Sunday, November 28, 2010

Tips for Making True RMS AC Measurements with a DMM

True RMS responding DMMs measure the "heating" potential of an applied voltage. Power dissipated in a resistor is proportional to the square of an applied voltage, independent of the waveshape of the signal. Todays general purpose DMMs can accurately measures true RMS voltage or current, as long as the wave shape contains negligible energy above the meter’s effective bandwidth (more on this in a bit). Most DMM's ACV and ACI functions measure the AC–coupled true rms value (DC is rejected). For symmetrical waveforms like sinewaves, triangle waves, and square waves, the ac–coupled and ac+dc values are equal, since these waveforms do not contain a dc offset. However, for non–symmetrical waveforms (such as pulse trains) there is a dc voltage content, which is rejected by ac–coupled true RMS measurements. DC rejection is desirable in certain applications such as when you want to measure the ac ripple present on DC power supplies. For situations where you want to know the AC+DC true rms value, you can determine it by combining results from dc and ac measurements, as shown below:

A common misconception is that "since an ac multimeter is true rms, its sine wave accuracy specifications apply to all waveforms." Actually, the shape of the input signal can dramatically affect measurement accuracy for any multimeter, especially when that input signal contains high–frequency components which exceed the instrument’s bandwidth. As an example, consider a pulse train, one of the most challenging waveforms for a multimeter. The pulse–width of that waveform largely determines its high–frequency content. The frequency spectrum of an individual pulse is determined by its Fourier Integral. The frequency spectrum of the pulse train is the Fourier Series that samples along the Fourier Integral at multiples of the input pulse repetition frequency (PRF).

The below figure shows the Fourier Integral of two different pulses: one of broad width (200 μs); the other narrow (6.7 μs). Agilent's 34410A/11A series of DMMs have an effective AC measurement bandwidth of 300 KHz.  If we used one of these DMMs to measure the RMS ACV value of both pulses in the figure the measured value of the broader pulse will be more accurate than the measured value of the narrow pulse since its frequency components outside of the DMM's bandwidth are larger in amplitude.
When making true RMS measurements on non-symmetrical waveforms, accuracy drops as the crest factor and/or the frequency of the waveform increases (for more info on crest factor click here). Here is a list of other tips when making true RMS AC measurements:
1. For maximum accuracy, measure as close to full scale as you can. You might need to override auto scaling in some cases. Be careful with high-crest-factor signals not to overload and saturate the meter’s input circuitry.
2. Be sure to select your DMMs appropriate low-frequency filter to allow for the fundamental to be captured. The lower the filter the longer the measurement will take.
3. You may not want to use the first measured value because many DMMs have a large-value DC-blocking capacitor in the input path. You need to allow this capacitor to charge, especially when you are measuring low-frequency signals or when you are switching between measurement points that have a large DC offset.
4. When you measure AC voltages less than 100 mV, be aware that these measurements are especially susceptible to errors introduced by extraneous noise sources. An exposed test lead will serve as an antenna and the DMM will measure these unwanted signals as well. Reduce the area of the “antenna,” use
good shielding techniques, and make sure the AC source and the DMM are connected to the same electrical outlet to minimize ground loops.
5. AC loading errors: The input impedance of a DMM is often in the region of 10 MΩ in parallel with 100 pF. The cabling you use to connect signals to the multimeter adds additional capacitance and loading. As frequency increases, loading will change. For example, at 1 kHz, the input resistance will now be closer to 850 kΩ, and at 100 kHz it will be closer to 16 kΩ.