AC voltmeters and ammeters
AC electromechanical meter movements come
in two basic arrangements: those based on DC movement designs, and those
engineered specifically for AC use. Permanent-magnet moving coil (PMMC)
meter movements will not work correctly if directly connected to
alternating current, because the direction of needle movement will
change with each half-cycle of the AC. Permanent-magnet meter movements,
like permanent-magnet motors, are devices whose motion depends on the
polarity of the applied voltage (or, you can think of it in terms of the
direction of the current).
In order to use a DC-style meter movement
such as the D'Arsonval design, the alternating current must be
rectified into DC. This is most easily accomplished through the use
of devices called diodes. We saw diodes used in an example
circuit demonstrating the creation of harmonic frequencies from a
distorted (or rectified) sine wave. Without going into elaborate detail
over how and why diodes work as they do, just remember that they each
act like a one-way valve for electrons to flow: acting as a conductor
for one polarity and an insulator for another. Oddly enough, the
arrowhead in each diode symbol points against the permitted
direction of electron flow rather than with it as one might expect.
Arranged in a bridge, four diodes will serve to steer AC through the
meter movement in a constant direction throughout all portions of the AC
cycle:
Another strategy for a practical AC meter
movement is to redesign the movement without the inherent polarity
sensitivity of the DC types. This means avoiding the use of permanent
magnets. Probably the simplest design is to use a nonmagnetized iron
vane to move the needle against spring tension, the vane being attracted
toward a stationary coil of wire energized by the AC quantity to be
measured.
Electrostatic attraction between two
metal plates separated by an air gap is an alternative mechanism for
generating a needle-moving force proportional to applied voltage. This
works just as well for AC as it does for DC, or should I say, just as
poorly! The forces involved are very small, much smaller than the
magnetic attraction between an energized coil and an iron vane, and as
such these "electrostatic" meter movements tend to be fragile and easily
disturbed by physical movement. But, for some high-voltage AC
applications, the electrostatic movement is an elegant technology. If
nothing else, this technology possesses the advantage of extremely high
input impedance, meaning that no current need be drawn from the circuit
under test. Also, electrostatic meter movements are capable of measuring
very high voltages without need for range resistors or other, external
apparatus.
When a sensitive meter movement needs to
be re-ranged to function as an AC voltmeter, series-connected
"multiplier" resistors and/or resistive voltage dividers may be employed
just as in DC meter design:
Capacitors may be used instead of
resistors, though, to make voltmeter divider circuits. This strategy has
the advantage of being non-dissipative (no true power consumed and no
heat produced):
If the meter movement is electrostatic,
and thus inherently capacitive in nature, a single "multiplier"
capacitor may be connected in series to give it a greater voltage
measuring range, just as a series-connected multiplier resistor gives a
moving-coil (inherently resistive) meter movement a greater voltage
range:
The Cathode Ray Tube (CRT) mentioned in
the DC metering chapter is ideally suited for measuring AC voltages,
especially if the electron beam is swept side-to-side across the screen
of the tube while the measured AC voltage drives the beam up and down. A
graphical representation of the AC wave shape and not just a measurement
of magnitude can easily be had with such a device. However, CRT's have
the disadvantages of weight, size, significant power consumption, and
fragility (being made of evacuated glass) working against them. For
these reasons, electromechanical AC meter movements still have a place
in practical usage.
With some of the advantages and
disadvantages of these meter movement technologies having been discussed
already, there is another factor crucially important for the designer
and user of AC metering instruments to be aware of. This is the issue of
RMS measurement. As we already know, AC measurements are often cast in a
scale of DC power equivalence, called RMS (Root-Mean-Square)
for the sake of meaningful comparisons with DC and with other AC
waveforms of varying shape. None of the meter movement technologies so
far discussed inherently measure the RMS value of an AC quantity. Meter
movements relying on the motion of a mechanical needle ("rectified"
D'Arsonval, iron-vane, and electrostatic) all tend to mechanically
average the instantaneous values into an overall average value for the
waveform. This average value is not necessarily the same as RMS,
although many times it is mistaken as such. Average and RMS values rate
against each other as such for these three common waveform shapes:
Since RMS seems to be the kind of
measurement most people are interested in obtaining with an instrument,
and electromechanical meter movements naturally deliver average
measurements rather than RMS, what are AC meter designers to do? Cheat,
of course! Typically the assumption is made that the waveform shape to
be measured is going to be sine (by far the most common, especially for
power systems), and then the meter movement scale is altered by the
appropriate multiplication factor. For sine waves we see that RMS is
equal to 0.707 times the peak value while Average is 0.637 times the
peak, so we can divide one figure by the other to obtain an average-to-RMS
conversion factor of 1.109:
In other words, the meter movement will
be calibrated to indicate approximately 1.11 times higher than it would
ordinarily (naturally) indicate with no special accommodations. It must
be stressed that this "cheat" only works well when the meter is used to
measure pure sine wave sources. Note that for triangle waves, the ratio
between RMS and Average is not the same as for sine waves:
With square waves, the RMS and Average
values are identical! An AC meter calibrated to accurately read RMS
voltage or current on a pure sine wave will not give the proper
value while indicating the magnitude of anything other than a perfect
sine wave. This includes triangle waves, square waves, or any kind of
distorted sine wave. With harmonics becoming an ever-present phenomenon
in large AC power systems, this matter of accurate RMS measurement is no
small matter.
The astute reader will note that I have
omitted the CRT "movement" from the RMS/Average discussion. This is
because a CRT with its practically weightless electron beam "movement"
displays the Peak (or Peak-to-Peak if you wish) of an AC waveform rather
than Average or RMS. Still, a similar problem arises: how do you
determine the RMS value of a waveform from it? Conversion factors
between Peak and RMS only hold so long as the waveform falls neatly into
a known category of shape (sine, triangle, and square are the only
examples with Peak/RMS/Average conversion factors given here!).
