NOTES ON MULTIMETERS

Transcription

1 NOTES ON MULTMETES

2 VOLTAGE, CUENT AND ESSTANCE MEASUNG NSTUMENTS To easure voltage (ac,dc), current (ac, dc) and resistance, two types of instruents, analog and digital eters, are utilized. The easureents of these fundaental electrical quantities are based on either one of the following: i) Current sensing. The instruents are ostly of the electroagnetic eter oveent type, such as an analog ultieter. ii) Voltage sensing. The instruents are ostly electronic in nature, using aplifiers and seiconductor devices, such as a digital ultieter. ) ANALOG MULTMETE The ain part of an analog ultieter is the D Arsonval eter oveent also known as the peranent-agnet oving-coil (PMMC) oveent. This coon type of oveent is used for dc easureents. The basic construction of a such eter oveent is shown in Figure. Figure. When the eter current flows in the wire coil in the direction indicated in Figure, a agnetic field is produced in the coil. This electrically induced agnetic field interacts with the agnetic field of the horseshoe-type peranent agnet. The result of such an interaction is a force causing a echanical torque to be exerted on the coil. Since the coil is wound and peranently fixed on a rotating cylindrical dru as shown, the torque produced will cause the rotation of the dru around its pivoted shaft.

3 When the dru rotates, two restraining springs, one ounted in the front onto the shaft and the other ounted onto the back part of the shaft, will exhibit a countertorque opposing the rotation and restraining the otion of the dru. This spring-produced countertorque depends on the angle of deflection of the dru, θ, or the pointer. At a certain position (or deflection angle), the two torques are in equilibriu. Each eter oveent is characterized by two electrical quantites:. : the eter resistance which is due to the wire used to construct the coil. 2. FS : the eter current which causes the pointer to deflect all the way up to the full-scale position on the fixed scale (this is arked FS in Figure ). This value of the eter current is always referred to as the fullscale current of the eter oveent. Figure 2 indicates the electrical circuit sybol of the eter oveent that will be used. Figure 2. The eter sensitivity S, also referred as the oh/volt rating of the eter oveent, is the reverse of the full-scale current. S = Ω V () FS FS or S (fixed value) is defined for a given eter oveent and is usually noted on its casing or in the anufacturer's data sheets. The eter becoes ore sensitive as its full-scale current decreases. Typically the iniu value of FS is 50 µa and hence the axiu value of S is 20 KΩ/V. The PMMC oveent cannot be used directly for ac easureents since the inertia of PMMC acts as an averager. Because ac current has zero average value and it produces a torque that has also zero average value, the pointer just vibrates around zero on the scale. n order to ake ac easureents, a bridge rectifier circuit is cobined with PMMC as shown in Figure 3. i

4 i(t) i (t) Bridge rectifier i (t) i (t) - T/2 T 0 Figure 3. T/2 T n Figure 3 the bridge rectifier rectifies the ac current i and produces the current i = i which has a ean value (average or dc value). T / 2 T / 2 i 2,ean = i(t) dt = sin( ωt)dt = T / 2 T / 2 π (2) 0 The rs (root-ean-square) value of a periodic wavefor i(t) of period T is defined as T 0 2 i rs = i (t) dt (3) T The for factor of the sae wavefor is the rs value divided by the ean value of the full-wave rectified wavefor or equivalently 0 i i rs For Factor (FF) = (4) On the ac scale, an analog ultieter is calibrated to read the rs value of a sine wave. Since the rs value and the for factor of a sine wave of peak value are / 2 and.,,ean respectively, the eter indication corresponds to the value. i ( / 2)., ean =

