Simple circuit computes RMS value of AC power line
Keywords:rootmeansquare AC signal rmstodc
Mathematically the RMS value of a voltage is defined as:
This formula represents the standard deviation of a zeroaverage statistical signal.
Simple relationships include the following:
In general, measuring the RMS value requires an RMStodc 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 RMStoDC converters is only a few volts. To be useful for RMStoDC 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 RMStoDC 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 programmablegain difference amplifier, configured for a gain of 1/25, scales the power line signal before applying it to the AD8436 rmstodc converter, which can only accept voltages within 0.7 V of either supply. The difference amplifier has a ±120V commonmode input and differentialmode range, making it well suited for dividing down the highvoltage power line. The precise DC equivalent of the RMS value of the AC waveform is provided at RMS OUT. Figure 2 shows the 330V AC pp, 60Hz home power line, the scaled output from the difference amplifier, and the DC output of the RMStoDC converter.
Figure 1: Simple circuit measures the RMS value of a power line. 
Figure 2: Input, intermediate, and output waveforms. 
The complete design draws only 2 mA, making it ideal for lowpower applications. The external input resistor, 150 kΩ as shown, can be scaled up for use with signals larger than 400 V pp. 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 shortcircuit protected system can operate on dual supplies up to ±18 V.
This circuit computes the true rootmeansquare 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 ACcoupled 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.
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