RICHLAND COLLEGE
School of
Engineering Business & Technology
INTC 1307
Instrumentation Test Equipment
Teaching Unit 2
Rev. 0 – W. Slonecker
Rev. 1 – (8/26/2012)– J. Bradbury
Direct Current Meters
Unit 2 – Direct Current Meters
Objectives:
Describe the construction of a D’Arsonval meter movement.
Explain the operation of a D’Arsonval meter movement.
Determine the effects of shunts across the meter movement.
Understand the purpose of resistance in series with the meter movement.
Define meter sensitivity.
Analyze a circuit in terms of voltmeter loading or ammeter insertion errors.
Understand the construction of an ammeter and voltmeter.
Understand the construction and operation of a basic ohmmeter.
Understand ammeter, voltmeter, and ohmmeter schematic diagrams.
Understand procedures necessary to safeguard meters.
D’Arsonval Meter Movement
The D’Arsonval meter movement is the basic mechanism used in analog meters. This movement
is also called the permanent magnetized moving coil (PMMC) type. Developed by D’Arsonval in
1881, this meter has retained general usage until very recently. It is general displaced today by
inexpensive digital meters.
The meter operates on the principle of a dc motor. The field of an extremely strong permanent
magnet acts to repel or attract a soft iron core bobbin which is magnetized by an externally applied
current. Very many turns of fine wire wrap the
bobbin. The bobbin is axially mounted on a jewel
bearing to minimize friction. A pointer is attached
to the bobbin cylinder. Rotation of the cylinder
permanent magnet
provides the pointer deflection that indicates how
much current is flowing in the bobbin coil.
Opposite magnetic poles attract while like magnetic
poles repel. The amount of motoring or rotating
force determines the degree of rotation of the meter
movement. The strength of the bobbin field
intensity is given by current multiplied by the
number of bobbin turns. Increasing current
increases the movement rotation. The spiral spring
provides restoring torque to return the pointer to its
leftmost rest position. The spring is attached at the
axis of the bobbin cylinder at one end and to a lever
at the other. The lever can be manually rotated to
adjust the zero position of the pointer. A small slot
pointer
bobbin
coil
pole
shoes
spiral
spring
counte
r
weight
Page 1 of 9
on the underside of the spring attachment lever can be rotated against holding friction to make
slight changes in the pointer zero position. This is called Zero Adjust, and must be done with no
current flowing.
1. The diagram on the left shows magnetic poles on the meter
pointer
movement. Since unlike poles attract and like poles repel, the
shown
pointer is being deflected toward the South pole shoe. The bobbin
deflected
rotation is countered by spring tension pushing counter-clockwise.
½ scale
from zero
Deflection is shown for about half of the total deflection range.
position
With zero current, the pointer is at its leftmost position. The fullFull-scale
Zero
scale pointer deflection is shown to the right of the pointer. FullN
scale does not correspond to the absolute maximum rotation
S
N
possible, but it represents the maximum linear rotation of the
bobbin against opposing spring torque. The zero position, marked
S
to the left of the pointer position represents a spring neutral
position. Meter test leads are polarized. If a current were applied with polarity opposite
the meter polarity, the pointer would deflect to the left of the zero line. If this connection
were not immediately corrected, damage could result to the meter.
Meter Safety Concerns:
1. Always set the meter range to a scale higher than you would expect to read, then change to
a lower scale to obtain the best reading.
2. Always be careful to observe meter polarity when making the measurement. If you don’t
know the polarity, start with a short tapping connection to see if the pointer deflection is in
the right direction before committing to a hard connection.
3. Current measurements require that the circuit be broken and the break bridged by the
ammeter. Electron flow will be into the meter – and out of the meter +. Power should be
off before connecting the ammeter into a circuit since the voltage will be a higher value
across an open circuit.
4. Ohmmeters should never be used while circuit power is ON. Even with power off, time
must be allowed for capacitors to bleed off stored charge before using an ohmmeter. Keep
in mind that an ohmic measurement across a circuit resistor will include the effects of all
circuit resistance paralleling the resistor.
Current for Full-Scale Deflection:
Ifsd is the current required to deflect the meter pointer to the maximum safe value on the meter.
The deflection at Ifsd will be to the maximum value on the meter scale set by the range switch.
The Ifsd for a Simpson 260 meter movement is 50µA. You will not see a 50µA range on the
meter. The lowest range is 1mA full scale. This allows some internal protection for the meter
movement. A meter movement has internal resistance, Rm, due to the resistance of the fine wire
wound on the movement bobbin. The Rm of the Simpson 260 is 2kΩ. Do not attempt to measure
this resistance with an ohmmeter. A meter resistance measurement will be made in a lab
experiment.