One answer is to design the meter
movement around the very definition of RMS: the effective heating value
of an AC voltage/current as it powers a resistive load. Suppose that the
AC source to be measured is connected across a resistor of known value,
and the heat output of that resistor is measured with a device like a
thermocouple. This would provide a far more direct measurement means of
RMS than any conversion factor could, for it will work with ANY waveform
shape whatsoever:
While the device shown above is somewhat
crude and would suffer from unique engineering problems of its own, the
concept illustrated is very sound. The resistor converts the AC voltage
or current quantity into a thermal (heat) quantity, effectively squaring
the values in real-time. The system's mass works to average these values
by the principle of thermal inertia, and then the meter scale itself is
calibrated to give an indication based on the square-root of the thermal
measurement: perfect Root-Mean-Square indication all in one device! In
fact, one major instrument manufacturer has implemented this technique
into its high-end line of handheld electronic multimeters for "true-RMS"
capability.
Calibrating AC voltmeters and ammeters
for different full-scale ranges of operation is much the same as with DC
instruments: series "multiplier" resistors are used to give voltmeter
movements higher range, and parallel "shunt" resistors are used to allow
ammeter movements to measure currents beyond their natural range.
However, we are not limited to these techniques as we were with DC:
because we can to use transformers with AC, meter ranges can be
electromagnetically rather than resistively "stepped up" or "stepped
down," sometimes far beyond what resistors would have practically
allowed for. Potential Transformers (PT's) and Current Transformers
(CT's) are precision instrument devices manufactured to produce very
precise ratios of transformation between primary and secondary windings.
They can allow small, simple AC meter movements to indicate extremely
high voltages and currents in power systems with accuracy and complete
electrical isolation (something multiplier and shunt resistors could
never do):
Shown here is a voltage and current meter
panel from a three-phase AC system. The three "donut" current
transformers (CTs) can be seen in the rear of the panel. Three AC
ammeters (rated 5 amps full-scale deflection each) on the front of the
panel indicate current through each conductor going through a CT. As
this panel has been removed from service, there are no current-carrying
conductors threaded through the center of the CT "donuts" anymore:
Because of the expense (and often large
size) of instrument transformers, they are not used to scale AC meters
for any applications other than high voltage and high current. For
scaling a milliamp or microamp movement to a range of 120 volts or 5
amps, normal precision resistors (multipliers and shunts) are used, just
as with DC.
- REVIEW:
- Polarized (DC) meter movements must
use devices called diodes to be able to indicate AC quantities.
- Electromechanical meter movements,
whether electromagnetic or electrostatic, naturally provide the
average value of a measured AC quantity. These instruments may be
ranged to indicate RMS value, but only if the shape of the AC waveform
is precisely known beforehand!
- So-called true RMS meters use
different technology to provide indications representing the actual
RMS (rather than skewed average or peak) of an AC waveform.
Frequency and phase measurement
An important electrical quantity with no
equivalent in DC circuits is frequency. Frequency measurement is
very important in many applications of alternating current, especially
in AC power systems designed to run efficiently at one frequency and one
frequency only. If the AC is being generated by an electromechanical
alternator, the frequency will be directly proportional to the shaft
speed of the machine, and frequency could be measured simply by
measuring the speed of the shaft. If frequency needs to be measured at
some distance from the alternator, though, other means of measurement
will be necessary.
One simple but crude method of frequency
measurement in power systems utilizes the principle of mechanical
resonance. Every physical object possessing the property of elasticity
(springiness) has an inherent frequency at which it will prefer to
vibrate. The tuning fork is a great example of this: strike it once and
it will continue to vibrate at a tone specific to its length. Longer
tuning forks have lower resonant frequencies: their tones will be lower
on the musical scale than shorter forks.
Imagine a row of progressively-sized
tuning forks arranged side-by-side. They are all mounted on a common
base, and that base is vibrated at the frequency of the measured AC
voltage (or current) by means of an electromagnet. Whichever tuning fork
is closest in resonant frequency to the frequency of that vibration will
tend to shake the most (or the loudest). If the forks' tines were flimsy
enough, we could see the relative motion of each by the length of the
blur we would see as we inspected each one from an end-view perspective.
Well, make a collection of "tuning forks" out of a strip of sheet metal
cut in a pattern akin to a rake, and you have the vibrating reed
frequency meter:
The user of this meter views the ends of
all those unequal length reeds as they are collectively shaken at the
frequency of the applied AC voltage to the coil. The one closest in
resonant frequency to the applied AC will vibrate the most, looking
something like this:
Vibrating reed meters, obviously, are not
precision instruments, but they are very simple and therefore easy to
manufacture to be rugged. They are often found on small engine-driven
generator sets for the purpose of setting engine speed so that the
frequency is somewhat close to 60 (50 in Europe) Hertz.
While reed-type meters are imprecise,
their operational principle is not. In lieu of mechanical resonance, we
may substitute electrical resonance and design a frequency meter using
an inductor and capacitor in the form of a tank circuit (parallel
inductor and capacitor). One or both components are made adjustable, and
a meter is placed in the circuit to indicate maximum amplitude of
voltage across the two components. The adjustment knob(s) are calibrated
to show resonant frequency for any given setting, and the frequency is
read from them after the device has been adjusted for maximum indication
on the meter. Essentially, this is a tunable filter circuit which is
adjusted and then read in a manner similar to a bridge circuit (which
must be balanced for a "null" condition and then read).
This technique is a popular one for
amateur radio operators (or at least it was before the advent of
inexpensive digital frequency instruments called counters),
especially because it doesn't require direct connection to the circuit.
So long as the inductor and/or capacitor can intercept enough stray
field (magnetic or electric, respectively) from the circuit under test
to cause the meter to indicate, it will work.
In frequency as in other types of
electrical measurement, the most accurate means of measurement are
usually those where an unknown quantity is compared against a known
standard, the basic instrument doing nothing more than indicating
when the two quantities are equal to each other. This is the basic
principle behind the DC (Wheatstone) bridge circuit and it is a sound
metrological principle applied throughout the sciences. If we have
access to an accurate frequency standard (a source of AC voltage holding
very precisely to a single frequency), then measurement of any unknown
frequency by comparison should be relatively easy.
For that frequency standard, we turn our
attention back to the tuning fork, or at least a more modern variation
of it called the quartz crystal. Quartz is a naturally occurring
mineral possessing a very interesting property called
piezoelectricity. Piezoelectric materials produce a voltage across
their length when physically stressed, and will physically deform when
an external voltage is applied across their lengths. This deformation is
very, very slight in most cases, but it does exist.