5 When easuring the rs values of other wavefors, the analog ultieter easures the ean value of the rectified signal and ultiplies with. as if it is a sine wave. Thus, the analog ultieter gives wrong results for rs values of other wavefors. n order to calculate true rs values of other wavefors, their for factors should be taken into account, e.g., the factor of a triangular wave is.55 and the for factor of a square wave is.0. Then for a triangular wave the analog ultieter indication corresponds to./.55 ties the true rs value and it corresponds to./.0 ties the true rs value for a square wave. A) AMMETE As pointed out above, the deflection of the pointer in the D Arsonval eter oveent is proportional to the eter current. Therefore, this instruent can be used to easure current. However, the eter oveent by itself is of liited use and capability, since its full-scale current value FS is practically too sall (at ost in the order of illiaperes). f the current allowed to flow in the oveent,, exceeds FS, peranent daage can result, in particular to the restraining springs. To be able to easure currents higher in value than FS of a given eter oveent, the division principle is applied. Figure 4 shows the construction of an aeter. A Sybol Aeter Actual circuit sh sh Here Figure 4. sh = (5) + sh where is the oveent current, the circuit current being easured, the resistance of the oveent, and sh the "shunt" resistance connected in parallel with the oveent to provide a path for the portian of the circuit's current not allowed to flow though the eter oveent.

6 A given eter oveent can be used to build a ultirange aeter. Each range requires a different value of the shunt resistance. A three-range aeter, requiring three different shunt resistors, is shown in Figure 5. Multi-position switch sh sh2 sh3 Figure 5. The resistance of the aeter A is thus sh A = (6) + sh Because usually sh << then A sh that is the equivalent resistance, A is approxiately equal to the saller of the two parallel connected resistors, sh. t is indicated that as the range of a ultirange aeter is changed, sh will be different and the aeter's resistance, A, will be different for the different ranges. The aeter ust be connected in series with a terinal pair through whieh the current is to be easured. For exaple, to easure the current flowing through terinals A and B in Figure 6(a), the aeter is conneeted as shown in Figure 6(b). A A A E E (a) B (b) B Figure 6. n order for this easureent process not to disturb the value of the current being easured, the resistance of the aeter (which is series connected) should ideally be zero so that the circuit reains unchanged. However, a practical aeter has a finite but sall

7 resistance, A, which could disturb the circuit conditions and change the current distribution in the circuit. This is what is called the eter's loading effect. B) VOLTMETE The eter oveent is odelled as a resistance of value, as shown in Figure 7. Therefore, Oh's law applied to this oveent provides (8) V = (7) where V is the voltage across the eter oveent when the current flowing in it is. When the current in the oveent is FS, FS V = (8) To increase the full-scale voltage range of the oveent when functioning as a volteter, the eter oveent current has to be lowered. This can easily be achieved by inserting a large resistance, called the ultiplier resistance, ult, in series with the eter oveent, as shown in Figure 7. FS Volteter Actual circuit V V Sybol ult V Figure 7. The resistance of the volteter, v, is the series cobination of and ult as can be seen fro Figure 7. Vax = ult + = = Vax = range of volteter S (9) v FS FS Eq. (9) is quite iportant. t indicates that the higher the range of the volteter, the larger would be internal resistance of the volteter, v. This is a clear since a higher voltage range requires a larger ultiplier resistance. Also, Eq. (9) indicates that a ore sensitive eter oveent (higher S or lower FS ) also results using a larger volteter resistance.

8 Using the sae eter oveent, a ultirange volteter can be designed. A three-range volteter is shown scheatically in Figure 8. Multi-position switch ult ult2 ult3 Figure 8. The volteter ust be connected in parallel with a terinal pair across which the potential difference is to be easured. For exaple, to easure the voltage V across the terinals A and B in Figure 9(a) the volteter is connected as shown in Figure 9(b). A A E V E V (a) B (b) B Figure 9. n order for this easureent process not to disturb the value of the potential difference being easured, the resistance of the volteter (which is parallel connected) should ideally be infinity so that the circuit reains unchanged. However, a practical volteter has a finite but large resistance, v, which could disturb the circuit conditions and result in reading errors called loading effect errors. To reduce the loading effect, ust be very sall or v ust be ade as large as possible. Exaining Eq. (0) reveals that v is increased by using a higher sensitivity eter oveent or 'by using a higher range to read the voltage which ay not always be acceptable because of the reading errors near the lower end of the scale. C) OHMMETE f the eter oveent current is soehow ade to be proportional to the value of an unknown resistance to be easured, the eter's scale can be calibrated to read resistance directly. Here, however, a voltage source (e.g., a battery) ust be added to the eter s circuit to drive the current necessary for the deflection of the pointer. A typical oheter circuit is

