Elliott Sound Products

Project 140

True RMS Converter
© Rod Elliott, 09 December
2012

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Introduction

Many AC waveforms we need to measure are not nice friendly sinewaves, and
there is a significant error if you measure the value using a standard AC
voltmeter. These are typically average responding, but calibrated to show RMS.
The only problem is that the reading is only accurate when the waveform is a
sinewave. Other waveforms typically read much lower than the real value and give
a false reading that isn't actually useful for anything. If you happen to be
checking the current rating (vs. current drawn) of building wiring, you
could make a very dangerous mistake if the waveform is other than a sinewave and
you use an 'ordinary' meter.

RMS stands for 'root mean squared', which defines what an RMS converter does
internally. The input signal is (precision) rectified to give a unipolar
voltage. The signal is then squared and averaged, and the circuit finally takes
the square root of the average (mean) value. As noted in Analog Devices'
application notes and other material, the actual circuit is configured
differently to limit the internal dynamic range and provide greater accuracy
than would be possible if the squarer circuit had to operate over a range of
around 10,000:1. The IC itself is basically an analogue computer. To gain a full
understanding of the IC operation, I suggest the reader looks at the references.

This project is ideally suited to either of the current monitor projects
presented (see Project
139 and/or Project
139a), but is equally suited for anywhere that true RMS metering will give
improved performance. The accuracy and linearity of RMS converters are usually
better than expected, and (at least in theory) you can rely on the IC to give
you a good result, even without calibration. The device I used is a
laser-trimmed true RMS converter, the AD737 [1].
It is claimed to be within 0.3% accurate, and will handle a crest factor of 5.

"Crest factor?" You may well ask. Crest factor is defined as the ratio
between the peak and RMS value of a waveform. With a sinewave, this ratio is
well known ... 1.414 (the square root of 2). This simply means that the peak
value of a sinewave is 1.414 times the RMS value. With other waveforms, the
crest factor varies widely. The following table is adapted from the AD737
datasheet.

Waveform - 1 V Peak

Crest Factor
VPEAK /
VRMS

True RMS

Avg/RMS meter *

Error (%)

Undistorted Sine Wave

1.414

0.707

0.707

0

Symmetrical Square Wave

1.00

1.00

1.11

+11.0

Undistorted Triangle Wave

1.73

0.577

0.555

-3.8

Gaussian Noise (98% of Peaks <1 V)

3

0.333

0.295

-11.4

Rectangular

2

0.5

0.278

-44

Pulse Train

10

0.1

0.011

-89

SCR Waveform - 50% Duty Cycle

2

0.495

0.354

-28

SCR Waveform - 25% Duty Cycle

4.7

0.212

0.150

-30

Table 1 - Reading Error With Different
Waveforms

* Reading of an Average Responding Circuit Calibrated to an
RMS Sine Wave Value (V)

As you can see from the table, some waveforms have enormous errors, and the
worst (a pulse train with a crest factor of 10) will continue to give a false
reading, even with an RMS converter. Like any signal processing system (analogue
or digital), there is a maximum level that can't be exceeded. When the input
signal has a crest factor greater than 5, the internal circuitry of the AD737
will become non-linear and the RMS core within the IC is overloaded. For this
reason, the maximum recommended input level is 200mV to ensure that there is
always enough internal headroom.

Although the AD737 is claimed to be able to operate with up to ±15V, all
application notes show it using ±5V, and that has been retained in this design.
One of the less attractive features of the IC is that the output is negative.
With 200mV RMS input, the output will be -200mV DC, and although you can connect
a panel meter (or any other DC voltmeter) with the leads reversed, it's more
sensible to use an inverter to get the correct polarity and to isolate the high
impedance output from the outside world.

There are a few other RMS converter ICs available, but some are not suited to
making normal AC voltage measurements. For example the THAT2252 might look
suitable, but its output is logarithmic. This is fine for dB measurements but is
of no use whatsoever for measuring AC voltage or current. We need dB
measurements for audio levels, not for mains current! The 2252 is designed for
use in audio compressors and expanders. It's not intended for test and
measurement equipment, and it has a limited high frequency response.

