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How is RMS Value Measured?

Published in Electrical Measurement 3 mins read

RMS value (Root Mean Square) is measured by filtering the voltage, squaring both the unfiltered and filtered values, subtracting the square of the filtered value from the square of the unfiltered value, and then taking the square root of the result. This yields the true-rms value of the energy that was not filtered, within the meter's bandwidth.

Here's a breakdown of the process:

Steps to Measure RMS Value

  1. Filter the Voltage: Use a low-pass filter to obtain the DC component of the signal. This filter removes the AC components, leaving only the average DC level.

  2. Measure and Record Filtered Voltage: Record the voltage after it has passed through the low-pass filter. This is your DC (average) voltage value. Let's call this VDC.

  3. Measure and Record Unfiltered Voltage: Measure the original, unfiltered voltage signal. This includes both the DC and AC components. Some meters will square this measured voltage internally.

  4. Square Both Values: Square both the filtered voltage (VDC2) and the unfiltered voltage (VTotal2).

  5. Subtract Squared Values: Subtract the square of the filtered voltage from the square of the unfiltered voltage (VTotal2 - VDC2). This step isolates the contribution of the AC components to the RMS value.

  6. Take the Square Root: Finally, take the square root of the result obtained in step 5: √(VTotal2 - VDC2). This gives you the RMS value of the AC component.

Simplified Equation

The entire process can be summarized with the following equation:

RMS = √(VTotal2 - VDC2)

Where:

  • RMS is the Root Mean Square value of the AC component
  • VTotal is the measured unfiltered voltage
  • VDC is the measured voltage after low-pass filtering

Instruments Used

  • True RMS Multimeter: A digital multimeter specifically designed to accurately measure RMS values, especially for non-sinusoidal waveforms. These multimeters generally perform the calculations described above internally.
  • Oscilloscope: An oscilloscope can be used to visualize the waveform, allowing for manual calculation of the RMS value through point-by-point analysis.

Why is RMS Value Important?

The RMS value provides a way to represent the "effective" DC voltage that would deliver the same amount of power as the AC voltage. It is crucial for applications involving power calculations, heating effects, and ensuring proper equipment operation.

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