Quartz rock is elastic (springy) within
that small range of bending which an external voltage would produce,
which means that it will have a mechanical resonant frequency of its own
capable of being manifested as an electrical voltage signal. In other
words, if a chip of quartz is struck, it will "ring" with its own unique
frequency determined by the length of the chip, and that resonant
oscillation will produce an equivalent voltage across multiple points of
the quartz chip which can be tapped into by wires fixed to the surface
of the chip. In reciprocal manner, the quartz chip will tend to vibrate
most when it is "excited" by an applied AC voltage at precisely the
right frequency, just like the reeds on a vibrating-reed frequency
meter.
Chips of quartz rock can be precisely cut
for desired resonant frequencies, and that chip mounted securely inside
a protective shell with wires extending for connection to an external
electric circuit. When packaged as such, the resulting device is simply
called a crystal (or sometimes "xtal"), and its schematic
symbol looks like this:
Electrically, that quartz chip is
equivalent to a series LC resonant circuit. The dielectric properties of
quartz contribute an additional capacitive element to the equivalent
circuit, and in the end it looks something like this:
The "capacitance" and "inductance" shown
in series are merely electrical equivalents of the quartz's mechanical
resonance properties: they do not exist as discrete components within
the crystal. The capacitance shown in parallel due to the wire
connections across the dielectric (insulating) quartz body is real, and
it has an effect on the resonant response of the whole system. A full
discussion on crystal dynamics is not necessary here, but what needs to
be understood about crystals is this resonant circuit equivalence and
how it can be exploited within an oscillator circuit to achieve an
output voltage with a stable, known frequency.
Crystals, as resonant elements, typically
have much higher "Q" (quality) values than tank circuits built
from inductors and capacitors, principally due to the relative absence
of stray resistance, making their resonant frequencies very definite and
precise. Because the resonant frequency is solely dependent on the
physical properties of quartz (a very stable substance, mechanically),
the resonant frequency variation over time with a quartz crystal is
very, very low. This is how quartz movement watches obtain their
high accuracy: by means of an electronic oscillator stabilized by the
resonant action of a quartz crystal.
For laboratory applications, though, even
greater frequency stability may be desired. To achieve this, the crystal
in question may be placed in a temperature stabilized environment
(usually an oven), thus eliminating frequency errors due to thermal
expansion and contraction of the quartz.
For the ultimate in a frequency standard
though, nothing discovered thus far surpasses the accuracy of a single
resonating atom. This is the principle of the so-called atomic clock,
which uses an atom of mercury (or cesium) suspended in a vacuum, excited
by outside energy to resonate at its own unique frequency. The resulting
frequency is detected as a radio-wave signal and that forms the basis
for the most accurate clocks known to humanity. National standards
laboratories around the world maintain a few of these hyper-accurate
clocks, and broadcast frequency signals based on those atoms' vibrations
for scientists and technicians to tune in and use for frequency
calibration purposes.
Now we get to the practical part: once we
have a source of accurate frequency, how do we compare that
against an unknown frequency to obtain a measurement? One way is to use
a CRT as a frequency-comparison device. Cathode Ray Tubes typically have
means of deflecting the electron beam in the horizontal as well as the
vertical axis. If metal plates are used to electrostatically deflect the
electrons, there will be a pair of plates to the left and right of the
beam as well as a pair of plates above and below the beam.
If we allow one AC signal to deflect the
beam up and down (connect that AC voltage source to the "vertical"
deflection plates) and another AC signal to deflect the beam left and
right (using the other pair of deflection plates), patterns will be
produced on the screen of the CRT indicative of the ratio of
these two AC frequencies. These patterns are called Lissajous figures
and are a common means of comparative frequency measurement in
electronics.
If the two frequencies are the same, we
will obtain a simple figure on the screen of the CRT, the shape of that
figure being dependent upon the phase shift between the two AC signals.
Here is a sampling of Lissajous figures for two sine-wave signals of
equal frequency, shown as they would appear on the face of an
oscilloscope (an AC voltage-measuring instrument using a CRT as its
"movement"). The first picture is of the Lissajous figure formed by two
AC voltages perfectly in phase with each other:
If the two AC voltages are not in phase
with each other, a straight line will not be formed. Rather, the
Lissajous figure will take on the appearance of an oval, becoming
perfectly circular if the phase shift is exactly 90o between
the two signals, and if their amplitudes are equal:
Finally, if the two AC signals are
directly opposing one another in phase (180o shift), we will
end up with a line again, only this time it will be oriented in the
opposite direction:
When we are faced with signal frequencies
that are not the same, Lissajous figures get quite a bit more complex.
Consider the following examples and their given vertical/horizontal
frequency ratios:
The more complex the ratio between
horizontal and vertical frequencies, the more complex the Lissajous
figure. Consider the following illustration of a 3:1 frequency ratio
between horizontal and vertical:
. . . and a 3:2 frequency ratio
(horizontal = 3, vertical = 2):
In cases where the frequencies of the two
AC signals are not exactly a simple ratio of each other (but close), the
Lissajous figure will appear to "move," slowly changing orientation as
the phase angle between the two waveforms rolls between 0o
and 180o. If the two frequencies are locked in an exact
integer ratio between each other, the Lissajous figure will be stable on
the viewscreen of the CRT.
The physics of Lissajous figures limits
their usefulness as a frequency-comparison technique to cases where the
frequency ratios are simple integer values (1:1, 1:2, 1:3, 2:3, 3:4,
etc.). Despite this limitation, Lissajous figures are a popular means of
frequency comparison wherever an accessible frequency standard (signal
generator) exists.
- REVIEW:
- Some frequency meters work on the
principle of mechanical resonance, indicating frequency by relative
oscillation among a set of uniquely tuned "reeds" shaken at the
measured frequency.
- Other frequency meters use electric
resonant circuits (LC tank circuits, usually) to indicate frequency.
One or both components is made to be adjustable, with an accurately
calibrated adjustment knob, and a sensitive meter is read for maximum
voltage or current at the point of resonance.
- Frequency can be measured in a
comparative fashion, as is the case when using a CRT to generate
Lissajous figures. Reference frequency signals can be made with a
high degree of accuracy by oscillator circuits using quartz crystals
as resonant devices. For ultra precision, atomic clock signal
standards (based on the resonant frequencies of individual atoms) can
be used.
