Basic D.C. AVIM 121 Lab 7
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rev. 08.09
Laboratory Exercise - Seven
Objectives
•
•
•
Determine milliammeter equivalent resistance.
Calculate and apply meter shunts and multipliers.
Determine voltmeter loading effect.
Reading Assignment
Chapter 8, Basic Electronics, Grob
List of Materials
1.
2.
3.
4.
VOM (Note: The student must use an analog meter for this Laboratory Exercise)
VPS
1 kΩ potentiometer
Resistors - all at least ½ watt:
1kΩ(two) 15kΩ (one)
3.3kΩ(one) 100kΩ (two)
Alternate Materials
* 10kΩ potentiometer (consult Figure 7-7)
Procedural Notes
•
•
•
•
•
Observe meter polarity when connecting the meter into the circuit.
Recall that a voltmeter is an ammeter that has been designed to read voltage.
Remember that the VOM, whether used as a voltmeter or an ammeter, will load the circuit and
introduce some error.
DO NOT ATTEMPT TO MEASURE THE RESISTANCE OF AN AMMETER WITH AN
OHMMETER.
Record all measurements and calculations in the data table.
Introduction and Objectives
The insertion of a meter, such as the VOM, into a circuit introduces error. The error is caused by current
passing through the internal resistance of the basic meter movement and its associated shunt and
multiplier circuits. In this exercise, basic design criteria are given for extending the range of an analog
meter movement through the use of shunts or multipliers. You will learn to determine the internal
resistance of a meter movement, and to observe the effects of inserting a meter into a circuit. You will
also learn to compensate for erroneous readings caused by meter loading.
Once you have read through the theory and worked through the laboratory exercise, you will be able to:
• Calculate shunts and multipliers.
• Understand the loading effect of the VOM.
• Determine meter resistance from meter specifications.
The Basic Meter Movement
The VOM is an extremely versatile test instrument. It is versatile because it can be used to measure a
variety of circuit conditions. Also, for each of its functions (voltage, resistance, and current), there are
several ranges available. This measuring capability is made possible through internal circuitry that extends the range of the basic meter movement of the VOM. Although this internal circuitry is too complex
to be completely discussed at this time, the circuits and design factors used by manufacturers to increase
the voltage and current ranges of basic meter movements can be discussed.
Two factors that must be known before any analog meter movement can have its range increased are:
1. The manufacturer's rating of the full scale deflection current. A marking of "f.s. = 1mA", or "f.s. =
10mA", etc. is sometimes printed on the lowest visible portion of the meter scale. If this
information is not available for the meter scale or manufacturer specification and data sheets, it
can be determined by direct measurement.
2. The internal resistance of the meter. (This information must be determined from the manufacturer
specifications or measured with special circuitry.)
Basic D.C. AVIM 121 Lab 7
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rev. 08.09
Change Basic Meter Movement to an Ammeter
Essentially, every meter movement is an ammeter and its range is increased through a process called
shunting. See Figure 7-1. Observe that the circuit current is 100mA. Also, note that the 1mA meter has
99mA shunted around it. The process of shunting the meter is nothing more than the concepts of the
parallel circuit put into practice. Example 1 shows the technique for determining the value of the shunt
resistor.
1mA
50Ω
Rm
100mA
Rshunt
99mA
RL
100mA
-
ESource +
Figure 7-1
Example 1:
Determine the value of the shunt resistance needed to increase the range of a 50 Ω - 1mA meter to
100mA. (See Figure 7-1.)
SOLUTION: Since Rm and Rshunt are in parallel, the solution is obtained through Ohm's law for parallel
circuits.