For an Ifsd of 50µA and Rm of 2kΩ, calculate the maximum voltage that can be applied across the
meter movement without exceeding Ifsd and damaging the movement.
1:
Vfsd = Ifsd × Rm
50µA × 2kΩ = 100mV or 0.1V
The full scale deflection voltage for a meter is important. It is the key parameter used in designing
meter shunts to change the range of an ammeter.
Page 2 of 9
The approach to designing ammeter shunt resistance is
based on the Vfsd (which is based on Ifsd and Ohm’s Law).
In the schematic on the right, suppose we want the meter to
be at full scale when the input current, I, is equal to 10mA.
It should be clear that when the voltage across the meter
shunt equals Vfsd, then meter current will equal to Ifsd, or
full scale deflection. We reason that if I is 10mA and Im is
50µA, then Ish must be 10mA - 50µA = 9.95mA. We also
know that the Rsh voltage must equal 100mV. So we use
Ohm’s law, which tells us that Rsh = Vfsd/9.95mA or
10.05Ω. Notice that to have an accurate meter, the meter
shunt must have very high precision.
2:
Rsh=
+
Rm
Im
Rsh
Ish
+
I
-
Vfsd
Im ax−Ifsd
Using the same meter movement for a 100mA full scale ammeter gives us
Ish = 100mA – 0.05mA = ______________. Rsh is then Vfsd/Ish = ___________ (1.0005Ω)
The total in-line resistance of an ammeter, Rin, is the parallel combination of Rm and Rsh. For
the 10mA example, this comes to 10.05||2k = 9.99975Ω. That is a lot less than if there were no
meter shunt, but it is still a lot more than a short circuit. Remember that the power to deflect the
meter pointer comes from the current being measured. This means that some power is lost to the
meter (I2×Rin). Whenever a meter is used, the circuit is changed a bit. A tech has to understand
how meter use affects circuits. It is easy to see that the 100mA meter has an Rin of about an ohm,
so that it would have less of an effect than a 10mA (10Ω) meter.
Ammeter Loading:
In the circuit on the right, the 10mA meter is inserted in
Rmeter
series with the load to measure the current. Without the
meter it is evident that the current is 1v/100Ω, or 10mA.
The meter adds another 9.995Ω of series resistance to
100
the 100Ω, making the total resistance 109.995Ω. With
1 V
the meter in the circuit, the current is 1v/109.995Ω, or
9.0913mA. Absolute error is
10.0 – 9.0913 = 0.90867mA for a percentage error of
9.09%. Notice that the meter reading of 9.0913mA is
close to 10mA full scale. If the load were 1000Ω instead of 100Ω, the meter resistance would
have a much smaller effect. However, the measured current would be a little less than 1mA
(1v/1009.995Ω) so that reading the scale would be less accurate.
Multi-Range Designs:
There are two designs for a switchable resistor shunt for an ammeter.
One uses a make-before-break rotary switch with contacts like those
shown on the right. Each resistor is designed for a full scale current just
as we saw above. It is important that the switch not have an interval
when there is no shunt connected to the meter since that would expose the
movement to large currents.
Page 3 of 9
Ohm
The schematic diagram to the right depicts a multi-range
ammeter with a rotary range selector switch. If the three
ranges had full scale currents of 100mA, 10mA, and
1mA, we have already calculated a 1.0005Ω shunt for
the 100mA scale and a 10.05Ω shunt for the 10mA
scale. The 1mA scale follows a similar calculation:
1mA – 0.05mA = 0.95mA shunt current for a 100mV
full scale voltage across the movement. 0.1/0.00095 =
105.236Ω shunt resistance for the 1mA scale. With the
three shunt resistors and the meter movement, the meter
is designed.
The second type of ammeter does not require a make-beforebreak range switch. The circuit on the right shows how the
shunt resistors are connected. These shunt resistors are
harder to calculate. In position B, R2 + R3 shunt the meter
movement, which is in series with R1. In position C, R3
shunts the meter movement in series with R1 + R2. Only in
position A, where the shunt resistance is the sum of the three
resistors is the computation comparable to the shunt
calculations for the standard switching arrangement. This
design is called the Ayrton Shunt. We will not examine the
design equations.
