Voltmeter impact on
measured circuit
Every meter impacts the circuit it is
measuring to some extent, just as any tire-pressure gauge
changes the measured tire pressure slightly as some air is
let out to operate the gauge. While some impact is
inevitable, it can be minimized through good meter design.
Since voltmeters are always connected in
parallel with the component or components under test, any
current through the voltmeter will contribute to the overall
current in the tested circuit, potentially affecting the
voltage being measured. A perfect voltmeter has infinite
resistance, so that it draws no current from the circuit
under test. However, perfect voltmeters only exist in the
pages of textbooks, not in real life! Take the following
voltage divider circuit as an extreme example of how a
realistic voltmeter might impact the circuit it's measuring:
With no voltmeter connected to the circuit,
there should be exactly 12 volts across each 250 MΩ resistor
in the series circuit, the two equal-value resistors
dividing the total voltage (24 volts) exactly in half.
However, if the voltmeter in question has a lead-to-lead
resistance of 10 MΩ (a common amount for a modern digital
voltmeter), its resistance will create a parallel subcircuit
with the lower resistor of the divider when connected:
This effectively reduces the lower
resistance from 250 MΩ to 9.615 MΩ (250 MΩ and 10 MΩ in
parallel), drastically altering voltage drops in the
circuit. The lower resistor will now have far less voltage
across it than before, and the upper resistor far more.
A voltage divider with resistance values of
250 MΩ and 9.615 MΩ will divide 24 volts into portions of
23.1111 volts and 0.8889 volts, respectively. Since the
voltmeter is part of that 9.615 MΩ resistance, that is what
it will indicate: 0.8889 volts.
Now, the voltmeter can only indicate the
voltage it's connected across. It has no way of "knowing"
there was a potential of 12 volts dropped across the lower
250 MΩ resistor before it was connected across it.
The very act of connecting the voltmeter to the circuit
makes it part of the circuit, and the voltmeter's own
resistance alters the resistance ratio of the voltage
divider circuit, consequently affecting the voltage being
measured.
Imagine using a tire pressure gauge that
took so great a volume of air to operate that it would
deflate any tire it was connected to. The amount of air
consumed by the pressure gauge in the act of measurement is
analogous to the current taken by the voltmeter movement to
move the needle. The less air a pressure gauge requires to
operate, the less it will deflate the tire under test. The
less current drawn by a voltmeter to actuate the needle, the
less it will burden the circuit under test.
This effect is called loading, and it
is present to some degree in every instance of voltmeter
usage. The scenario shown here is worst-case, with a
voltmeter resistance substantially lower than the
resistances of the divider resistors. But there always will
be some degree of loading, causing the meter to indicate
less than the true voltage with no meter connected.
Obviously, the higher the voltmeter resistance, the less
loading of the circuit under test, and that is why an ideal
voltmeter has infinite internal resistance.
Voltmeters with electromechanical movements
are typically given ratings in "ohms per volt" of range to
designate the amount of circuit impact created by the
current draw of the movement. Because such meters rely on
different values of multiplier resistors to give different
measurement ranges, their lead-to-lead resistances will
change depending on what range they're set to. Digital
voltmeters, on the other hand, often exhibit a constant
resistance across their test leads regardless of range
setting (but not always!), and as such are usually rated
simply in ohms of input resistance, rather than "ohms per
volt" sensitivity.
What "ohms per volt" means is how many ohms
of lead-to-lead resistance for every volt of range
setting on the selector switch. Let's take our example
voltmeter from the last section as an example:
On the 1000 volt scale, the total resistance
is 1 MΩ (999.5 kΩ + 500Ω), giving 1,000,000 Ω per 1000 volts
of range, or 1000 ohms per volt (1 kΩ/V). This ohms-per-volt
"sensitivity" rating remains constant for any range of this
meter:
The astute observer will notice that the
ohms-per-volt rating of any meter is determined by a single
factor: the full-scale current of the movement, in this case
1 mA. "Ohms per volt" is the mathematical reciprocal of
"volts per ohm," which is defined by Ohm's Law as current
(I=E/R). Consequently, the full-scale current of the
movement dictates the Ω/volt sensitivity of the meter,
regardless of what ranges the designer equips it with
through multiplier resistors. In this case, the meter
movement's full-scale current rating of 1 mA gives it a
voltmeter sensitivity of 1000 Ω/V regardless of how we range
it with multiplier resistors.
To minimize the loading of a voltmeter on
any circuit, the designer must seek to minimize the current
draw of its movement. This can be accomplished by
re-designing the movement itself for maximum sensitivity
(less current required for full-scale deflection), but the
tradeoff here is typically ruggedness: a more sensitive
movement tends to be more fragile.
Another approach is to electronically boost
the current sent to the movement, so that very little
current needs to be drawn from the circuit under test. This
special electronic circuit is known as an amplifier,
and the voltmeter thus constructed is an amplified
voltmeter.
The internal workings of an amplifier are
too complex to be discussed at this point, but suffice it to
say that the circuit allows the measured voltage to
control how much battery current is sent to the meter
movement. Thus, the movement's current needs are supplied by
a battery internal to the voltmeter and not by the circuit
under test. The amplifier still loads the circuit under test
to some degree, but generally hundreds or thousands of times
less than the meter movement would by itself.
Before the advent of semiconductors known as
"field-effect transistors," vacuum tubes were used as
amplifying devices to perform this boosting. Such
vacuum-tube voltmeters, or (VTVM's) were once
very popular instruments for electronic test and
measurement. Here is a photograph of a very old VTVM, with
the vacuum tube exposed!
