Digital Multimeter HDM3055 Series Manual

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Other Primary Measurement Functions

Frequency and Period Measurement Errors

           

The multimeter uses a reciprocal counting technique to measure frequency and period. This method

generates constant measurement resolution for any input frequency. The multimeter's AC voltage

measurement section performs input signal conditioning. All frequency counters are susceptible to

errors when measuring low–voltage, low–frequency signals. The effects of both internal noise and

external noise pickup are critical when measuring "slow" signals. The error is inversely proportional

to frequency. Measurement errors also occur if you attempt to measure the frequency (or period)

of an input following a DC offset voltage change. You must allow the multimeter's input DC blocking

capacitor to fully settle before making frequency measurements.

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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.

Example

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 ?s. The prf can be calculated to be 1000 Hz, as follows:

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Thus, from the table above, this AC waveform can be measured with 0.18 percent additional error.

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The following table shows the typical error for various pulse waveforms as a function of input pulse

frequency.

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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 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).

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Estimating High–Frequency (Out–of–Band) Error

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.

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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.

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True RMS Accuracy and High–Frequency Signal Content

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 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 ?s); the other narrow (6.7 ?s). The bandwidth 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.

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You can determine this value by combining results from DC and AC measurements, as shown

below:

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For the best AC noise rejection, you should perform the DC measurement using an integration time

of at least 10 power–line cycles (PLCs).

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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 Hantek’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.

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