Rm =50Ω Im =1mA Ishunt = 99mA
Eshunt = Em = Im × Rm = 1mA × 50Ω = 50mV
Rshunt = Eshunt ÷ Ishunt = 50mv ÷ 99mA = 0.505Ω
where: Rm = meter resistance
Rshunt = shunt resistance
Em = voltage dropped across meter
Eshunt = voltage dropped across the shunt
Im = full scale current of the meter
Ishunt = current through shunt
The following Equation, Equation 7-1, has been developed from Example 1. Thus:
Rshunt = (Im × Rm) ÷ Ishunt
Equation 7-1
Changing the Basic Meter Movement to a Voltmeter
With the exception of the electrostatic voltmeter, all analog voltmeters are actually current meters that
have been modified to measure voltage. The conversion of the current meter to a voltmeter requires the
relatively simple task of inserting an appropriate resistor in series with the meter movement. A reevaluation of the meter used in Example 1 shows that it has a 50 ohm - 1mA movement. According to
Ohm's law, if 1mA is flowing through a 50Ω load, then 50mV is developed across the resistance. Now
suppose a voltage source adjustable from 0 to 50mA is available. The meter could then be calibrated
Basic D.C. AVIM 121 Lab 7
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rev. 08.09
directly in millivolts and used as a voltmeter for the power supply. Admittedly, it may be difficult to obtain
such a power supply and a 50mV voltmeter would have very limited application. Consequently, it is
desirable to extend the range of the meter. Since the current is really the limiting factor, design considerations must include some type of current limiting device. Example 2 shows the steps required to
determine the value of the resistor used to limit the current meter.
Example 2:
Determine the value of the multiplier resistance needed to increase the range of a 0-50mV (50Ω - 1mA)
meter to 0-1 volt.
SOLUTION: The circuit should first be sketched. See Figure 7-2.
950mV
50mV
Rmult = ?
Rm = 50Ω
+
E = 1V
-
FIGURE 7-2: circuit used for Example 2.
Notice that the multiplier resistor Rmult is placed in series with the meter and that it must limit the current to
the full scale value by dropping the excess voltage. In this circuit, the resistance of the meter movement
will only drop 50mV; current in excess of 1mA may damage the meter. The voltage dropped by the
multiplier, 950mV, is the difference between the voltage to be measured, 1volt (1000mV), and the 50mV
the meter can safely measure. Since Rmult and Rm are in series, the solution is based on series circuit
concepts Therefore:
Em= Im × Rm = 1mA × 50Ω = 50mV
Emult = E - Em = 1000mV - 50mV = 950mV
Rmult = Emult ÷ Imult = 950mV ÷ 1mA = 950Ω
where: E = voltage to be measured
Em = voltage drop across meter
Emult = voltage drop across the multiplier
Im = full scale current through the meter
Rm = meter resistance
Rmult = multiplier resistance
Equation 7-2 can considerably reduce the effort in determining Rmult.
Rmult = (E ÷ Im) - Rm
Equation 7-2
VOM Loading Effects
Now that the principles of meter shunts and multipliers are understood, some of the problems encountered when using the VOM must be considered. Whether the VOM is used as a voltmeter or as a
milliammeter, a certain amount of inaccuracy is introduced by the meter resistance (Rm) and the associated shunt and multiplier resistances. This inaccuracy is called the loading effect. The calculation of the
loading effect of a voltmeter is different from the ammeter, so each will be considered separately.
Ammeter Loading
Basic D.C. AVIM 121 Lab 7
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The loading of the circuit, caused by the insertion of a milliammeter, can be calculated when the current
meter sensitivity is known. Current sensitivity of the meter movement is defined as the amount of current
required for full scale deflection. In addition, in order to relate this sensitivity to the loading effect, the
voltage necessary for the full scale deflection must be known. This specification can be obtained from the
operator's manual or an industrial parts catalog. it can, if necessary, be determined by special measurement. (This measurement technique is developed in Section A of this laboratory exercise.)
As an illustration of the meaning of the ammeter sensitivity specification, suppose that a VOM manufacturer advertises his meter to have a full scale sensitivity of 50uA at 100 mV, 1mA at 250mV, and 10mA
at 250mV. From these specifications, the meter equivalent resistance (Rmeq - the meter movement
resistance including any shunt) can be calculated. Example 3 uses these specifications to determine the
amount of resistance introduced in the circuit by the insertion of the meter.
Example 3:
What is the equivalent resistance of a milliammeter when the range selector is set at 1mA and the meter
sensitivity is given as 1mA at 250 mV?