9 shown in Figure 0. Zero-adjust resistor E 2 Black x esistance being easured Oheter s circuit ed Figure 0. The total resistance seen by the voltage source E is = (0) T x = x + + MS where the quantity 2 + is denoted by MS. The current flowing in the source and + E E = = () + T x The eter oveent current can be deterined using the current-division principle, MS + = = (2) x E + MS + When x = (i.e., an open circuit), = 0 but when x = 0 (i.e., a short circuit), should be at its axiu value, as the total resistance of the circuit is at its iniu value [see Eqs. () and (2)]. Therefore, x = 0 Ω should correspond to becoing FS, the full-scale current of the eter oveent. Thus fro Eq. (2), FS E = (3) MS + Hence, the oheter (resistance) scale is inverted with respect to the current and voltage scales (Figure ). Eq. (2) indicates that the resistance scale is nonlinear; it is sparse near the x = 0 position and crowded near the x = position. When x = MS is substituted in Eq. (2), then

10 E FS = (4) = MS This indicates that the eter oveent current will be half its full-scale value when the value of the unknown resistance is MS. Figure. eferring to Figure 0, one should note that. The battery is connected so that it drives the eter oveent current into the positive (red) terinal of the oveent, in order to cause an upscale deflection of the pointer. Therefore, the current in the external resistance flows fro the negative (black) terinal toward the positive (red) terinal, as shown, due to the battery polarity connections is a series connection of two resistors: one of the fixed and the other one (about 20% of ı) variable. The variable resistor is called the "zero-adjust resistor". When is zero (i.e., a short circuit is connected across the oheter terinals), the pointer should deflect all the way up to the full-scale position [see Eq. (3)]. Because the battery voltage E does decay (change) with tie, readjustent of the value of 2, through the zero-adjust resistor, is necessary to copensate for this battery voltage change. This is usually an initial checking procedure to ensure that the oheter would function properly; otherwise, the source should be replaced by a new battery.

11 Figure 2. The analog ultieter used in the laboratory. D) CUENT MEASUEMENT To easure current, the instruent should be set to a A.C. or D.C. range (lower-left part in Figure 2), and the range should be set fro lower-right part. ed values and black values, which are axiu values to be easured, are for AC current and DC current easureents, respectively. Then ultieter should be connected in series apparatus to be tested. The currents are easured fro the iddle-upper part of the ultieter that again red and black scales are for AC and DC current easureents, respectively. To give an exaple, if it is set to DC and 5 A scales, then the current should be easured fro 0-50 scale on the highest scale which 50 corresponds to 5 A. Then if the dru is steady at 0, the current easured is A. Generally speaking, the power absorbed in the instruent is negligible, but in cases of low voltage heavy current networks, theinclusion of a eter ay reduce the current appreciably below the value which would otherwise prevail. The potential drop at full scale deflection across the eter terinals is in the order of 500 V on all D.C. ranges, except the 50 µa range which has a drop of 25 V. n the case of A.C., it is less than 250 V on all ranges. The care should be taken to ensure that the circuit is "dead" before breaking into it to ake current easureents.