Power measurement
Power measurement in AC circuits can be
quite a bit more complex than with DC circuits for the simple reason
that phase shift makes complicates the matter beyond multiplying voltage
by current figures obtained with meters. What is needed is an instrument
able to determine the product (multiplication) of instantaneous
voltage and current. Fortunately, the common electrodynamometer movement
with its stationary and moving coil does a fine job of this.
Three phase power measurement can be
accomplished using two dynamometer movements with a common shaft linking
the two moving coils together so that a single pointer registers power
on a meter movement scale. This, obviously, makes for a rather expensive
and complex movement mechanism, but it is a workable solution.
An ingenious method of deriving an
electronic power meter (one that generates an electric signal
representing power in the system rather than merely move a pointer) is
based on the Hall effect. The Hall effect is an unusual effect first
noticed by E. H. Hall in 1879, whereby a voltage is generated along the
width of a current-carrying conductor exposed to a perpendicular
magnetic field:
The voltage generated across the width of
the flat, rectangular conductor is directly proportional to both the
magnitude of the current through it and the strength of the magnetic
field. Mathematically, it is a product (multiplication) of these two
variables. The amount of "Hall Voltage" produced for any given set of
conditions also depends on the type of material used for the flat,
rectangular conductor. It has been found that specially prepared
"semiconductor" materials produce a greater Hall voltage than do metals,
and so modern Hall Effect devices are made of these.
It makes sense then that if we were to
build a device using a Hall-effect sensor where the current through the
conductor was pushed by AC voltage from an external circuit and the
magnetic field was set up by a pair or wire coils energized by the
current of the AC power circuit, the Hall voltage would be in direct
proportion to the multiple of circuit current and voltage. Having no
mass to move (unlike an electromechanical movement), this device is able
to provide instantaneous power measurement:
Not only will the output voltage of the
Hall effect device be the representation of instantaneous power at any
point in time, but it will also be a DC signal! This is because the Hall
voltage polarity is dependent upon both the polarity of the
magnetic field and the direction of current through the conductor. If
both current direction and magnetic field polarity reverses -- as it
would ever half-cycle of the AC power -- the output voltage polarity
will stay the same.
If voltage and current in the power
circuit are 90o out of phase (a power factor of zero, meaning
no real power delivered to the load), the alternate peaks of Hall
device current and magnetic field will never coincide with each other:
when one is at its peak, the other will be zero. At those points in
time, the Hall output voltage will likewise be zero, being the product
(multiplication) of current and magnetic field strength. Between those
points in time, the Hall output voltage will fluctuate equally between
positive and negative, generating a signal corresponding to the
instantaneous absorption and release of power through the reactive load.
The net DC output voltage will be zero, indicating zero true power in
the circuit.
Any phase shift between voltage and
current in the power circuit less than 90o will result in a
Hall output voltage that oscillates between positive and negative, but
spends more time positive than negative. Consequently there will be a
net DC output voltage. Conditioned through a low-pass filter circuit,
this net DC voltage can be separated from the AC mixed with it, the
final output signal registered on a sensitive DC meter movement.
Often it is useful to have a meter to
totalize power usage over a period of time rather than instantaneously.
The output of such a meter can be set in units of Joules, or total
energy consumed, since power is a measure of work being done
per unit time. Or, more commonly, the output of the meter can be set
in units of Watt-Hours.
Mechanical means for measuring Watt-Hours
are usually centered around the concept of the motor: build an AC motor
that spins at a rate of speed proportional to the instantaneous power in
a circuit, then have that motor turn an "odometer" style counting
mechanism to keep a running total of energy consumed. The "motor" used
in these meters has a rotor made of a thin aluminum disk, with the
rotating magnetic field established by sets of coils energized by line
voltage and load current so that the rotational speed of the disk is
dependent on both voltage and current.
Power quality measurement
It used to be with large AC power systems
that "power quality" was an unheard-of concept, aside from power factor.
Almost all loads were of the "linear" variety, meaning that they did not
distort the shape of the voltage sine wave, or cause non-sinusoidal
currents to flow in the circuit. This is not true anymore. Loads
controlled by "nonlinear" electronic components are becoming more
prevalent in both home and industry, meaning that the voltages and
currents in the power system(s) feeding these loads are rich in
harmonics: what should be nice, clean sine-wave voltages and currents
are becoming highly distorted, which is equivalent to the presence of an
infinite series of high-frequency sine waves at multiples of the
fundamental power line frequency.
Excessive harmonics in an AC power system
can overheat transformers, cause exceedingly high neutral conductor
currents in three-phase systems, create electromagnetic "noise" in the
form of radio emissions that can interfere with sensitive electronic
equipment, reduce electric motor horsepower output, and can be difficult
to pinpoint. With problems like these plaguing power systems, engineers
and technicians require ways to precisely detect and measure these
conditions.
Power Quality
is the general term given to represent an AC power system's freedom from
harmonic content. A "power quality" meter is one that gives some form of
harmonic content indication.
A simple way for a technician to
determine power quality in their system without sophisticated equipment
is to compare voltage readings between two accurate voltmeters measuring
the same system voltage: one meter being an "averaging" type of unit
(such as an electromechanical movement meter) and the other being a
"true-RMS" type of unit (such as a high-quality digital meter). Remember
that "averaging" type meters are calibrated so that their scales
indicate volts RMS, based on the assumption that the AC voltage being
measured is sinusoidal. If the voltage is anything but sinewave-shaped,
the averaging meter will not register the proper value, whereas
the true-RMS meter always will, regardless of waveshape. The rule of
thumb here is this: the greater the disparity between the two meters,
the worse the power quality is, and the greater its harmonic content. A
power system with good quality power should generate equal voltage
readings between the two meters, to within the rated error tolerance of
the two instruments.
