Chapter 3.3
DC voltmeters
• Given a basic PMMC movement with sensitivity IFSD and coil resistance Rm, What is
the maximum voltage that can be measured?
IFSD
VFSD
Rm
• Clearly, this value VFSD , is IFSD Rm, since this is the voltage that will cause IFSD to flow
in the PMMC ammeter.
• For a typical 50µA, 2kΩ PMMC VFSD is 0.1V
• As before, the consideration is how can we extend this range?
• With the ammeter a shunt was added to divert the excess current from the PMMC
meter. Here we want to limit the current caused by voltages higher than VFSD to be
<= IFSD. We therefore want to add resistance in series with the movement
• We call this resistor a multiplier. From this arrangement, we can then say the
following:
RT =
where
VT
I FSD
RT = RS + Rm
RS = RT − Rm
V
RS = T − Rm
I FSD
Example
Convert a 50µA, 3kΩ PMMC into a 0-10VDC voltmeter.
10V
RS =
− 3kΩ = 197kΩ
50 ×10 − 6
The voltmeter looks like this:
197k
3k
IFSD
0-10V
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• What is the total resistance of the voltmeter?
– 200k
Voltmeter Sensitivity
• We defined the sensitivity of a measurement system before.
– For PMMC it is usually taken as IFSD
• For a voltmeter it is defined as:
Total Resistance of meter
S=
Range of voltmeter
• The units are Ω /V
• Note that this can also be stated as:
1
S=
I FSD
• Therefore for the above example S = 20kΩ/V
• We can use this to derive an alternative expression for the multiplier resistor, namely:
RS = S × Range − Rm
• Revisiting our example, we get:
RS = S × Range − Rm
Ω
RS = 20 × 103 ×10V − 3 ×103 Ω
V
∴ RS = 197kΩ
Multi-range voltmeters
• How can we extend the range of the basic voltmeter to encompass several ranges?
• Consider this:
Rm
V1
R1
R2
R3
V2
V3
V4
Co
m
• As before, we can add multipliers for each range to create a multi-range voltmeter.
• Does this method suffer from any disadvantages like in the analogous case for the
ammeter?
– Does it require a make before break switch?
• Let us examine another calculation:
Example:
Using a 1mA, 100Ω PMMC movement, design a multi- range voltmeter with the
following ranges: 0-10V, 0-50V, 0-250V and 0-500V.
Solution:
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What is the maximum voltage measurable by the given PMMC?
V= 1mA × 100Ω = 0.1V
Therefore we need a multiplier for all ranges
Rm
R1
10
R2
50
R3
250
R4
500
Com
• From before:
RS = S × Range − Rm
• S = 1/1mA = 1000Ω/V
• Therefore:
• Similarly:
R1 = S × Range − Rm
R1 = 1000Ω / V ×10 −100
∴ R1 = 9900Ω
R2 = S × Range − Rm
R2 = 1000Ω / V × 50 − 100
∴ R2 = 49.9 kΩ
R3 = S × Range − Rm
R3 = 1000Ω / V × 250 − 100
∴ R3 = 249.9 kΩ; and
R4 = 499.9 kΩ
• Summarising the values obtained:
R1
9900
R2
49.9k
R3
249.9k
R4
499.9k
• Note the non-standard values for the shunt resistors.
• This is the main disadvantage of this type of approach to making a multi-range
voltmeter.
• Let us consider another approach
• Using the same PMMC as in the previous example, but with the following circuit.
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Rm
R1
R2
2
R3
R4
3
1
4
5
• Here the multiplier is composed of a series connection of resistors.
• Would the input ranges be increasing from 1 to 5 or from 5 to 1?
• From our previous discussions, position 1 would represent the basic 0.1V range of the
PMMC.
• For position 2 the 0-10V range:
R1 = S × Range − Rm
R1 = 1000Ω / V ×10 −100
∴ R1 = 9900Ω
• For position 3, the 0 to 50V range:
RS = S × Range − Rm
RS = 1000Ω / V × 50 − 100
∴ RS = 49.9kΩ
But RS = R2 + R1 ;
∴ R2 = 49.9k − 9.9k = 40k
• For position 4, the 0 to 250V range:
RS = S × Range − Rm
RS = 1000Ω / V × 250 −100
∴ RS = 249.9kΩ
But RS = R3 + R2 + R1 ;
∴ R3 = 249.9k − 40k − 9.9 k = 200 k
• Finally for position 5, the 0 to 500V range:
RS = S × Range − Rm
RS = 1000Ω / V × 500 − 100
∴ RS = 499.9kΩ
But RS = R4 + R3 + R2 + R1 ;
∴ R4 = 499.9k − 200 k − 40k − 9.9k = 250 k
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• Summarising as before:
R1
Separate
Multipliers
9900
Series
Multiplier
9900
R2
49.9k
40k
R3
249.9k
200k
R4
499.9k
250k
• Note that in the latter method, only the first resistor, 9.9k, has an odd value.
• The remaining values, 40k, 200k and 250k, are all commercially obtainable
• When separate multipliers are used for each range, the resulting values for the
resistors, 49.9k, 249.9k and 499.9k, are be non-standard.
• The series multiplier suffers the same disadvantage as the Ayrton shunt should one
resistor open circuit or vary its value.
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