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12.1 THE D'ARSONVAL METER The D'Arsonval meter consists of a moving coil of fine wire suspended between the poles of a permanent magnet, and has long been the most popular analog measuring instrument. The tautband meter, a recent improvement, replaces the jeweled pivot with a torsion band suspension to eliminate hysteresis (stickiness) in the movement of the pointer. Precision meters have mirrored scales to eliminate parallax, the error incurred when the eye views the meter from a side angle. Keeping the mirror image of the pointer directly behind the pointer ensures that you are viewing the meter "headon." D'Arsonval meters are specified in terms of their fullscale current sensitivity and their coil resistance. Sensitive D'Arsonval meters (often called galvanometers) can be used to produce a voltmeter, ammeter, or ohmmeter of any desired range using the Ohm's law calculations outlined in the next three sections. The resistance of an unknown meter should not be determined by measuring it with an ohmmeter because a VOM may inject enough current to destroy a sensitive meter. Instead, bleed fullscale current though the meter and a highvalue resistor (100 kOhm 10 kOhm), measure the voltage across the meter coil and calculate Rc = Vc/I, as illustrated in Fig. 121.
12.2 THE VOLTMETER CIRCUIT A voltmeter circuit is shown in Fig. 122(a). A multiplying resistor, Rm, is placed in series with the meter to drop all the input voltage except that required by the meter itself. To calculate the value of the multiplying resistor: . Calculate the fullscale voltage drop across the meter itself: Ve = I t, Rc. Select the fullscale voltage input, Vin . . Subtract to find the voltage on the resistor: VRm =  Vc. . Calculate Rm using the fullscale meter current: Rm = VRm/I, s
EXAMPLE 121 A meter with /f,= 100 /iA and Rc = 2 kOhm is to be used to make a 5V fullscale metering circuit. Find Rm. Solution =48 kOhm Voltmeter Loading is an undesirable effect produced when the meter circuit siphons away an appreciable portion of the current from the circuit under test. The result is an actual lowering of the voltage between the test points when the meter is connected. The extent of voltmeter loading can be calculated by Ohm, s law if the meter resistance and circuit resistances are known. EXAMPLE 122 Find the error that will be encountered if the meter of Example 121 is used to measure in the circuit of Fig. 122(b). Solution The voltage before the meter is connected is 0.5 X 8 V, or 4 V, by inspection. The meter circuit resistance totals 50 kOhm (Rc + Rm). =33% Voltmeter loading error can be held to a maximum of 10% if the meter has a resistance at least 10 times the lower of or R2 in Fig. 122(b), to 1% if is 100 times or R2, and 0.1% if R_meter is 1000 times R1 or R2. Voltmeter Resistance is, therefore, an important property with which the technician should be familiar. Electronic meters (VTVMs, DVMs, and FET meters) generally have input resistances of about 10 Ml. The standard oscilloscope input impedance is 1 Ml, or 10 Ml when used with a X 10 probe. The common portable VOM has an input sensitivity of 20 k Ohm/V, which means that it has a resistance of 200 k Ohm on the 10V scale, 2 Mohm on the 100V scale, 5 Mohm R on the 250V scale, and so on. Many instruments also have an appreciable capacitance in shunt with their input resistance, and this adds to the loading effect at high frequencies. For example, a ' scope with 20 pF of input capacitance measuring a 1 MHz signal presents an input impedance of about 8 kohm capacitive, and its loading effect must be reckoned with this in mind. If two metering devices are available (e.g., a VOM and an oscilloscope), the loading effect of one can actually be observed on the other as they are alternately connected and disconnected to the points under test. This technique is often more practical than trying to calculate the relative impedances of the circuit versus the meter. 