Another qualitative measurement of power
quality is the oscilloscope test: connect an oscilloscope (CRT) to the
AC voltage and observe the shape of the wave. Anything other than a
clean sine wave could be an indication of trouble:
Still, if quantitative analysis
(definite, numerical figures) is necessary, there is no substitute for
an instrument specifically designed for that purpose. Such an instrument
is called a power quality meter and is sometimes better known in
electronic circles as a low-frequency spectrum analyzer. What
this instrument does is provide a graphical representation on a CRT or
digital display screen of the AC voltage's frequency "spectrum." Just as
a prism splits a beam of white light into its constituent color
components (how much red, orange, yellow, green, and blue is in that
light), the spectrum analyzer splits a mixed-frequency signal into its
constituent frequencies, and displays the result in the form of a
histogram:
Each number on the horizontal scale of
this meter represents a harmonic of the fundamental frequency. For
American power systems, the "1" represents 60 Hz (the 1st harmonic, or
fundamental), the "3" for 180 Hz (the 3rd harmonic), the "5" for
300 Hz (the 5th harmonic), and so on. The black rectangles represent the
relative magnitudes of each of these harmonic components in the measured
AC voltage. A pure, 60 Hz sine wave would show only a tall black bar
over the "1" with no black bars showing at all over the other frequency
markers on the scale, because a pure sine wave has no harmonic content.
Power quality meters such as this might
be better referred to as overtone meters, because they are
designed to display only those frequencies known to be generated by the
power system. In three-phase AC power systems (predominant for large
power applications), even-numbered harmonics tend to be canceled out,
and so only harmonics existing in significant measure are the
odd-numbered.
Meters like these are very useful in the
hands of a skilled technician, because different types of nonlinear
loads tend to generate different spectrum "signatures" which can clue
the troubleshooter to the source of the problem. These meters work by
very quickly sampling the AC voltage at many different points along the
waveform shape, digitizing those points of information, and using a
microprocessor (small computer) to perform numerical Fourier analysis
(the Fast Fourier Transform or "FFT" algorithm) on those
data points to arrive at harmonic frequency magnitudes. The process is
not much unlike what the SPICE program tells a computer to do when
performing a Fourier analysis on a simulated circuit voltage or current
waveform.
AC bridge circuits
As we saw with DC measurement circuits,
the circuit configuration known as a bridge can be a very useful
way to measure unknown values of resistance. This is true with AC as
well, and we can apply the very same principle to the accurate
measurement of unknown impedances.
To review, the bridge circuit works as a
pair of two-component voltage dividers connected across the same source
voltage, with a null-detector meter movement connected between
them to indicate a condition of "balance" at zero volts:
Any one of the four resistors in the
above bridge can be the resistor of unknown value, and its value can be
determined by a ratio of the other three, which are "calibrated," or
whose resistances are known to a precise degree. When the bridge is in a
balanced condition (zero voltage as indicated by the null detector), the
ratio works out to be this:
One of the advantages of using a bridge
circuit to measure resistance is that the voltage of the power source is
irrelevant. Practically speaking, the higher the supply voltage, the
easier it is to detect a condition of imbalance between the four
resistors with the null detector, and thus the more sensitive it will
be. A greater supply voltage leads to the possibility of increased
measurement precision. However, there will be no fundamental error
introduced as a result of a lesser or greater power supply voltage
unlike other types of resistance measurement schemes.
Impedance bridges work the same, only the
balance equation is with complex quantities, as both magnitude
and phase across the components of the two dividers must be equal in
order for the null detector to indicate "zero." The null detector, of
course, must be a device capable of detecting very small AC voltages. An
oscilloscope is often used for this, although very sensitive
electromechanical meter movements and even headphones (small speakers)
may be used if the source frequency is within audio range.
One way to maximize the effectiveness of
audio headphones as a null detector is to connect them to the signal
source through an impedance-matching transformer. Headphone speakers are
typically low-impedance units (8 Ω), requiring substantial current to
drive, and so a step-down transformer helps "match" low-current signals
to the impedance of the headphone speakers. An audio output transformer
works well for this purpose:
Using a pair of headphones that
completely surround the ears (the "closed-cup" type), I've been able to
detect currents of less than 0.1 µA with this simple detector circuit.
Roughly equal performance was obtained using two different step-down
transformers: a small power transformer (120/6 volt ratio), and an audio
output transformer (1000:8 ohm impedance ratio). With the pushbutton
switch in place to interrupt current, this circuit is usable for
detecting signals from DC to over 2 MHz: even if the frequency is far
above or below the audio range, a "click" will be heard from the
headphones each time the switch is pressed and released.
Connected to a resistive bridge, the
whole circuit looks like this:
Listening to the headphones as one or
more of the resistor "arms" of the bridge is adjusted, a condition of
balance will be realized when the headphones fail to produce "clicks"
(or tones, if the bridge's power source frequency is within audio range)
as the switch is actuated.
When describing general AC bridges, where
impedances and not just resistances must be in proper ratio for
balance, it is sometimes helpful to draw the respective bridge legs in
the form of box-shaped components, each one with a certain impedance:
For this general form of AC bridge to
balance, the impedance ratios of each branch must be equal:
Again, it must be stressed that the
impedance quantities in the above equation must be complex,
accounting for both magnitude and phase angle. It is insufficient that
the impedance magnitudes alone be balanced; without phase angles in
balance as well, there will still be voltage across the terminals of the
null detector and the bridge will not be balanced.
Bridge circuits can be constructed to
measure just about any device value desired, be it capacitance,
inductance, resistance, or even "Q." As always in bridge measurement
circuits, the unknown quantity is always "balanced" against a known
standard, obtained from a high-quality, calibrated component that can be
adjusted in value until the null detector device indicates a condition
of balance. Depending on how the bridge is set up, the unknown
component's value may be determined directly from the setting of the
calibrated standard, or derived from that standard through a
mathematical formula.
A couple of simple bridge circuits are
shown below, one for inductance and one for capacitance:
Simple "symmetrical" bridges such as
these are so named because they exhibit symmetry (mirror-image
similarity) from left to right. The two bridge circuits shown above are
balanced by adjusting the calibrated reactive component (Ls
or Cs). They are a bit simplified from their real-life
counterparts, as practical symmetrical bridge circuits often have a
calibrated, variable resistor in series or parallel with the reactive
component to balance out stray resistance in the unknown component. But,
in the hypothetical world of perfect components, these simple bridge
circuits do just fine to illustrate the basic concept.