SOLUTION:
Rmeq = Em ÷ Im = 250mV ÷ 1mA = 250Ω
where: Em = voltage developed across the VOM
Im = current flowing through the VOM
Rmeq =equivalent resistance that represents the internal resistance of the VOM. This includes the
meter, and/or shunt, and series resistance.
Voltmeter Loading
An error is also introduced by the paralleling effect when making a voltmeter measurement. The
magnitude of this error is determined by the voltmeters sensitivity. The method of expressing this
sensitivity is in ohms-per-volt.
Ohms-per-volt = Ω /V = 1 ÷ Im
Where: Im = full scale current of the basic meter movement
Equation 7-3
Equation 7-3 states that if a meter requires 50 microamperes to deflect the needle full scale, then the
meter must have an equivalent resistance of 20kΩ/V. This ratio of resistance to voltage is constant for all
range scales but the equivalent meter resistance changes.
Figure 7-3 shows a circuit condition where it is desired to measure the voltage developed across R1. An
evaluation of circuit conditions indicates that a 1 volt drop should appear across each resistor. If the
equivalent resistance of the meter, as shown in figure 7-3(b), is given as 30kΩ, will the meter read 1 volt?
No! It will read 0.67V because of the meter loading effect. To reduce the voltmeter loading effect, the
technician can use a voltmeter with a higher ohms-per-volt rating. Suppose that the 20,000 ohms-per-volt
meter is replaced with a 1,000,000 ohms-per-volt meter in Figure 7-3(b). A quick calculation shows that
the percentage of error due to loading has been reduced to - 1.48%. The logical conclusion, then, is that if
the ohms-per-volt sensitivity is increased, the voltmeter loading effect will be decreased.
Basic D.C. AVIM 121 Lab 7
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rev. 08.09
30kΩ
V-Meter
V-Meter
Rmeg
30kΩ
30kΩ
30kΩ
30kΩ
R2
R1
R2
R1
+
E = 2V
-
+
(a) Meter equivalent resistance not shown.
E = 2V
-
(b) Meter equivalent resistance shown.
FIGURE 7-3
Procedures
Section A: Milliameter Equivalent Resistance
1. Set the VOM to measure 1mA. This is a typical value. However, if the meter being used does not
have this range, then use the 100µA range.
2. Use the circuit of Figure 7-4 to determine the equivalent resistance of the meter. With Rshunt (1 k
potentiometer) out of the circuit, connect the meter in series with a 15 k resistor and the VPS, as
shown in Figure 7-4. Slowly increase the supply voltage until the meter reads full scale. Now
connect the potentiometer (Rshunt) in parallel with the meter. Do not disturb the power supply
setting. With the Rshunt resistance connected in parallel, current will be shunted (bypassed)
around Rmeq. When Rmeq and the shunt are equal in resistance, the current through each parallel
path will also be equal. So, after the potentiometer is adjusted to the same resistive value in the
next step (step 3), Rmeq and Rshunt will have the same current and also the same resistance.
Reading the resistive value of the shunt resistor will give the student the value of Rmeq.
3. Adjust the pot (potentiometer) until the meter reads half scale. Shut off the supply, remove the
pot, and without disturbing the pot setting, measure its resistance. This resistance is equal to the
milliammeter equivalent resistance Rmeq.
4. Using the equivalent meter resistance, just determined in step 3 and the full scale current Ifs,
write the current specifications for this range setting. For example, a meter that has a 10mA
movement and an internal resistance of 5 ohms will have 50mV developed across it (50mV =
10mA x 5Ω ). The current specifications for this meter would be written as 10\mA at 50mV.
5. Using the current sensitivity rating obtained from the operator's manual, or from the instructor,
calculate the milliammeter equivalent resistance.
6. Calculate the percent difference between the calculated and measured meter resistance (Steps 5
and 3).
Basic D.C. AVIM 121 Lab 7
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mA
Rmeg
(*100kΩ)
15kΩ
Rseries
Rshunt
1kΩ
(*10k Ω)
+
VPS
-
FIGURE 7-4: Test circuit for Section A.
Section B: Milliameter Shunts
1. Calculate the current that is flowing in the circuit shown in Figure 7-5.
3.3kΩ
RL
+18V VPS FIGURE 7-5: Test circuit for Section B.