12.3 AMMETER CIRCUITS A galvanometer is converted to an ammeter of any desired range by connecting a shunt resistor across it which bypasses all the measured current except that required by the meter itself. The circuit is shown in Fig. 123(a). To calculate the value of the shunt: . Calculate the full scale voltage across the meter: V_ts = I tsRc . Select the fullscale input current I_in. . Subtract the meter’s fullscale current to find the current that must be carried by the shunt resistor: IRsb = / m  / fs. . Calculate Rsh using the fullscale voltage which appears across the meter and shunt resistor together: Rsh = VfJIRsh. EXAMPLE 123 A 0 to 1mA meter movement with a coil resistance of 50 is to be converted to a 0 to 15mA meter. Find the required shunt resistance. Solution = 3.57 ohm Ammeter Loading: Notice that this metering circuit has a resistance of 50  3.57, or 3.33 Q, which must be considered when the meter is inserted in a line. This resistance will cause a linevoltage drop of 50 mV at fullscale current. Generally, these facts will present no serious problem, but in some cases meter voltage Vfs may be an appreciable fraction of the source voltage Vs, or changes in the load current may produce objectionable output voltage changes due to the IR drop across the meter. Both of these ammeter loading problems are represented in extreme degree by Fig. 123(b). The meter here is 150 mA with a 3.3K coil. MultipleRange Ammeters can be constructed by simply switching in different shunt resistors, as shown in Fig. 123(c). If this circuit is used, however, it is essential that a makebeforebreak (also called shorting) type of switch be used. Otherwise, the entire input current would flow through the sensitive meter coil while the switch wiper was in transition between positions, and a bent meter pointer or burnedout coil would be the likely result. If such a switch is not available, an Ayrton shunt arrangement, shown in Fig. 123(d) can be used. Note that the measured current is interrupted during switch transitions with the Ayrton shunt. This may be objectionable in some applications, such as those involving inductive loads.
12.4 OHMMETER CIRCUITS A series ohmmeter circuit is shown in Fig. 124(a). In operation the probe lines are first shorted together, and zeroing resistance Rt is adjusted for fullscale meter deflection. Then the unknown resistor is connected and its value is read from a specially calibrated scale.
Any ohmmeter constructed according to this circuit will have a righthand limit of 0 ohm and a lefthand limit of infinity. Nevertheless, ohmmeter sensitivities do vary, and we can conveniently quantify this by specifying the centerscale ohms reading for a particular circuit. Highersensitivity ohmmeters (those having higher centerscale ohms readings) can be produced by increasing the battery voltage or by increasing the galvanometer current sensitivity, and conversely, lowerscaled meters can be produced by lowering either of these parameters. EXAMPLE 124 Find the value of Rz and the centerscale reading for the ohmmeter of Fig. 124(a). Solution First the total series circuit resistance for fullscale current is found: V 1 5 RT=~= , . = 15 kOhm. The meter coil has 2 kohm of resistance, and the battery is assumed to have zero resistance. = 15k ohm2k ohm = 13k ohm The total resistance at halfscale current is R _ y = i.sv _30ko 1/2) ~ TV/1 0.05 mA The meter and Rz account for 15 kl, so R /i is found: EXAMPLE 125 Find the battery voltage required to produce a centerscale reading of 100 k Q using the circuit and meter movement of Fig. 124(a). Solution Although shortcuts are possible, the most general solution is to write equations for fullscale deflection with zeroing resistance only (Rt includes Rc in this example) and partial deflection with the required resistance added: Vs = I„Rz 0.5 Kt = 5V Any desired deflection (other than half scale) could have been specified by choosing the appropriate value in place of /ctr. An expanded lowohms range can be obtained by lowering the effective source voltage, as shown in Fig. 124(b). EXAMPLE 126 Find the values of Rx and R2 in Fig. 124 such that the available 1.5V battery produces a onequarter scale deflection for a resistance of 600 ohm. Solution First it is necessary to draw the Thevenin equivalent of Vs, Rt, and R2 Then we proceed as in Example 125. Now it is only necessary to determine Rt and R2 to divide the 1.5 V down to 0.2 V while making their Thevenin resistance equal the required zeroing resistance. EXAMPLE 127 Note that in the circuit of Fig. 124(b), R1 and R2 draw current from the battery even with no external resistor connected. Meet the specifications of Example 126 by shunting the meter to decrease its sensitivity, thus avoiding this problem. Refer to Fig. 125. Solution The lowohms circuit offered in Fig. 125 is the one that is generally used in commercial instruments, but it does considerably increase the current in the external resistor, whereas the circuit of Fig. 124(b) does not.