An example of a little extra complexity
added to compensate for real-world effects can be found in the so-called
Wien bridge, which uses a parallel capacitor-resistor standard
impedance to balance out an unknown series capacitor-resistor
combination. All capacitors have some amount of internal resistance, be
it literal or equivalent (in the form of dielectric heating losses)
which tend to spoil their otherwise perfectly reactive natures. This
internal resistance may be of interest to measure, and so the Wien
bridge attempts to do so by providing a balancing impedance that isn't
"pure" either:
Being that there are two standard
components to be adjusted (a resistor and a capacitor) this bridge will
take a little more time to balance than the others we've seen so far.
The combined effect of Rs and Cs is to alter the
magnitude and phase angle until the bridge achieves a condition of
balance. Once that balance is achieved, the settings of Rs
and Cs can be read from their calibrated knobs, the parallel
impedance of the two determined mathematically, and the unknown
capacitance and resistance determined mathematically from the balance
equation (Z1/Z2 = Z3/Z4).
It is assumed in the operation of the
Wien bridge that the standard capacitor has negligible internal
resistance, or at least that resistance is already known so that it can
be factored into the balance equation. Wien bridges are useful for
determining the values of "lossy" capacitor designs like electrolytics,
where the internal resistance is relatively high. They are also used as
frequency meters, because the balance of the bridge is
frequency-dependent. When used in this fashion, the capacitors are made
fixed (and usually of equal value) and the top two resistors are made
variable and are adjusted by means of the same knob.
An interesting variation on this theme is
found in the next bridge circuit, used to precisely measure inductances.
This ingenious bridge circuit is known as
the Maxwell-Wien bridge (sometimes known plainly as the
Maxwell bridge), and is used to measure unknown inductances in terms
of calibrated resistance and capacitance. Calibration-grade inductors
are more difficult to manufacture than capacitors of similar precision,
and so the use of a simple "symmetrical" inductance bridge is not always
practical. Because the phase shifts of inductors and capacitors are
exactly opposite each other, a capacitive impedance can balance out an
inductive impedance if they are located in opposite legs of a bridge, as
they are here.
Another advantage of using a Maxwell
bridge to measure inductance rather than a symmetrical inductance bridge
is the elimination of measurement error due to mutual inductance between
two inductors. Magnetic fields can be difficult to shield, and even a
small amount of coupling between coils in a bridge can introduce
substantial errors in certain conditions. With no second inductor to
react with in the Maxwell bridge, this problem is eliminated.
For easiest operation, the standard
capacitor (Cs) and the resistor in parallel with it (Rs)
are made variable, and both must be adjusted to achieve balance.
However, the bridge can be made to work if the capacitor is fixed
(non-variable) and more than one resistor made variable (at least the
resistor in parallel with the capacitor, and one of the other two).
However, in the latter configuration it takes more trial-and-error
adjustment to achieve balance, as the different variable resistors
interact in balancing magnitude and phase.
Unlike the plain Wien bridge, the balance
of the Maxwell-Wien bridge is independent of source frequency, and in
some cases this bridge can be made to balance in the presence of mixed
frequencies from the AC voltage source, the limiting factor being the
inductor's stability over a wide frequency range.
There are more variations beyond these
designs, but a full discussion is not warranted here. General-purpose
impedance bridge circuits are manufactured which can be switched into
more than one configuration for maximum flexibility of use.
A potential problem in sensitive AC
bridge circuits is that of stray capacitance between either end of the
null detector unit and ground (earth) potential. Because capacitances
can "conduct" alternating current by charging and discharging, they form
stray current paths to the AC voltage source which may affect bridge
balance:
The problem is worsened if the AC voltage
source is firmly grounded at one end, the total stray impedance for
leakage currents made far less and any leakage currents through these
stray capacitances made greater as a result:
One way of greatly reducing this effect
is to keep the null detector at ground potential, so there will be no AC
voltage between it and the ground, and thus no current through stray
capacitances. However, directly connecting the null detector to ground
is not an option, as it would create a direct current path for
stray currents, which would be worse than any capacitive path. Instead,
a special voltage divider circuit called a Wagner ground or
Wagner earth may be used to maintain the null detector at ground
potential without the need for a direct connection to the null detector.
The Wagner earth circuit is nothing more
than a voltage divider, designed to have the voltage ratio and phase
shift as each side of the bridge. Because the midpoint of the Wagner
divider is directly grounded, any other divider circuit (including
either side of the bridge) having the same voltage proportions and
phases as the Wagner divider, and powered by the same AC voltage source,
will be at ground potential as well. Thus, the Wagner earth divider
forces the null detector to be at ground potential, without a direct
connection between the detector and ground.
There is often a provision made in the
null detector connection to confirm proper setting of the Wagner earth
divider circuit: a two-position switch, so that one end of the null
detector may be connected to either the bridge or the Wagner earth. When
the null detector registers zero signal in both switch positions, the
bridge is not only guaranteed to be balanced, but the null detector is
also guaranteed to be at zero potential with respect to ground, thus
eliminating any errors due to leakage currents through stray
detector-to-ground capacitances:
- REVIEW:
- AC bridge circuits work on the same
basic principle as DC bridge circuits: that a balanced ratio of
impedances (rather than resistances) will result in a "balanced"
condition as indicated by the null-detector device.
- Null detectors for AC bridges may be
sensitive electromechanical meter movements, oscilloscopes (CRT's),
headphones (amplified or unamplified), or any other device capable of
registering very small AC voltage levels. Like DC null detectors, its
only required point of calibration accuracy is at zero.
- AC bridge circuits can be of the
"symmetrical" type where an unknown impedance is balanced by a
standard impedance of similar type on the same side (top or bottom) of
the bridge. Or, they can be "nonsymmetrical," using parallel
impedances to balance series impedances, or even capacitances
balancing out inductances.
- AC bridge circuits often have more
than one adjustment, since both impedance magnitude and phase
angle must be properly matched to balance.
- Some impedance bridge circuits are
frequency-sensitive while others are not. The frequency-sensitive
types may be used as frequency measurement devices if all component
values are accurately known.
- A Wagner earth or Wagner
ground is a voltage divider circuit added to AC bridges to help
reduce errors due to stray capacitance coupling the null detector to
ground.
AC instrumentation transducers
Just as devices have been made to measure
certain physical quantities and repeat that information in the form of
DC electrical signals (thermocouples, strain gauges, pH probes, etc.),
special devices have been made that do the same with AC.
