True rms responding multimeters, like the Agilent Truevolt Series, 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. This multimeter accurately measures true rms voltage or current, as long as the wave shape contains negligible energy above the meter’s effective bandwidth.
Note that the Agilent Truevolt Series uses the same techniques to measure true rms voltage and true rms current. The effective AC voltage bandwidth is 300 kHz, while the effective AC current bandwidth is 10 kHz.
The DMM's AC voltage and AC current functions measure the AC-coupled true rms value. In this DMM, the "heating value" of only the AC components of the input waveform are measured (dc is rejected). As seen in the figure above; for sine waves, triangle waves, and square waves, the AC–coupled and AC+DC values are equal, because 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 Agilent’s AC–coupled true rms measurements. This can provide a significant benefit.
An AC–coupled true rms measurement is desirable when you are measuring small AC signals in the presence of large DC offsets. For example, this situation is common when measuring AC ripple present on DC power supplies. There are situations, however, where you might want to know the AC+DC true rms value. You can determine this value by combining results from DC and AC measurements, as shown below:
For the best AC noise rejection, you should perform the DC measurement using an integration time of at least 10 power–line cycles (PLCs).
A common misconception is that because an AC multimeter is true rms, its sine wave accuracy specifications apply to all waveforms. Actually, the shape of the input signal dramatically affects measurement accuracy for any multimeter, especially when that input signal contains high–frequency component sbeyond the instrument’s bandwidth.
For 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 figure below shows the Fourier Integral of two very different pulses: one of broad width (200 µs); the other narrow (6.7 µs). The bandwith of the ACV path in the DMM is 300 kHZ; therefore, frequency content above 300 kHz is not measured.
Notice that the sin(πfT)/πfT spectrum of the narrow pulse significantly exceeds the effective bandwidth of the instrument. The net result is a less accurate measurement of the narrow, high–frequency pulse.
In contrast, the frequency spectrum of the broad pulse has fallen off significantly below the multimeter’s 300 kHz (approximately) bandwidth, so measurements of this pulse are more accurate.
Reducing the prf increases the density of lines in the Fourier spectrum, and increases the portion of the input signal’s spectral energy within the multimeter’s bandwidth, which improves accuracy.
In summary, error in rms measurements arise when there is significant input signal energy at frequencies above the multimeter’s bandwidth.
A common way to describe signal waveshapes is to refer to their "Crest Factor". Crest factor is the ratio of the peak value to rms value of a waveform. For a pulse train, for example, the crest factor is approximately equal to the square root of the inverse of the duty cycle.
Notice that crest factor is a composite parameter, dependent upon the pulse width and repetition frequency; crest factor alone is not enough to characterize the frequency content of a signal.
Traditionally, DMMs include a crest factor derating table that applies at all frequencies. The measurement algorithm used in the Truevolt Series DMMs is not inherently sensitive to crest factor, so no such derating is necessary. With this multimeter, as discussed in the previous section, the focal issue is high–frequency signal content which exceeds the multimeter’s bandwidth.
For periodic signals, the combination of crest factor and repetition rate can suggest the amount of high–frequency content and associated measurement error. The first zero crossing of a simple pulse occurs at f1 = 1/tp.
This gives an immediate impression of the high-frequency content by identifying where this crossing occurs as a function of crest factor: f1=(CF2)(prf).
The following table shows the typical error for various pulse waveforms as a function of input pulse frequency:
| Typical error for square wave, triangle wave, and pulse trains of CF=3, 5, or 10 | |||||
|---|---|---|---|---|---|
| prf | square wave | triangle | CF=3 | CF=5 | CF=10 |
| 200 | -0.02% | 0.00% | -0.04% | -0.09% | -0.34% |
| 1000 | -0.07% | 0.00% | -0.18% | -0.44% | -1.71% |
| 2000 | -0.14% | 0.00% | -0.34% | -0.88% | -3.52% |
| 5000 | -0.34% | 0.00% | -0.84% | -2.29% | -8.34% |
| 10000 | -0.68% | 0.00% | -1.75% | -4.94% | -26.00% |
| 20000 | -1.28% | 0.00% | -3.07% | -8.20% | -45.70% |
| 50000 | -3.41% | -0.04% | -6.75% | -32.0% | -65.30% |
| 100000 | -5.10% | -0.12% | -21.8% | -50.6% | -75.40% |
This table gives an additional error for each waveform, to be added to the value from the accuracy table provided in the instrument's data sheet
The specifications are valid for CF ≤ 10, provided there is insignificant signal energy above the 300 kHz bandwidth for voltage, or the 10 kHz bandwidth for current. Multimeter performance is not specified for CF > 10, or when significant out-of-band signal content is present.
A pulse train with level 1 Vrms, is measured on the 1 V range. It has pulse heights of 3 V (that is, a Crest Factor of 3) and duration 111 µs. The prf can be calculated to be 1000 Hz, as follows:
Thus, from the table above, this AC waveform can be measured with 0.18 percent additional error.