Description

As described above, most AC meters are average-responding, but calibrated in
RMS. It's worth knowing just what this means, and you certainly won't find the
details in the manual that comes with the meter. No AC waveform can be measured
with a digital meter or moving coil meter without being rectified. This involves
using a precision rectifier (see Precision
Rectifiers), followed by an averaging circuit - typically a simple
resistor-capacitor integrator. The average value of a 1V peak sinewave
(rectified) is 0.636V, and all that's done is to provide a small amount of
amplification to make the meter read 0.707V instead. Unfortunately, this
relationship only works with an undistorted sinewave, so measurements of
all other waveforms are in error.

Even now, true RMS meters are typically far more expensive than 'standard'
types. This is a shame because all AC readings on standard meters are
wrong except with purely resistive loads and sinewave voltage and current
waveforms. As a result, a vast number of AC measurements taken are invalid,
regardless of how careful one might be. The only valid AC measurement is
true RMS - anything else is probably in error. The error can be huge, as shown
in Table 1.

True RMS measurements have been available for some time, but early versions
were cumbersome and slow, relying on heating effect. The input waveform was
applied to a heater, and the temperature monitored with a suitable sensor. This
was compared to an identical unit supplied with DC. A 1V RMS signal has exactly
the same heating ability as 1V DC, regardless of the AC waveform or frequency.

The normal application for this project is as an RMS converter/adaptor for a
dedicated metering system, and it can drive a digital panel meter or a moving
coil analogue meter. While having to use a buffer and inverter is a nuisance, it
does allow you to change the gain to suit the meter you have. The AD737 has an
output impedance of around 8k, and any load across the output will cause loss of
accuracy. While any necessary scaling can be done around the IC, the range is
limited and IMO it's not very useful.

The complete schematic is shown below. Because we are working with millivolt
levels at DC, being able to adjust the DC zero point is important. Most common
opamps are pretty good, having fairly low input offset voltage and current, and
you can use a TL072 or an MC4558 (for example). While offset for both is
typically only around 1mV, it does vary with temperature and worst case is shown
in the datasheets as 6mV. That's a significant percentage of 200mV, so an offset
null adjustment is required. The arrangement shown gives an adjustment range of
±11.5mV which should be plenty. If you need more, either try a different opamp
or reduce the value of R4.

Figure 1 - Schematic Of The RMS Converter

The AD737 is not an inexpensive device, so I recommend that you use a socket.
Don't insert the IC until you are certain that all voltages are correct and of
the right polarity. The first opamp (u2A) following the converter is a buffer,
with offset null circuitry added using VR1. The second stage (U2B) is an
inverting amplifier, and the gain can be set to whatever you need via VR2 -
range is 0.1 - 6 as shown. If the readout is a panel meter (LED or LCD), these
have a normal full scale sensitivity of 200mV, so the second stage gain will be
unity (or close to it). The feedback network around U2B can be tailored to suit
your needs. If you need a gain of between (say) 3 to 12 (600mV - 2.4V), then
simply increase VR2 to 100k and make R7 22k. You'll have some leeway, because
the full range will provide gain of between 2.2 and 12.2

Should you be driving a moving coil analogue movement then a suitable scaling
resistor has to be used in series with the movement (see Meters, Multipliers & Shunts for more information).
Other than setting the DC offset to zero, calibration can be based on the
selection of the series resistor (which can include a trimpot). There is no real
need to calibrate the RMS converter itself in this case, provided it can supply
a maximum output that's high enough to drive the meter movement.

The datasheet for the AD737 has a bewildering array of options for CAVG and CF (C2 and C3
respectively). Having experimented, I found that 100uF is the best compromise
for both. I suggest that low-leakage electrolytic caps be used in both
locations. If you need faster settling time, you can reduce either or both - see
the datasheet for more info, but be prepared to see more options and compromises
than you can poke a stick at (it really is a minefield).

The offset circuit arrangement shown has been tested thoroughly, using 4558
opamps in an opamp test board. With no shielding or even precision resistors, I
was able to get the offset voltage down to less than 2µV fairly easily. I found
that after power was applied, it would take about 5 minutes to stabilise,
starting from around 25µV and gradually reducing towards zero. Once the opamps
had reached operating temperature there was no further drift. Since the smallest
useful resolution is several millivolts, having a worst case DC offset of
0.025mV is more than satisfactory. There is no reason to expect stability over
time to cause problems, though you might need to re-calibrate the DC offset
every few years.