It is often necessary to be able to
detect and transmit the physical position of mechanical parts via
electrical signals. This is especially true in the fields of automated
machine tool control and robotics. A simple and easy way to do this is
with a potentiometer:
However, potentiometers have their own
unique problems. For one, they rely on physical contact between the
"wiper" and the resistance strip, which means they suffer the effects of
physical wear over time. As potentiometers wear, their proportional
output versus shaft position becomes less and less certain. You might
have already experienced this effect when adjusting the volume control
on an old radio: when twisting the knob, you might hear "scratching"
sounds coming out of the speakers. Those noises are the result of poor
wiper contact in the volume control potentiometer.
Also, this physical contact between wiper
and strip creates the possibility of arcing (sparking) between the two
as the wiper is moved. With most potentiometer circuits, the current is
so low that wiper arcing is negligible, but it is a possibility to be
considered. If the potentiometer is to be operated in an environment
where combustible vapor or dust is present, this potential for arcing
translates into a potential for an explosion!
Using AC instead of DC, we are able to
completely avoid sliding contact between parts if we use a variable
transformer instead of a potentiometer. Devices made for this
purpose are called LVDT's, which stands for Linear Variable
Differential Transformers. The design of an LVDT looks
like this:
Obviously, this device is a
transformer: it has a single primary winding powered by an external
source of AC voltage, and two secondary windings connected in
series-bucking fashion. It is variable because the core is free
to move between the windings. It is differential because of the
way the two secondary windings are connected. Being arranged to oppose
each other (180o out of phase) means that the output of this
device will be the difference between the voltage output of the
two secondary windings. When the core is centered and both windings are
outputting the same voltage, the net result at the output terminals will
be zero volts. It is called linear because the core's freedom of
motion is straight-line.
The AC voltage output by an LVDT
indicates the position of the movable core. Zero volts means that the
core is centered. The further away the core is from center position, the
greater percentage of input ("excitation") voltage will be seen at the
output. The phase of the output voltage relative to the excitation
voltage indicates which direction from center the core is offset.
The primary advantage of an LVDT over a
potentiometer for position sensing is the absence of physical contact
between the moving and stationary parts. The core does not contact the
wire windings, but slides in and out within a nonconducting tube. Thus,
the LVDT does not "wear" like a potentiometer, nor is there the
possibility of creating an arc.
Excitation of the LVDT is typically 10
volts RMS or less, at frequencies ranging from power line to the high
audio (20 kHz) range. One potential disadvantage of the LVDT is its
response time, which is mostly dependent on the frequency of the AC
voltage source. If very quick response times are desired, the frequency
must be higher to allow whatever voltage-sensing circuits enough cycles
of AC to determine voltage level as the core is moved. To illustrate the
potential problem here, imagine this exaggerated scenario: an LVDT
powered by a 60 Hz voltage source, with the core being moved in and out
hundreds of times per second. The output of this LVDT wouldn't even look
like a sine wave because the core would be moved throughout its range of
motion before the AC source voltage could complete a single cycle! It
would be almost impossible to determine instantaneous core position if
it moves faster than the instantaneous source voltage does.
A variation on the LVDT is the RVDT, or
Rotary Variable Differential Transformer.
This device works on almost the same principle, except that the core
revolves on a shaft instead of moving in a straight line. RVDT's can be
constructed for limited motion of 360o (full-circle) motion.
Continuing with this principle, we have
what is known as a Synchro or Selsyn, which is a device
constructed a lot like a wound-rotor polyphase AC motor or generator.
The rotor is free to revolve a full 360o, just like a motor.
On the rotor is a single winding connected to a source of AC voltage,
much like the primary winding of an LVDT. The stator windings are
usually in the form of a three-phase Y, although synchros with more than
three phases have been built:
Voltages induced in the stator windings
from the rotor's AC excitation are not phase-shifted by 120o
as in a real three-phase generator. If the rotor were energized with DC
current rather than AC and the shaft spun continuously, then the
voltages would be true three-phase. But this is not how a synchro is
designed to be operated. Rather, this is a position-sensing
device much like an RVDT, except that its output signal is much more
definite. With the rotor energized by AC, the stator winding voltages
will be proportional in magnitude to the angular position of the rotor,
phase either 0o or 180o shifted, like a regular
LVDT or RVDT. You could think of it as a transformer with one primary
winding and three secondary windings, each secondary winding oriented at
a unique angle. As the rotor is slowly turned, each winding in turn will
line up directly with the rotor, producing full voltage, while the other
windings will produce something less than full voltage.
Synchros are often used in pairs. With
their rotors connected in parallel and energized by the same AC voltage
source, their shafts will match position to a high degree of accuracy:
Such "transmitter/receiver" pairs have
been used on ships to relay rudder position, or to relay navigational
gyro position over fairly long distances. The only difference between
the "transmitter" and the "receiver" is which one gets turned by an
outside force. The "receiver" can just as easily be used as the
"transmitter" by forcing its shaft to turn and letting the synchro on
the left match position.
If the receiver's rotor is left unpowered,
it will act as a position-error detector, generating an AC voltage at
the rotor if the shaft is anything other than 90o or 270o
shifted from the shaft position of the transmitter. The receiver rotor
will no longer generate any torque and consequently will no longer
automatically match position with the transmitter's:
This can be thought of almost as a sort
of bridge circuit that achieves balance only if the receiver shaft is
brought to one of two (matching) positions with the transmitter shaft.
One rather ingenious application of the
synchro is in the creation of a phase-shifting device, provided that the
stator is energized by three-phase AC:
As the synchro's rotor is turned, the
rotor coil will progressively align with each stator coil, their
respective magnetic fields being 120o phase-shifted from one
another. In between those positions, these phase-shifted fields will mix
to produce a rotor voltage somewhere between 0o, 120o,
or 240o shift. The practical result is a device capable of
providing an infinitely variable-phase AC voltage with the twist of a
knob (attached to the rotor shaft).
So far the transducers discussed have all
been of the inductive variety. However, it is possible to make
transducers which operate on variable capacitance as well, AC being used
to sense the change in capacitance and generate a variable output
voltage.