The Shunt Ohmmeter circuit of Fig. 126 is used occasionally where a very low scale ohmmeter is required. It also has the disadvantage of drawing battery current continuously. Its scale has zero on the left, and hence it cannot use the same scale as the higherrange series meters on a X 1, X 10, X 100 basis. The zeroing resistor is adjusted for full scale (infinity) with the probes open circuited. Very low ranges can be realized with this circuit only if the metercoil resistance is low.
12.5 METER PROTECTION D'Arsonval movement meters can typically withstand overloads of X 5 or X 10 without damage. Very fastacting instrument fuses are available in ratings from a few amperes down to a few milliamperes for the protection of meter movements, but this range falls short of being able to protect the very common (and very expensive) meter movements in the 50 to 100uA range. Solidstate electronic circuit breakers provide the ultimate protection, but a simpler and very effective expedient is shown in Fig. 127. The current drawn by a silicon junction diode is less than 1 uA for voltages below 0.4 V, but reaches about 1 A at 1 V forward. Thus if a meter movement has a fullscale voltage between 0.1 and 0.4 V (which is common) a pair of diodes connected across it will not conduct in the meter’s normal operating range, but will turn on heavily and shunt large overload currents around it. Of course, serious overloads would destroy the diode, but an inexpensive jA fast fuse can be used to open the line before this happens.
12.6 EXPANDED AND COMPRESSED SCALES Occasionally, it is desired to have a meter scale that does not read linearly from zero to full scale. One example of this is a 117V line monitor, which may read from 105 to 125 V but will certainly never read in the 0 to 100V range. The circuit of Fig. 128(a) can be used to provide an expanded 100 to 130V scale for easier reading. Tuning meters and null detectors are more convenient if they are very sensitive to small signals, yet do not overload and pin on large signals. A silicon diode in the circuit of Fig. 128(b) can be used to reduce the sensitivity of the meter at midscale by switching part of the input current around the meter. EXAMPLE 128 What is the fullscale input voltage of the metering circuit of Fig. 128(b)? Solution = 6.0 V
12.7 AC METERS Ac ammeters and voltmeters are generally constructed using two electromagnets, rather than one electromagnet and one permanent magnet as in the D'Arsonval meter. These twocoil meters are called electrodynamometers. The torque that turns the pointer is proportional to the product of the currents in the two coils, which is positive for either current direction if they are connected in series. Torque is then proportional to I^2 , so scale linearity is a problem. Sensitivity is also a problem, since the fixed coil cannot generally rival the field strength of the permanent magnet in the D'Arsonval meters. Electrodynamometer ammeters down to 100 mA ac and voltmeters down to 5 V ac full scale are commonly available. D’Arsonvalmovement microammeters are often used in conjunction with solidstate rectifiers to provide ac voltage indication. However, even the special metallic rectifiers that are generally used have forward voltage drops in excess of 0.1 V, resulting in a 0.1 to 0.2V dead zone at the bottom end of the scale. This dead zone is not significant on highvoltage scales, but causes serious nonlinearities on scales of 5 V and below. The voltage drop is generally held to be too great to tolerate in a current meter, so rectifiertype ammeters are not generally used. Figure 129 shows a simple halfwaverectifier type ac voltmeter. The second diode, shown in dashed lines, is used to shunt out reverse meter currents when metallic rectifiers, which are very leaky in the reverse direction, are employed. It also allows source current to flow in both directions so that a capacitor can be inserted in series with the circuit. This will keep any dc that may be present from influencing the ac reading. As illustrated, the meter current lows only on one halfcycle, and varies with the sinewave voltage. The meter responds to the average value of this current which, for large sine waves, is: (121) ...where VD is the diode voltage drop and R includes both the series multiplier resistance and the metercoil resistance. EXAMPLE 129 The meter in Fig. 129 is 100 /x A full scale, with a 2 kOhm coil. The diode is silicon with VD  0.6 V. What value of multiplier resistance will make a 10Vrms full scale? Solution = 40.93 kOhm
12.8 WATTMETERS The most common type of wattmeter is an electrodynamometer with one fixed coil of heavy wire to sense current and one movable coil of fine wire to sense voltage to the load. The wires may be brought out as shown in Fig. 1210(a) or (b). Such a meter will respond to true power, even if a reactive load produces a phase difference between V and I, or if Vs contains a dc component or is not a sine wave.

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