# Circuit measures true-rms and average value

-September 26, 2002

The circuit in Figure 1 measures both the true-rms value and the rectified average value of an ac signal. This design uses two low-cost ICs in SOIC packages and consumes only 180 µA of quiescent current. Operating from a single 5V supply, the circuit has an input dynamic range of less than 30 mV to greater than 3V rms. Sine-wave accuracy is good (Table 1), and bandwidth is approximately 100 kHz, depending on input level. The circuit can also measure a 1V rms, crest-factor-of-five pulse train with lower than 1%-of-reading error. Most ac measurements use rectified-average-value circuits. Although these can be accurate if you calibrate their scale factor to read the rms value of one waveform, such as a sine wave, they exhibit large errors if you use them for other waveform types. In contrast, the rms value of an ac signal is the amount of dc required to produce an equivalent amount of heat in the same load. Therefore, the rms value is independent of waveform shape or duty cycle; it's often useful for measuring the power of a complex ac waveform.

Average-responding and rms measurements have traditionally used different circuits. However, in some cases it may be useful to know both the rms and the rectified average value of an ac waveform. The ratio of rms to rectified average value is one way to determine the characteristics of a waveform without actually seeing it on an oscilloscope. For example, the rms/average-value ratio is 0.707V/0.636V or 1.11 for a 1V peak undistorted sine wave, 1.0 for a symmetrical square wave, 1.155 for a triangular wave, and 1.253 for Gaussian noise. An AD737 rms-converter IC drives an AD8541AR micropower op amp (Figure 1). Resistors R7 and R8 form a voltage divider to allow operation from a single supply voltage or battery. Capacitors C4 and C5 bypass any signal currents on VCC or VCC/2 to ground. The rms-converter IC has two inputs: a high-impedance (1012Ω) input (at Pin 2) and an 8-kΩ, wide-dynamic-range input via Pin 1. The rms converter's full-scale input range is normally 200 mV. You can greatly increase this range by adding an external resistance—in this case, resistor R1 and trimming potentiometer R2—between the signal input and Pin 1. This addition has the added advantage of increasing the circuit's input impedance.

The AD737JR measures the true-rms value when switch S1 connects its averaging capacitor, CAV, to Pin 5. The averaging capacitor performs the "mean" portion of the rms function. Removing CAV by opening S1 converts the circuit to rectified-average-value operation. Resistor R6 allows a small leakage current to flow past the switch, keeping the capacitor charged and preventing any large surge currents from flowing into or out of CAV when the switch is closed. The AD737JR drives the AD8541AR op amp with a negative-flowing output current. The op amp operates as a current-to-voltage converter and also inverts the signal, providing an output voltage that swings more positive with increasing input levels. Resistor R5's value of 80.6 kΩ matches the effective input resistance of the AD737 (R1+R2+8 kΩ), so that input/output scaling is 1-to-1. Resistor R3 and trimming potentiometer R4 cause a current to flow from the supply to the op amp's summing junction. This action offsets the op amp's output, such that the circuit's output is approximately 0V with no voltage applied. Note that this circuit has a maximum supply-voltage limit of 5.5V; you can extend operation to 12V by substituting an OP-196GS op amp for the AD8541AR. Circuit calibration is easy:

Adjust trimming potentiometer R4 to mid-scale and set S1 for rms.

1. Apply a 2.000V rms, 1-kHz sine-wave input signal.

2. Adjust R2 until the circuit's output voltage is 2.000V dc.

3. Reduce the input to 100 mV rms and adjust offset trimming potentiometer R4 for a reading of 100 mV dc.

4. Repeat Step 2.

Because the dc-offset circuitry is ratiometric, it remains calibrated with modest variations in supply voltage. The measured power-supply-rejection ratio of this circuit over a 4.5 to 5.5V supply range is approximately 61 dB. The measured errors versus crest factor for a 5V supply and a 1V rms, 100-µsec pulse are: crest factor=3, error=0.67%; crest factor=5, error=0.98%; and crest factor=10, error=4.7%. Some additional points to consider: The peak rms value of a sine wave is 0.707V peak, and the peak rectified-average value is 0.636V. This ratio of 0.707V-to-0.636V is equivalent to an 11% scale-factor difference between the two measurement methods. If you want this circuit to accurately read the rms value for sine waves in the rectified-average-value mode, S1 can be a two-pole switch. The second pole can connect a 523-kΩ, 1% resistor in parallel with R1 to increase the scale factor in the average-value mode. However, the true rectified-average value is more useful in most cases.

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