Rm
+
-
R1
A
R2
B
R3
C
Rm
+
R1
-
R2
R3
B
A
C
DC Voltmeters:
The dc voltmeter utilizes the meter movement and a series
resistor to change a current-reading movement into a
voltmeter. Ohm’s law states that V/R = I. The voltmeter
resistance is the series resistor, Rs, plus the movement resistance, Rm. The full scale current of
50µA (or whatever it is for a given meter movement) is given as Vin/(Rs + Rm). If we wish to
calculate Rs for a full scale voltage reading of 25v, then 25/(Rs + 2000) = 50µA. Or (25 – Vfsd)/
50µA = Rs. So for Vfsd = 0.1v, Rs = 24.9/0.00005 = 498,000Ω. Rs + Rm = 498kΩ + 2kΩ =
500kΩ and 25v/500kΩ = 50µA.
3:
Rs=
Vmfs−Vfsd
Im
Vmfs = meter input voltage for full scale deflection
Using equation 3 it is easy to see that for a 10v full scale
voltmeter the series resistance is
10− 0. 1
=198 k Ω
0. 00005
A multi-range voltmeter is constructed with
Rs
+
Rm
Im
a switch that selects the series resistor for the desired range. For
protection of the meter movement, the resistor series resistor for
the least range is not switched and the higher range resistors
simply add their resistance to the lower range.
+
-
Page 4 of 9
For the multi-range voltmeter shown on the right, range C has a
full scale deflection at 2 volts dc. The meter movement has Vfsd
of 100mV and Ifsd of 50µA. We first calculate R3 for the range
for the 2 volt range. R3 = (2 – 0.1)/ 50µA = 38kΩ. We next
calculate the sum, R2 + R3, for a 20 volt range.
20− 0. 1
=398 k Ω
0. 00005
+
Rm
Im
R2
so that R2 = 398k – 38k = 360 kΩ. Finally
we calculate R1 + R2 + R3 for a 100 volt range.
100−0 . 1
=1998 k Ω
0 . 00005
R3
R1
A
B
C
so that R1 = 1998k – 398k = 1600 kΩ. This completes the design
of a 3-range voltmeter with ranges of 2 volts, 20 volts, and 100
volts. Notice that it would DAMAGE the meter movement to
connect 100 volts on the 2 volt scale. The current would be
100v/38kΩ = 2.63mA exceeding the 50µA capability of the meter
movement by a factor of 52.6 times; a sure way to destroy the meter. However, if a 2.5 volt zener
diode were connected from the C switch terminal to the meter common, then the meter movement
would only “see” 2.5v/38kΩ = 65.8µA, probably safe for the movement. The one zener would
protect the meter on all scales.
Sensitivity of the Meter and Circuit Loading:
The sensitivity of a meter with an Ifsd = 50µA is simply 1/Ifsd = 1/50µA = 20 kΩ/volt. Thus the
total resistance for a 100 volt range would be 100×20k = 2MΩ. That includes the Rm of the
meter, which is 2kΩ, leaving 1998kΩ for the total Rs on that range. It is important to know the
sensitivity of a meter so that you can know how much resistance the voltmeter will place in series
with the circuit being measured.
4:
Meter Sensitivity = 1/Ifsd
If you are measuring voltage across a 2kΩ resistor on a 20 volt range with a 20kΩ/volt meter, the
meter resistance puts 400kΩ in parallel with the 2kΩ, barely changing the circuit (1.99kΩ).
However, if the resistor were a 400kΩ resistor, then the meter would “load” the circuit by
changing the resistance to 200kΩ. The measurement would be practically worthless unless you
knew precisely how the loading would alter the original voltage so the alteration could be
accounted for. It is important for a tech to know the loading effects of instruments used to make
measurements.
Rule of Thumb: If Rin of a voltmeter is 9 times greater than
Rth
the circuit resistance for which the voltage is measured, the
error will be 10%. If Rin of a voltmeter is 20 times greater,
the error will be roughly 5%. The difference in measured
Rx +
Vth
0.000
V
voltage compared to actual circuit voltage depends on the
equivalent resistance of the rest of the circuit. Remember
Thevenin equivalent circuits? If one resistor is isolated in a
circuit, the remainder of the circuit can be considered as a
voltage source, Vth, and a source resistance, Rth. The voltage measured across Rx can be found
using voltage division.
Page 5 of 9
Vmeter=Vth
Rx∣∣Rmeter
Rx ∣∣Rmeter + Rth
You should be able to reason from the equation that if Rth is
very small compared to the loaded Rx, then the meter reading is not greatly affected by meter
loading. However, when Rth is about equal to the loaded Rx, error can be 50%.