12 E) VOLTAGE MEASUEMENT To easure voltage, the instruent should be set to a suitable A.C. or D.C. range, and then connected parallel across the source of voltage to be easured. The range should be set fro upper-right part. f the expected agnitude of the voltage is within the range of the eter, but its actual value is unknown, the instruent should be set to its highest range, connected up and if below 000 V the appropriate selector knob should be rotated decreasing the ranges step by step, until the ost suitable range has been selected. On D.C. ranges, the eter consues only 50 µa at full scale deflection, this sensitivity corresponding to 20,000 ohs/volt. n the case of A.C. ranges fro 0 V upwards, full-scale deflection is obtained with a consuption of A (000 ohs/volt). The 2.5 V A.C. range consues 0 A at full scale deflection. F) ESSTANCE MEASUEMENT On resistance ranges, the eter ust not erely start fro its instruent zero, but ust have, in addition a resistance zero corresponding to the full scale deflection of the eter. Before carrying out tests for resistance a check and, if necessary, adjustent should be carried out to ensure that when the leads are joined, together the eter actually indicates zero ohs, irrespective of the condition of the battery (within the liits of adjustent). The ethod of adjustent is given below.. Set left-hand knob at Ω-OHMS. 2. Join probes together. 3. Set right-hand knob to x kω or x 00 Ω fro the iddle-right part (green part). 4. The dru should be steady at zero on the green scale. f it is not, arrange knob on the upper-left part until the dru is steady at zero. f it is not possible to obtain zero ohs setting, or furtherore the pointer position does not reain constant, falls steadily, the internal battery (or batteries) should replaced. To test a resistance, the right-hand knob should be at the range required, the leads being connected across unknown coponent. However, the value, where the dru is steady, should be ultiplied by the selected oh range. For exaple, if x kω is selected and the dru is on 0 on the green scale, the value of the resistance is 0 kω. t should be noted that a positive potential appears at the negative terinal of the

13 instruent when set for resistance tests. A resistance of coponent should be easured when it is not connected to any circuit that resistance test should never be carried out on coponents which are already carrying current on or when it is connected to a circuit. 2) DGTAL MULTMETE While ost analog eters require no power supply, give a better visual indication of trends and changes, suffer less fro electric noise and isolation probles, and, are siple and inexpensive, digital eters offer higher accuracy and input ipedance, unabiguous readings at greater viewing distances, saller size, and a digital electrical output (for interfacing with external equipent) in addition to visual readout. The ain part of ost of the digital ultieter (DMMs) is the analog to digital converter (A/D) which converts an analog input signal to a digital output. While specifications ay vary, virtually such ultieters are developed around the sae block diagra of Figure 3. Figure 3. Since the DMM is a voltage sensing eter; current is converted to volts by passing it through a precision low resistance shunt while ac is converted to dc at the AC converter by eploying rectifiers and filters. Most of the AC converters detect the peak value of the signal and are calibrated to give the rs value of a sine wave. However, soe easures the ean of the rectified signal such as the digital ultieter Agilent 3440A. Finally, this dc level is applied to the A/D converter to obtain the digital inforation.

14 For resistance easureent, the eter includes a precision low current source that is applied across the unknown resistor. Then the dc voltage drop across the resistor, which is proportional to the value of the unknown resistor, is easured. For AC easureents, the digital ultieter is a true rs instruent that it easures true rs value of any periodic signal. Figure 4. The digital ultieter used in this laboratory. A) VOLTAGE MEASUEMENT To easure voltage, the instruent should be set to a A.C. or D.C. range (the buttons of DC V and AC V ). The red probe should be connected to upper-right socket and black one to iddle-right socket as indicated in Figure 4. The digital ultieter is an auto-range device that it is not needed to arrange the range of voltage. B) CUENT MEASUEMENT To easure current, the instruent should be set to a suitable A.C. or D.C. range. For this purpose, firstly, blue Shift button is depressed then DC V or AC V button is depressed. The red probe should be connected to lower-right socket and black one to iddle-right socket. C) ESSTANCE MEASUEMENT To easure resistance, the Ω 2W button should be depressed without selecting blue Shift button. The red probe should be connected to upper-right socket and black one to iddle-right socket as in voltage easureent.