If the output opamp (U2B) is operated with gain, offset will be amplified
along with the signal. However, both will be amplified equally and the net
percentage will remain the same. You will probably get some additional offset
from U2B, but the trimpot should allow it to be zeroed out (reduce R4 to get
more range if needed).

Calibration

The first step is to set the DC offset to zero. Short the input to the RMS
converter so it doesn't pick up any noise (use a very short link!). Carefully
adjust VR1 until the output of TP1 is exactly zero. Next, check that the output
of the second stage is also at zero - if not, you will need to adjust VR1
accordingly. Calibration will be an iterative process - if the output gain is
changed using VR2, you will almost certainly need to reset the zero offset
(VR1). Allow the circuit to operate in its normal environment (usually room
temperature) for at least 30 minutes and verify that the DC offset remain at
zero. This tedious messing around can be eliminated by using opamps with highly
specified and very low input offset voltage and current, but they will be hard
to get and expensive. However, even budget opamps are surprisingly stable if set
up properly.

For calibration, you will need an accurate standard (or true RMS) AC/DC meter
and a source of undistorted sinewaves. Calibration is relatively
straightforward. You need to use a frequency of around 100Hz or so, mainly
because most meters have rather poor frequency response. If you apply an AC
input voltage of 200mV, you should see a DC output of 200mV at TP1 (the output
of the buffer).

If you plan to use the RMS adaptor within an instrument (such as a distortion
meter), the circuit needs to be arranged so that the normal full-scale voltage
is around 200mV. You can extend that up to 1V if needs be, but be aware
that the maximum allowable crest factor will be reduced. Output level is then
set using VR2, and can range from 0.1 up to 10 times by adjusting resistor
values. As shown, the output gain range is from 0.6 to 1.3 as set by VR2.

Where Would I use It?

A perfect candidate for a true RMS meter is a distortion meter. The input
waveform is always a sinewave, but the output waveform is anything but
sinusoidal. Because of the distorted residual waveform, virtually all distortion
meters read low - the displayed distortion is less than the real value, and
could read low by as much as 20%. Where a true RMS reading meter accurately
displays the value for high crest factors (which can be common with distortion
waveforms), the typical average reading meter does not.

If you build a distortion meter, it's usually a fairly simple matter to
include the facility for a millivoltmeter as well, since that's what's used to
measure the output of the distortion meter. Alternatively, you can make a
stand-alone millivoltmeter - this is covered in a bit more detail below. You can
choose to use a moving coil analogue meter movement (preferred) or a digital
panel meter as the display. The latter can be obtained quite cheaply these days,
although some have very irritating power requirements that may demand a
completely separate power supply.

As noted above, either of the current monitor projects will also benefit from
using a true RMS metering system. Most common electronic devices draw a
non-linear current, and a standard average reading (but RMS calibrated) meter
will underestimate the current - often by a considerable degree. Bear in mind
that some waveforms will have such a high crest factor that even the RMS chip
will be unable to provide an accurate reading. A good example is a CFL (compact
fluorescent lamp) when run from a TRIAC dimmer (see Dimmer + CFL Test Results).

Just measuring the mains will provide something of a challenge for an
'ordinary' meter, because the waveform is almost invariably distorted. Even a
small amount of mains waveform 'flat-topping' will cause your standard meter to
read high, because the crest factor has been reduced. Look at Table 1
again - errors are positive (over-reading) when the crest factor is less than
1.414, and negative (under-reading) when the crest factor is greater than 1.414.
A standard meter can only ever be accurate when the waveform is an
undistorted sinewave. Provided the distortion of the mains waveform is less than
~5%, the error is fairly small, so I don't suggest that you fret too much
.