Remember that the capacitance between two
conductive surfaces varies with three major factors: the overlapping
area of those two surfaces, the distance between them, and the
dielectric constant of the material in between the surfaces. If two out
of three of these variables can be fixed (stabilized) and the third
allowed to vary, then any measurement of capacitance between the
surfaces will be solely indicative of changes in that third variable.
Medical researchers have long made use of
capacitive sensing to detect physiological changes in living bodies. As
early as 1907, a German researcher named H. Cremer placed two metal
plates on either side of a beating frog heart and measured the
capacitance changes resulting from the heart alternately filling and
emptying itself of blood. Similar measurements have been performed on
human beings with metal plates placed on the chest and back, recording
respiratory and cardiac action by means of capacitance changes. For more
precise capacitive measurements of organ activity, metal probes have
been inserted into organs (especially the heart) on the tips of catheter
tubes, capacitance being measured between the metal probe and the body
of the subject. With a sufficiently high AC excitation frequency and
sensitive enough voltage detector, not just the pumping action but also
the sounds of the active heart may be readily interpreted.
Like inductive transducers, capacitive
transducers can also be made to be self-contained units, unlike the
direct physiological examples described above. Some transducers work by
making one of the capacitor plates movable, either in such a way as to
vary the overlapping area or the distance between the plates. Other
transducers work by moving a dielectric material in and out between two
fixed plates:
Transducers with greater sensitivity and
immunity to changes in other variables can be obtained by way of
differential design, much like the concept behind the LVDT (Linear
Variable Differential Transformer). Here are a few examples of
differential capacitive transducers:
As you can see, all of the differential
devices shown in the above illustration have three wire
connections rather than two: one wire for each of the "end" plates and
one for the "common" plate. As the capacitance between one of the "end"
plates and the "common" plate changes, the capacitance between the other
"end" plate and the "common" plate is such to change in the opposite
direction. This kind of transducer lends itself very well to
implementation in a bridge circuit:
Capacitive transducers provide relatively
small capacitances for a measurement circuit to operate with, typically
in the picofarad range. Because of this, high power supply
frequencies (in the megahertz range!) are usually required to reduce
these capacitive reactances to reasonable levels. Given the small
capacitances provided by typical capacitive transducers, stray
capacitances have the potential of being major sources of measurement
error. Good conductor shielding is essential for reliable and
accurate capacitive transducer circuitry!
The bridge circuit is not the only way to
effectively interpret the differential capacitance output of such a
transducer, but it is one of the simplest to implement and understand.
As with the LVDT, the voltage output of the bridge is proportional to
the displacement of the transducer action from its center position, and
the direction of offset will be indicated by phase shift. This kind of
bridge circuit is similar in function to the kind used with strain
gauges: it is not intended to be in a "balanced" condition all the time,
but rather the degree of imbalance represents the magnitude of the
quantity being measured.
An interesting alternative to the bridge
circuit for interpreting differential capacitance is the twin-T.
It requires the use of diodes, those "one-way valves" for electric
current mentioned earlier in the chapter:
This circuit might be better understood
if re-drawn to resemble more of a bridge configuration:
Capacitor C1 is charged by the
AC voltage source during every positive half-cycle (positive as measured
in reference to the ground point), while C2 is charged during
every negative half-cycle. While one capacitor is being charged, the
other capacitor discharges (at a slower rate than it was charged)
through the three-resistor network. As a consequence, C1
maintains a positive DC voltage with respect to ground, and C2
a negative DC voltage with respect to ground.
If the capacitive transducer is displaced
from center position, one capacitor will increase in capacitance while
the other will decrease. This has little effect on the peak voltage
charge of each capacitor, as there is negligible resistance in the
charging current path from source to capacitor, resulting in a very
short time constant (τ). However, when it comes time to discharge
through the resistors, the capacitor with the greater capacitance value
will hold its charge longer, resulting in a greater average DC voltage
over time than the lesser-value capacitor.
The load resistor (Rload),
connected at one end to the point between the two equal-value resistors
(R) and at the other end to ground, will drop no DC voltage if the two
capacitors' DC voltage charges are equal in magnitude. If, on the other
hand, one capacitor maintains a greater DC voltage charge than the other
due to a difference in capacitance, the load resistor will drop a
voltage proportional to the difference between these voltages. Thus,
differential capacitance is translated into a DC voltage across the load
resistor.
Across the load resistor, there is both
AC and DC voltage present, with only the DC voltage being significant to
the difference in capacitance. If desired, a low-pass filter may be
added to the output of this circuit to block the AC, leaving only a DC
signal to be interpreted by measurement circuitry:
As a measurement circuit for differential
capacitive sensors, the twin-T configuration enjoys many advantages over
the standard bridge configuration. First and foremost, transducer
displacement is indicated by a simple DC voltage, not an AC voltage
whose magnitude and phase must be interpreted to tell which
capacitance is greater. Furthermore, given the proper component values
and power supply output, this DC output signal may be strong enough to
directly drive an electromechanical meter movement, eliminating the need
for an amplifier circuit. Another important advantage is that all
important circuit elements have one terminal directly connected to
ground: the source, the load resistor, and both capacitors are all
ground-referenced. This helps minimize the ill effects of stray
capacitance commonly plaguing bridge measurement circuits, likewise
eliminating the need for compensatory measures such as the Wagner earth.
This circuit is also easy to specify
parts for. Normally, a measurement circuit incorporating complementary
diodes requires the selection of "matched" diodes for good accuracy. Not
so with this circuit! So long as the power supply voltage is
significantly greater than the deviation in voltage drop between the two
diodes, the effects of mismatch are minimal and contribute little to
measurement error. Furthermore, supply frequency variations have a
relatively low impact on gain (how much output voltage is developed for
a given amount of transducer displacement), and square-wave supply
voltage works as well as sine-wave, assuming a 50% duty cycle (equal
positive and negative half-cycles), of course.
Personal experience with using this
circuit has confirmed its impressive performance. Not only is it easy to
prototype and test, but its relative insensitivity to stray capacitance
and its high output voltage as compared to traditional bridge circuits
makes it a very robust alternative.
Contributors
Contributors to this chapter are listed
in chronological order of their contributions, from most recent to
first.
Jason Starck
(June 2000): HTML document formatting, which led to a much
better-looking second edition.
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