2. Set the VOM to measure 1mA. (If this range is not available, then see Section A, Step 1.)
3. Using the equivalent resistance Rmeq determined in Section A - Step 4 and Equation 7-1,
calculate and build the shunt needed to expand the meter from 1mA full scale to 10mA full scale.
See Example 1 and Figure 7-1.
NOTE; Rmeq = Rm. The shunt may have to be built out of several fixed resistors. Have the instructor check
your calculations.
4. Connect the shunt across the meter.
5. Construct the circuit of Figure 7-5 and measure the current using the shunted meter of Step 4.
6. Compute the percent difference between the calculated and measured currents (Steps 1 and 5).
Section C: Voltmeter Loading Effects on Circuit Parameters
1. Construct Figure 7.6. Set the supply voltage to 2 V. Compute the voltage drop across either
resistor.
2. Using the VOM, measure the drop across one of the resistors.
3. Calculate the percent difference between the measured and calculated values.
4. Redraw Figure 7.6 using the voltmeter input resistance (Rmeq) to modify the voltmeter symbol.
Basic D.C. AVIM 121 Lab 7
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NOTE: The Voltmeter input resistance (Rmeq) is determined by multiplying the ohms/volt rating by the
voltmeter range setting.
5. Using the schematic of step 4, calculate the new voltage drop across R1 and Rmeq in parallel.
6. Compute the percent of difference between the meter reading in step 2 and the calculated
voltage in step 5.
mA
V-Meter
100kΩ
100kΩ
R2
R1
+2V VPS Figure 7-6
Rmult
1kΩ
1kΩ
R2
R1
+10V VPS Figure 7-7
SECTION D: Voltmeter Multiplier
This section shows how a current meter can be used as a voltmeter.
1. Construct the circuit of Figure 7-7. Set the source voltage (VPS) to 10 volts. Calculate the voltage
drop across each resistor.
2. Set the meter range to 1mA. Using Equation 7-2, calculate the multiplier resistance value needed
to convert the 1mA meter into a 10 volt meter.
NOTE: If a 1mA range is not available, then select a 100µA range.
3. Using the 1mA range setting and the multiplier of Step 2, construct a voltmeter with a 10 volt
range.
4. Using the meter constructed in Step 3, measure the voltage drop across R1 and the voltage drop
across R2.
5. Calculate the percent difference between the measured and computed value.
6. Calculate the ohms/volt sensitivity of the constructed meter.
Applications
Among the various devices utilizing shunts and multipliers are: (1) tachometers, (2) fuel gauges, (3) ammeters, (4) power supplies, and (5) relays.
Problems
1. A circuit consists of 2 resistors (4.7 k and 2.2 k) connected in series with a 10 volt source. Using a
1000 ohms/volt meter, determine the measured voltage across the 4.7 k resistor when the range
selector is set to 10 volts. What will the meter reading be? Draw a schematic of the circuit using
the meter equivalent resistance.
2. Why does the voltmeter loading effect of the VOM decrease when the range setting is increased?
3. Using an industrial parts catalog, select two different VOM voltmeter sensitivities and list the
manufacturer's name and meter model number. Compare the ohms/volt rating to the cost of the
VOM.
Basic D.C. AVIM 121 Lab 7
Notes:
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Basic D.C. AVIM 121 Lab 7
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7- Shunts and Multipliers
Data Tables
rev. 08.09
Name:
Date:
Section A: Milliameter Equivalent Resistance
3.
4.
5. Rmeg(cal.)
6. %Difference
Section B: Milliameter Shunts
1. Total Current (cal.)
3. Rshunt
5. Total Current (meas.)
6. % Difference
Section C: Voltmeter Loading Effects on Circuit Parameters
1. E 100kOhm (cal.)
2. E 100kOhm (meas.)
3. % Difference
4.
5. E 100kOhm (recal.)
6. % Difference
Section D: Voltmeter Multiplier
1. ER-1(cal.)
4. ER-1(meas.)
6. Sensitivity
ER-2(cal.)
ER-2(meas.)
Rmult
5. % Diff.