Basic D.C. AVIM 121 Lab 7 Page 1 of 9 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. VOM (Note: The student must use an analog meter for this Laboratory Exercise) 2. VPS 3. 1 kω potentiometer 4. 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 Page 2 of 9 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 R m 100mA 99mA R shunt R L 100mA - E Source + 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 R m and R shunt are in parallel, the solution is obtained through Ohm's law for parallel circuits. R m =50Ω I m =1mA I shunt = 99mA E shunt = E m = I m R m = 1mA 50Ω = 50mV R shunt = E shunt I shunt = 50mv 99mA = 0.505Ω where: R m = meter resistance R shunt = shunt resistance E m = voltage dropped across meter E shunt = voltage dropped across the shunt I m = full scale current of the meter I shunt = current through shunt The following Equation, Equation 7-1, has been developed from Example 1. Thus: R shunt = (I m R m ) I shunt 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 Page 3 of 9 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 R mult =? 50mV R m = 50Ω + E = 1V - FIGURE 7-2: circuit used for Example 2. Notice that the multiplier resistor R mult 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 R mult and R m are in series, the solution is based on series circuit concepts Therefore: E m = I m R m = 1mA 50Ω = 50mV E mult = E - E m = 1000mV - 50mV = 950mV R mult = E mult I mult = 950mV 1mA = 950Ω where: E = voltage to be measured E m = voltage drop across meter E mult = voltage drop across the multiplier I m = full scale current through the meter R m = meter resistance R mult = multiplier resistance Equation 7-2 can considerably reduce the effort in determining R mult. R mult = (E I m ) - R m 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 (R m ) 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 Page 4 of 9 rev. 08.09 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 (R meq - 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: R meq = Em I m = 250mV 1mA = 250Ω where: E m = voltage developed across the VOM I m = current flowing through the VOM R meq =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 I m Where: I m = 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, 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 Page 5 of 9 rev. 08.09 V-Meter R meg V-Meter R 2 R 1 R 2 R 1 + E = 2V - + E = 2V - (a) Meter equivalent resistance not shown. (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 R shunt (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 (R shunt ) in parallel with the meter. Do not disturb the power supply setting. With the R shunt resistance connected in parallel, current will be shunted (bypassed) around R meq. When R meq 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), R meq and R shunt 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 R meq. 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 R meq. 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 Page 6 of 9 rev. 08.09 ma (*100kΩ) 15kΩ R meg R series R shunt 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 R L +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 R meq 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; R meq = R m. 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 (R meq ) to modify the voltmeter symbol.
Basic D.C. AVIM 121 Lab 7 Page 7 of 9 rev. 08.09 NOTE: The Voltmeter input resistance (R meq ) 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 R meq in parallel. 6. Compute the percent of difference between the meter reading in step 2 and the calculated voltage in step 5. V-Meter R mult ma 100kΩ 100kΩ 1kΩ 1kΩ R 2 R 1 R 2 R 1 +2V VPS - +10V VPS - Figure 7-6 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 Page 8 of 9 rev. 08.09 Notes:
Basic D.C. AVIM 121 Lab 7 Page 9 of 9 rev. 08.09 7- Shunts and Multipliers Name: Data Tables Date: Section A: Milliameter Equivalent Resistance 3. 4. 5. R meg (cal.) 6. %Difference Section B: Milliameter Shunts 1. Total Current (cal.) 3. R shunt 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.) ER-2(cal.) R mult 4. ER-1(meas.) ER-2(meas.) 5. % Diff. 6. Sensitivity