Although some of the application data shows the use of an input attenuator,
great care is needed to make sure that excessive voltage can never be applied to
the input of the AD737. To keep errors due to stray capacitance low, an
attenuator should use relatively low value resistors. You also need to be aware
that the frequency response of the RMS converter is level dependent. At 200mV
input, the -3dB bandwidth is claimed to extend to 190kHz, but is only 5kHz at
1mV input. The useful input range starts from 10mV (55kHz), which is in keeping
with most measurements (accurate measurement is usually not possible when the
reading is less than 5% of full scale with any meter). See the datasheet for all
details of input level vs. bandwidth. In general, the input should be maintained
at a minimum of 20mV if at all possible.

Figure 2 - Input Attenuator For RMS Converter

Note that the diagram in Figure 2 is part of the complete schematic shown in
Figure 1. The point marked "Output" connects to point 'A' in Figure 1 - the
non-inverting input of U2A (pin 3).

You will also need to include input protection, as shown in the diagram above
(D3+D4). The attenuator I recommend is 1/10th the impedance of that suggested in
the data sheet, simply because of stray capacitance and bandwidth. For a wide
range, wide bandwidth attenuator, have a look at the one used in the AC Millivoltmeter project. It may need to be adapted,
because as shown it is based on 10dB steps which are not usable with a digital
display, although it will work fine with an analogue movement having a proper dB
scale.

Of course, if you are using a moving coil meter movement with 10dB steps (1V,
316mV etc.) Then you can use the attenuator shown in Project 16 without
modification.

This project is actually easily adapted to become an audio millivoltmeter in
its own right - all it needs is an input amplifier capable of enough gain to
allow measurement down to a level of around 3mV. The circuit shown in Project 16
is fairly easily modified, and details will be provided if there is enough
interest. Given the comparatively low bandwidth of the AD737 (55kHz at an input
level of 10mV), it can never be quite as good as the standard arrangement for
the AC millivoltmeter, but the fact that it measures true RMS does make it a
better meter overall - just don't expect to be able to measure out to several
hundred kHz, especially at low input levels.

Conclusion

Because this is intended as a building block rather than a complete project,
it's not possible to provide any final assembly information, because each case
will be different. When housed with other electronics, make sure that the
circuit is shielded against noise pickup from other parts of your circuit, or
low-level readings will be affected by noise. Also, make sure that the circuit
board is kept away from heat sources. If the AD737 or the opamp are allowed to
get hot from other parts, you'll suffer from DC drift around the zero point,
increasing the inaccuracy that's inherent at very low signal levels.

It's also worthwhile to offer a general warning about AC measurements in
general. Just because you have a true RMS meter (or the adaptor described here),
this does not guarantee that all your AC measurements will be accurate.
Some waveforms will have such a high crest factor that no RMS converter IC can
handle it and give a true reading, and others may be at a frequency that's
outside the allowable range.

Before relying on any meter, it's wise to know something about the
waveform you are measuring, and the best possible way to find out is with an
oscilloscope. This is (usually) not necessary when measuring mundane things like
AC mains voltage, but suddenly becomes very important indeed when measuring
mains current - especially with power supplies and other non-linear
loads.

For what it's worth, modern digital oscilloscopes have extensive maths
functions as well as the normal display. Mine can display RMS (among other
things), and does so more accurately than a high quality (true RMS) bench
multimeter when measuring pulse waveforms. Why? Because the 'scope
calculates the RMS value, and as long as the waveform fits the display
(therefore there's no overload) it can do an accurate calculation regardless of
crest factor. Even the horrible spiky current waveform from a CFL (compact
fluorescent lamp) causes the 'scope no problems, but the meter still gets it
wrong (reading low) because the crest factor is too high.

References

Analog Devices AD737 Data Sheet

Analog Devices, Application Note AN-268

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Copyright Notice.This
article, including but not limited to all text and diagrams, is the
intellectual property of Rod Elliott, and is Copyright © 2012.
Reproduction or re-publication by any means whatsoever, whether
electronic, mechanical or electro-mechanical, is strictly prohibited under
International Copyright laws. The author grants the reader the right to
use this information for personal use only, and further allow that one (1)
copy may be made for reference while constructing the project. Commercial
use is prohibited without express written authorisation from Rod
Elliott.

Page Created and Copyright © Rod Elliott 07 November
2012