaty** is a staff engineer in the Integrated Amplifier Products (IAP) group of Analog Devices, Inc., responsible for product and test engineering support of precision signal processing components with a focus on automotive products. He holds a BSEE from Northeastern University and a bachelor’s degree in electrical engineering technology from Wentworth Institute.

**Chau Tran** joined Analog Devices in 1984, where he works in the Instrumentation Amplifier Products (IAP) group. In 1990, he graduated with an MSEE degree from Tufts University. Tran holds more than 10 patents and has authored more than 10 technical articles.

Karpaty and Tran are based at ADI in Wilmington, Mass.