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Keysight Technologies
Make Better RMS Measurements
with Your Digital Multimeter
Application Note
Introduction
If you use a digital multimeter (DMM) for AC voltage measurements, it is important
to know if your meter is giving you peak value, average value, root-mean-square
(rms) value, or something else. If the answer is "something else," you may be in
trouble, and the trouble usually happens with rms measurements. This application
note will help you understand the different techniques DMMs use to measure rms
values, how the signal affects the quality of your measurements, and how to avoid
common measurement mistakes.
2011 NCSL International Workshop and Symposium
03 | Keysight | Make Better RMS Measurements with Your Digital Multimeter - Application Note
Measuring RMS
Measuring rms values is more responding or average-responding Two measurement challenges are
complicated than it appears at meters rely on these scaling factors. associated with high crest factors.
first glance. If it is complicated, The first involves input range.
why do we bother? Because The scaling factors apply only to Imagine a pulse train with a very
true rms is the only AC voltage pure sine waves. For every other low duty cycle but a relatively high
reading that does not depend on type of signal, using this approach peak amplitude. Signals like this
the shape of the signal. It often is produces misleading answers. If force the meter to simultaneously
the most useful measurement for you are using a meter that is not measure a high peak value and a
real-world waveforms. really designed for the task, you much lower rms value, possibly
easily can end up with significant creating overload problems on the
Often, rms is described as a measure error--as high as 40 percent or high end and resolution problems
of equivalent heating value, with more--depending on the meter on the low end.
a relationship to the amount of and the signal.
power dissipated by a resistive The second challenge is the
load driven by the equivalent DC The ratio of Vpk to Vrms known as amount of higher-frequency
value. For example, a 1Vpk sine the crest factor, is important to energy in the signal. In general,
wave will deliver the same power measurement accuracy. The crest high crest factors indicate more
to a resistive load as a 0.707Vdc factor is a measure of how high harmonics, which can cause
signal. A reliable rms reading on the waveform peaks, relative to its trouble for all meters. Peak- and
a signal will give you a better idea RMS value. The higher the crest average-responding meters that
of the effect the signal will have in factor, the more difficult it is to are trying to measure rms have a
your circuit. make an accurate AC measurement. particularly hard time.
Figure 1 shows four common voltage
parameters. Peak voltage (Vpk) and
peak-to-peak voltage (Vpk-pk) are
simple. Vavg is the average of all
Volume
the instantaneous values in one
complete cycle of the waveform. Vpk
You will learn how we calculate Vavg Vrms
Vrms below. Vpk-pk
Time
For sine waves, the negative half
of the waveform cancels out the
positive half and averages to
zero over one cycle. This type of
average would not provide much
insight into the signal's effective Figure 1. Common voltage parameters
amplitude, so most meters com-
pute Vavg based on the absolute
value of the waveform. For a sine
wave, this works out to Vpk x 0.637
(Figure 2).
Volume
You can derive Vrms by squaring
every point in the waveform, finding
Vpk
the average (mean) value of the Vavg
squares, then finding the square
root of the average. With pure sine
Time
waves, you can take a couple of
shortcuts: just multiply Vpk x 0.707
or Vavg x 1.11. Inexpensive peak- Figure 2. Vavg is calculated based on the absolute value of the waveform.
04 | Keysight | Make Better RMS Measurements with Your Digital Multimeter - Application Note
Tips for Making Better RMS Measurements
Given the importance--and diffi- The disadvantages of the thermal
culty-- of measuring rms, what is approach are cost and lack of
the best way to proceed with your flexibility in trading off measurement
day-to-day measurement tasks? speed with low-frequency accuracy.
The following tips will help you For these reasons, the technique
achieve better results. is not used in the latest-
generation DMMs.
Tip 1:
If you need to measure high-
Understand how your bandwidth and high-crest-factor
DMM measures rms. signals with great accuracy, you
When it comes to measuring rms may want to search for one of
values, multimeters are not created these thermal models. If high
equal. A general understanding of accuracy is important to you,
the technology your multimeter you may want to investigate
uses to measure rms will help you multimeters that use the digital
decide if it meets your needs. Here sampling method.
is a summary of the operational
advantages and disadvantages Peak and averaging
of four common multimeter AC-to-DC converters
technologies. The first three operate Inexpensive meters, particularly
by converting AC to DC; the last inexpensive hand-held meters,
one digitizes the analog input usually derive rms levels from
signal and then computes rms. either peak or average values.
They deliver true rms only for
Thermal AC-to-DC converters pure, undistorted sine waves. If
This older technology for rms you need true rms measurements
measurements uses the equivalent- on real-world signals, these
heating-value approach. The AC meters are not a viable option.
signal heats a thermocouple,
then the DC section of the meter Analog AC-to-DC converters
reads the thermocouple output. Many mid-range DMMs use a
Advantages include wide band- chain of analog circuits to compute
width and the ability to handle the square, then the mean, then
very high crest factors, meaning the square root of the mean to
this approach can deliver true rms deliver true rms for nearly all
for a wide variety of real-world signal types.
signals.
05 | Keysight | Make Better RMS Measurements with Your Digital Multimeter - Application Note
Digital sampling and the capability to create very Tip 2:
fast, effective sampling rates and Understand how the
This last method uses sampling
wider bandwidths, even with fairly
techniques similar to those in digital
slow analog-to-digital converters. signal affects the quality
oscilloscopes to create a set of your measurement.
This method, however, only works
of data points that are sent through
with repetitive signals. Let's look at several different
an rms algorithm. Synchronous
sampling uses multiple passes to signals, starting with a sine
If accurate rms measurements are wave. The crest factor for a pure
capture a signal as shown in Figure
important to you and you are likely sine wave is 1.414, and a peak-
3. Each subsequent pass is delayed
to run into pulse trains and other responding meter can provide
by a small amount, and with
complicated signals, a true rms accurate rms simply by scaling
enough passes, the signal can be
meter is the only solution. On the the value of Vpk. With a Vpk value of
digitized with very high resolution.
other hand, you can save some 500 mV, we expect an rms value
money with a peak--or average- around 350 to 357 mV (the range
This technique has several
responding meter. Just keep in accounts for the inaccuracy of the
advantages: true rms on a wide
mind what these meters can and signal generator used). Sure
range of signals, high accuracy,
cannot do. enough, a true rms meter reads
the signal as 353.53 mV. A less-
expensive average-responding
meter reads the signal as 351 mV.
Unlike the pure sine wave, the
triangle wave in Figure 4 has
some higher-frequency energy,
so the crest factor of 1.732 comes
as no surprise. Dividing the peak
value by the crest factor yields an
expected rms value of roughly 290
mV. Now, the average-responding
meter starts to get into trouble,
reading the signal as 276 mV, a 4
percent error compared to the true
2nd Trigger Point rms meter's reading of 288.68 mV.
1st Trigger Point
Now let's look at pulse trains,
Figure 3. Digital sampling
where the crest factor depends on
the duty cycle. You can get a close
approximation of crest factor with
the formula:
T
CF ` t
where:
CF = the crest factor
T = the period of the waveform
t = the on portion of that period
Figure 4. Measuring rms on a triangle wave
06 | Keysight | Make Better RMS Measurements with Your Digital Multimeter - Application Note
This also is equal to the square
rootof the reciprocal of the duty
cycle. So, for the pulse train in
Figure 5, which has a 2 percent
duty cycle, the crest factor is the
square root of 50, or 7.071.
Computing the rms value for sines
and triangles is quite simple; the
rms value is Vpk divided by the crest
factor. However, computing the AC
rms value for a pulse train is a bit
more complicated:
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