Voltmeter Design Example:
Using a meter movement with Ifsd = 80µA, Rm = 1.5kΩ, design
voltmeter with full scale ranges of 5v, 25v, and 100v. Use a
single zener diode for meter protection.
a
R3
+
Rm
Im
R2
The circuit is shown on the right. The task is easy. First
calculate the sensitivity. 1/80µA = 12.5kΩ/v
Vrange
Rmeter
Rs
Rrange
5v
62.5kΩ
61kΩ
R3 = 61kΩ
25v
312.5kΩ
311kΩ
R2 = 250kΩ
100v
1250kΩ
1248.5kΩ
R1 = 937.5kΩ
Vzener = 6v Giving the protection zener a 20% margin over the small scale voltage is
appropriate.
The Rmeter entries are simply Vrange times sensitivity.
The Rs entries are Rmeter – Rm.
The Rrange entries are the actual circuit resistors. R3 = Rs; R2 = Rs – R3; R3 = Rs – (R2 + R3)
R1
A
Voltmeter Loading Examples:
For voltmeter loading calculations, all you need to know
is the sensitivity.
1. Given: Sensitivity = 10kΩ/volt
Find Rin for meter for 100v, 50v, and 10v ranges.
100v
50v
10v
Rin =
1000 kΩ
500 kΩ
B
C
Rth
Vth
Rx
+
-
0.000
V
100 kΩ
For Vth = 25v, Rth = 50 kΩ and Rx = 50 kΩ, the unloaded voltage across Rx is 12.5v.
Solve for meter loading for each meter range.
100v Range
equivalent resistance of meter paralleling Rx =
Using voltage division,
25×
50 k×1M
= 47 . 62k Ω
1050 k
47 . 62k
=12. 195 vAbsolute
47 . 62k +50 k
error is 12.5 – 12.195 = 0.305
Percent error = (0.305/12.5)x100 = 2.44%
50v Range
equivalent resistance of meter paralleling Rx = 45.55kΩ
Using voltage division,
25×
Absolute error is 12.5 – 11.918 = 0.582
45 .55 k
=11. 918 v
45 .55 k +50 k
Percent error = (0.582/12.5)x100 = 4.66%
Page 6 of 9
10v Range
equivalent resistance of meter paralleling Rx = 33.33kΩ
Using voltage division,
25×
Absolute error is 12.5 – 9.999 = 2.501
33 . 33 k
=9. 999 v
33 . 33 k+50 k
Percent error = (2.501/12.5)x100 = 20%
Safe Voltmeter
Operation
Normally the meter common lead is connected first. When touching probes to component leads
this means that the – or common (black) lead touches first. Observe polarity. Watch needle
deflection while you touch the probes to leads. If deflection is backward, swap the probes.
Always start on a higher range than you may expect to read. Now you know why this is a good
idea. On a higher range the meter is better protected by a higher series resistance than on a lower
range. When done with measurements, always leave the meter range switch on a high voltage
range for maximum protection if it does not have an off position.
The Ohmmeter:
A schematic diagram for a basic ohmmeter is
depicted on the right. With the inclusion of a
battery, it is obvious than an ohmmeter is unlike
the ammeter and voltmeter circuits which take
power from the circuit being measured. The
internal battery is there to supply a current through
the unknown resistor, Rx. An ohmmeter should
never be used on a circuit with power turned on as
the ohmmeter supplied current can adversely affect
the circuit being measured and the measured circuit
can inject power into the ohmmeter that can
damage the meter.
Rs1
Rs2
50%
+
Rm
-
Rsh
V
Rx
The theory behind the operation is fairly simple. The total resistance in the loop is Rs1 + Rs2 +
Rm + Rx. So the total meter current is V divided by the total resistance. The potentiometer is
included as part of Rs so that the resistance can be varied to compensate for drooping battery
voltage, to give the battery a longer usable life. Notice that for minimum Rx, when Rx is replaced
by a short circuit, the current is maximum. So zero ohms is a full scale reading.
Suppose we want the meter designed so that a 1 ohm Rx will make the pointer drop to 95% of full
scale. VB/Rs = 100% full scale and VB/(Rs + 1Ω) = 95% full scale; a 1Ω change produces a 5%
reduction in full scale current. If we pick Rsh, the meter shunt, to set full scale current to 20mA,
then a 95% full scale is 19mA. In other words, a 1Ω increase in Rs corresponds to a 5% increase.
