### 1. Overview

AC signals are typically characterized by their rms amplitude, which is a measure of their total energy. Rms stands for root-mean-square; to compute the rms value of a waveform, you must take the square root of the mean value of the square of the signal level. Most digital multimeters do this nonlinear signal processing in the analog domain, but the NI 4070 Digital Multimeter uses an onboard digital signal processor (DSP) to compute the rms value from digitized samples of the AC waveform. The result is quiet, accurate, and fast-settling AC readings.

The rms algorithm used by the NI 4070 Digital Multimeter requires at least 4 cycles of the waveform to obtain a quiet reading. For example, it requires a measurement aperture of 4 ms to accurately measure a 1 kHz sine wave. The measurement aperture also needs to be long enough to obtain the requested resolution. For example, although a 40 µs aperture is long enough to measure the rms value of a 100 kHz sine wave, it is not long enough to obtain readings with 6½ digit accuracy. Thus, the period of the waveform being measured and the desired resolution both affect the necessary aperture. NI-DMM selects the shortest aperture to satisfy both requirements. Refer to the Measurement Defaults table for the aperture times used by the digital multimeter.

It is important to realize that it is the period of the measured waveform, and not the period of its lowest-frequency component, that determines the required minimum aperture as shown in Figures A, B, and C. Figure A shows a 1 kHz sine wave. That signal could be measured in 4 ms because that is 4 cycles of the waveform. Figure B shows a 1.1 kHz sine wave. It too could be measured in 4 ms because that is slightly more than 4 cycles of the waveform. Figure C shows a signal that is simply the sum of the signals in Figures A and B. Although the minimum frequency component of that signal is 1 kHz, 4 msec is clearly not long enough to measure the rms value of the whole signal. In this case, the signal has a period of 10 msec, so it requires a 40 msec aperture for an accurate measurement.

*Figure A*

*Figure B*

*Figure C*

### 2. DC and AC Coupling

The rms algorithm employed by the NI 4070 Digital Multimeter digital signal processor (DSP) is completely insensitive to any DC component of the signal being measured. Thus the AC coupling capacitor typically found on digital multimeters to block the DC signal component is not always necessary on the NI 4070 Digital Multimeter. A coupling capacitor is available for situations where a large DC offset must be blocked before digitization, but for applications without large DC components, such as AC powerline and audio signals, the capacitor can be bypassed by using the DC-coupled ACV mode. This mode does not have a long time constant associated with the input coupling capacitor, and thus offers very short settle time. To measure AC voltages in the presence of large DC offsets, such as ripple on a DC power supply, use standard ACV mode, which uses a coupling capacitor to eliminate the offset. AC current (amps) measurement is always DC-coupled, so it always offers quick settling, but it is subject to overload if the DC component of the signal exceeds the limits of the chosen range.

### 3. Frequency Response

The NI 4070 Digital Multimeter uses a digital filter to ensure AC accuracy for all frequencies up to the specified limits. This filter is factory-calibrated for every AC mode and range. However, if care is not taken, it is still possible to get frequency-dependent measurement errors with the NI 4070 Digital Multimeter . For example, a measurement of a source with a high impedance can yield lower-than-expected readings because of interaction with the input capacitance of the NI 4070 Digital Multimeter. The NI 4070 Digital Multimeter accurately measures the level of the signal at its input, but the signal can be smaller than expected because of the loading effect of the capacitance. In such cases, it is advisable to either allow for the error or buffer the signal being measured with a voltage buffer amplifier circuit. The voltage buffer will allow us to transfer a voltage from a first circuit with a high output impedance level to a second circuit with a low input impedance level.

### 4. AC RMS Noise

Any noise added to the signal being measured can increase the apparent rms value of a signal. This applies both to external noise sources and to noise originating inside the NI 4070 Digital Multimeter itself. Due to the nature of the rms computation, added noise increases the reading in a nonlinear fashion. Specifically, if *S* is the rms value of the signal and *N* is the rms value of the noise, the total reading is T = . In the case of noise originating in the NI 4070 Digital Multimeter, factory calibration and self-calibration measure the internal noise, and the DSP subtracts the measured noise from the result to improve accuracy. AutoZero can be used for the same purpose. The subtraction is not linear, but takes into account the nonlinear way in which noise increases measured readings.

The NI 4070 Digital Multimeter may sometimes appear to return noisier AC readings than other digital multimeters. In fact, it is quieter than most, but it appears noisy because it responds so quickly to changes in signal amplitude. It is very difficult to find an AC voltage source quiet enough to characterize the noise performance of the NI 4070 Digital Multimeter. If readings appear too noisy, increase your measurement aperture.

### 5. Crest Factor

Crest factor is determined by the following formula:

*Crest Factor = (V*

_{peak}/V_{rms})For a sine wave, the crest factor is 1.414; for a 50% duty cycle square wave, the crest factor is 1. This specification is important because it indicates the maximum peak value of a waveform that the digital multimeter can handle without overloading or introducing additional error. For example, given a certain digital multimeter with an AC accuracy of 0.03% (always specified for sine waves) with an additional error of 0.2% for crest factors between 1.414 and 5, then the total error for measuring a triangular wave (crest factor = 1.73) is 0.03% + 0.2% = 0.23%.

Historically, making AC measurements with digital multimeters has been very frustrating because many tradeoffs exist. Traditional methods are derated for high crest factor signals. If you do not know the crest factor, it is difficult to predict the accuracy of the measurement. Also, high-frequency, low-level signals are measured poorly by most 6½ digit digital multimeters because of the analog techniques. These devices employ active diode rectifiers that cannot keep up effectively as frequency increases, unless they are driven very hard (for example, high amplitudes).

The method used by the NI 4070 Digital Multimeter is insensitive to crest factor error and capable of low-level measurements, limited primarily by noise. So while the specification allows for signal amplitudes of 1% of range, in practice the useful measurement range extends at least a decade lower.

### 6. Offset Errors

Noise present on the input signal path of a digital multimeter results in offset on the AC_{rms} function. It is not advisable to reduce this error by doing a subtraction operation (or null in the DMM Soft Front Panel) because the value displayed is the rms sum of the inputs.

As an example, assume a 100-count offset error on the 10 V range exists. This represents 1 mV. If an input of 10 mV_{rms} is applied, the reading is:

*Reading =*

*Reading = 10.05 mV*

_{rms}What appeared to be a huge offset error now accounts for only a 0.5% error in the measurement because of the rms conversion. If instead you use the DMM Soft Front Panel null feature, the result is:

This represents a 10% error in the result.