Now, solid-state transistor amplifier
circuits accomplish the same task in digital meter designs.
While this approach (of using an amplifier to boost the
measured signal current) works well, it vastly complicates
the design of the meter, making it nearly impossible for the
beginning electronics student to comprehend its internal
workings.
A final, and ingenious, solution to the
problem of voltmeter loading is that of the
potentiometric or null-balance instrument. It
requires no advanced (electronic) circuitry or sensitive
devices like transistors or vacuum tubes, but it does
require greater technician involvement and skill. In a
potentiometric instrument, a precision adjustable voltage
source is compared against the measured voltage, and a
sensitive device called a null detector is used to
indicate when the two voltages are equal. In some circuit
designs, a precision potentiometer is used to provide
the adjustable voltage, hence the label potentiometric.
When the voltages are equal, there will be zero current
drawn from the circuit under test, and thus the measured
voltage should be unaffected. It is easy to show how this
works with our last example, the high-resistance voltage
divider circuit:
The "null detector" is a sensitive device
capable of indicating the presence of very small voltages.
If an electromechanical meter movement is used as the null
detector, it will have a spring-centered needle that can
deflect in either direction so as to be useful for
indicating a voltage of either polarity. As the purpose of a
null detector is to accurately indicate a condition of
zero voltage, rather than to indicate any specific
(nonzero) quantity as a normal voltmeter would, the scale of
the instrument used is irrelevant. Null detectors are
typically designed to be as sensitive as possible in order
to more precisely indicate a "null" or "balance" (zero
voltage) condition.
An extremely simple type of null detector is
a set of audio headphones, the speakers within acting as a
kind of meter movement. When a DC voltage is initially
applied to a speaker, the resulting current through it will
move the speaker cone and produce an audible "click."
Another "click" sound will be heard when the DC source is
disconnected. Building on this principle, a sensitive null
detector may be made from nothing more than headphones and a
momentary contact switch:
If a set of "8 ohm" headphones are used for
this purpose, its sensitivity may be greatly increased by
connecting it to a device called a transformer. The
transformer exploits principles of electromagnetism to
"transform" the voltage and current levels of electrical
energy pulses. In this case, the type of transformer used is
a step-down transformer, and it converts low-current
pulses (created by closing and opening the pushbutton switch
while connected to a small voltage source) into
higher-current pulses to more efficiently drive the speaker
cones inside the headphones. An "audio output" transformer
with an impedance ratio of 1000:8 is ideal for this purpose.
The transformer also increases detector sensitivity by
accumulating the energy of a low-current signal in a
magnetic field for sudden release into the headphone
speakers when the switch is opened. Thus, it will produce
louder "clicks" for detecting smaller signals:
Connected to the potentiometric circuit as a
null detector, the switch/transformer/headphone arrangement
is used as such:
The purpose of any null detector is to act
like a laboratory balance scale, indicating when the two
voltages are equal (absence of voltage between points 1 and
2) and nothing more. The laboratory scale balance beam
doesn't actually weight anything; rather, it simply
indicates equality between the unknown mass and the
pile of standard (calibrated) masses.
Likewise, the null detector simply indicates
when the voltage between points 1 and 2 are equal, which
(according to Kirchhoff's Voltage Law) will be when the
adjustable voltage source (the battery symbol with a
diagonal arrow going through it) is precisely equal in
voltage to the drop across R2.
To operate this instrument, the technician
would manually adjust the output of the precision voltage
source until the null detector indicated exactly zero (if
using audio headphones as the null detector, the technician
would repeatedly press and release the pushbutton switch,
listening for silence to indicate that the circuit was
"balanced"), and then note the source voltage as indicated
by a voltmeter connected across the precision voltage
source, that indication being representative of the voltage
across the lower 250 MΩ resistor:
The voltmeter used to directly measure the
precision source need not have an extremely high Ω/V
sensitivity, because the source will supply all the current
it needs to operate. So long as there is zero voltage across
the null detector, there will be zero current between points
1 and 2, equating to no loading of the divider circuit under
test.
It is worthy to reiterate the fact that this
method, properly executed, places almost zero load
upon the measured circuit. Ideally, it places absolutely no
load on the tested circuit, but to achieve this ideal goal
the null detector would have to have absolutely zero
voltage across it, which would require an infinitely
sensitive null meter and a perfect balance of voltage from
the adjustable voltage source. However, despite its
practical inability to achieve absolute zero loading, a
potentiometric circuit is still an excellent technique for
measuring voltage in high-resistance circuits. And unlike
the electronic amplifier solution, which solves the problem
with advanced technology, the potentiometric method achieves
a hypothetically perfect solution by exploiting a
fundamental law of electricity (KVL).
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REVIEW:
-
An ideal voltmeter has infinite
resistance.
-
Too low of an internal resistance in a
voltmeter will adversely affect the circuit being
measured.
-
Vacuum tube voltmeters (VTVM's),
transistor voltmeters, and potentiometric circuits are all
means of minimizing the load placed on a measured circuit.
Of these methods, the potentiometric ("null-balance")
technique is the only one capable of placing zero
load on the circuit.
-
A null detector is a device built
for maximum sensitivity to small voltages or currents. It
is used in potentiometric voltmeter circuits to indicate
the absence of voltage between two points, thus
indicating a condition of balance between an adjustable
voltage source and the voltage being measured.
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