This makes Rs = 20Ω. To get 20mA with a Rs resistance 20Ω, VB must be 0.4v. Using the same
meter movement that was used to design ammeters (Ifsd = 50µA, Rm = 2kΩ), the shunted meter
resistance is 5Ω (Vfsd/20mA = 5Ω). So of the 20Ω needed in the ohmmeter circuit, 5Ω are
provided by the shunted meter. So if Rs1 is make 12Ω, and Rs2 is a 6Ω pot adjusted for 3Ω, and
the battery provides 0.4Vdc, the meter is complete.
Page 7 of 9
Designing the pointer scale is interesting. Full scale is 20mA; 95% full scale is 19mA. 75% full
scale is 15mA corresponding to an external resistance of 6.666Ω (0.4v/26.666Ω = 15mA). Half
scale is 10mA corresponding to an external resistance of 20Ω (0.4v/40Ω = 10mA). Notice that
half way between 0Ω and 20Ω is not 10Ω but is 6.666Ω. The scale is not linear! 25% deflection
occurs for 5mA. This happens for an external resistance of 60Ω. To mark the scale in ohms
requires the 25% tick to be 60Ω, the 50% tick to be 20Ω, and the 75% tick to be 6.666Ω. This is
true because the meter is measuring current. Ohm’s Law states that I = V/R. R is in the denominator.
Designing an ohmmeter for a higher resistance scale requires correspondingly larger resistance
values and no meter shunting. Suppose we want 95% deflection for 1kΩ. This implies that 1kΩ
changes the total circuit resistance by 5%, or Rs1 + Rs2 + Rm = 20kΩ. If shorting the Rx input
gives 50µA, then VB = 50µA×20kΩ = 1.0 volts. Rs1 + Rs2 = 20kΩ - 2kΩ = 18kΩ. The actual
current with Rx = 1000Ω would be 1.0/21kΩ = 47.62µA or 95.24% deflection. Half scale
deflection would occur for Rx = 20kΩ. When the external resistance doubles the total circuit
resistance, the meter reads half scale.
Ohmmeter Summary:
• Ohmmeters require an internal power source, usually a battery for portable, hand-held
instruments.
• The ohmmeter is basically a series circuit with the external resistance adding its resistance
to the circuit total.
• Ohmmeter design is mainly concerned with the range scale calibration so that resistance
values within a selected range can be read from the scale. A short circuit gives maximum
current and maximum meter deflection.
• Design guidelines: Pick a resistor value for 95% deflection; total resistance should be 20
times that value. Pick a reasonable value for internal dc voltage. That value of voltage
divided by total resistance gives the full scale deflection current for the meter + shunt.
Safe Ohmmeter Operation:
Never connect an ohmmeter to a circuit that has power applied. Always be sure that the
component you wish to measure is isolated from the rest of the circuit. Always make sure that
anyone who wishes to borrow your meter knows the basic safety facts.
Calibration of Meters:
Shop_standard
+
50%
0.000
A
+
0.000
A
+
0.000
A
0.000
A
V
+
0.000
A
+
0.000
A
+
Page 8 of 9
The diagram above shows how 5 ammeters may be calibrated against a shop standard meter. The
shop standard is a meter that is trusted, perhaps because it has been calibrated by a calibration lab
and supplied with a certificate of calibration. Such certification always has a limited expiration
time, but when a freshly calibrated meter comes back from the cal lab, it’s a good idea to use it to
calibrate the rest of the meters in the lab. As you can see from the diagram, the potentiometer
allows you to check the meters at a number of places on the meter scale and in all ranges of
operation. The first point of adjustment is the meter zero, which is the mechanical adjustment of
the D’Arsonval movement spring.
50%
Shop_standard
+
V
-
0.000
V
+
-
0.000
V
+
-
0.000
V
+
-
0.000
V
RL
As you would expect, the calibration of voltmeters is done with the meters in parallel. A shop
standard meter is used in the same way as with ammeters. Notice the load resistor, RL. This
resistor is required for the potentiometer to implement a voltage divider to vary voltage. It would
not be needed if a variable dc voltage source were used.
Ohmmeters can also be compared to shop standards, but this must be done one meter at a time.
Why?
Answer: Since each meter would be putting current through the unknown Rx, the result would be
that no measurement would be correct. Having more than one ohmmeter attached to a resistor
would be similar to trying to measure resistance in a circuit without first turning off circuit power.
Page 9 of 9