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Transcript
EMT 462 ELECTRICAL SYSTEM TECHNOLOGY Chapter 4: AC Meters By: En. Muhammad Mahyiddin Ramli Alternating Current Waveform Sinusoidal wave Square wave Triangle wave Chap 4: AC Meters 2 Alternating Current Waveform Chap 4: AC Meters 3 Chap 4: AC Meters 4 Average and RMS Value Vavg = 0 Vrms = 0.707Vp Sine Wave Vavg = 0.636Vp Vrms = 0.707Vp Full Wave Chap 4: AC Meters 5 Con’t Vavg = 0.318Vp Vrms = 0.5Vp Half Wave Chap 4: AC Meters 6 Five Principal Meter Movements Used In AC Instrument 1. Electrodynamometer 2. Iron Vane 3. Electrostatic 4. Thermocouple 5. D’Arsonval with rectifier Chap 4: AC Meters 7 Application of Meter Movements Meter Movement DC Use AC Use Applications Electrodynamometer YES YES Standards meter, wattmeter, frequency meter “Indicator” applications such as in automobiles Iron Vane YES YES “Indicator” applications such as in automobiles Electrostatic YES YES Measurement of high voltage when very little current can be supplied by the circuit being measured Thermocouple YES YES Measurement of radio frequency ac signal D’Arsonval YES YES with rectifier Most widely used meter movement for measuring direct current or voltage and resistance Chap 4: AC Meters 8 PMMC Instrument on AC The PMMC instrument is polarized (terminals +ve & -ve) - it must be connected correctly for positive (on scale) deflection to occur. When an AC with a very low frequency is passed through a PMMC, the pointer tends to follow the instantaneous level of the AC As the current grows positively, the pointer deflection increases to a maximum at the peak of the AC As the instantaneous current level falls, the pointer deflection decreases toward zero. When the AC goes negative, the pointer deflected (off scale) to the left of zero This kind of pointer movement can occur only with AC having a frequency of perhaps 0.1Hz or lower Chap 4: AC Meters 9 PMMC Instrument on AC At 50Hz or higher supply frequencies - the damping mechanism of the instrument and the inertia of the meter movement prevent the pointer from following the changing instantaneous levels. The average value of purely sinusoidal AC is zero. Therefore, a PMMC instrument connected directly to measure 50Hz AC indicates zero average value. It is important to note that although a PMMC instrument connected to an ac supply may indicating zero, there can actually be very large rms current flowing in its coils Chap 4: AC Meters 10 Two Types of PMMC Meter Used In AC Measurement 1. Half wave rectification 2. Full wave rectification Chap 4: AC Meters 11 D’Arsonval meter movement used with half wave rectification To convert alternating current (AC) to unidirectional current flow, which produces positive deflection when passed through a PMMC, the diode rectifier is used. Several types of rectifiers are selected such as a copper oxide rectifier, a vacuum diode, or semiconductor or “crystal diode”. VP Vrms 2 Vave Vdc 0.318Vp Vave Chap 4: AC Meters Vp 2 Vrms 0.45Vrms 12 Con’t For example, if the output voltage from a half wave rectifier is 10Vrms so the dc voltmeter will provide an indication of approximately 4.5V dc Therefore, the pointer deflected full scale when 10V dc signal is applied. When we apply a 10Vrms sinusoidal AC waveform, the pointer will deflect to 4.5V This means that the AC voltmeter is not as sensitive as DC voltmeter. In fact, an AC voltmeter using half wave rectification is only approximately 45% as sensitive as a dc voltmeter. Chap 4: AC Meters 13 Con’t Actually, the circuit would probably be designed for full-scale deflection with a 10V rms AC applied, which means the multiplier resistor would be only 45% of the value of the multiplier resistor for 10V dc voltmeter. Since we have seen that the equivalent dc voltage is equal to 45% of the rms value of the ac voltage. E dc 0.45E rms Rs Rm Rm I dc I dc Sac = 0.45Sdc Chap 4: AC Meters 14 Con’t Commercially produced ac voltmeters that use half wave rectification also has an additional diode and a shunt as shown in Figure below: Chap 4: AC Meters 15 Con’t The additional diode D2 is reverse biased on the positive half cycle and has virtually no effect on the behavior of the circuit. In the negative half cycle, D2 is forward biased and provides an alternate path for reverse biased leakage current that would normally through the meter movement and diode D1. The purpose of the shunt resistor Rsh is to increase the current flow through D1 during positive half cycle so that the diode is operating in a more linear portion of its characteristic curve. Although this shunt resistor improves the linearity of the meter on its low voltage ac ranges, it also further reduces the AC sensitivity. Chap 4: AC Meters 16 Example 3.1 Compute the value of the multiplier resistor for a 10Vrms ac range on the voltmeter shown below: RS Ifs = 1mA Ein = 15Vrms Rm = 300Ω AC voltmeter using half wave rectification Chap 4: AC Meters 17 Solution Method 1 The sensitivity of meter movement 1 1 Sdc 1k / V I fs 1m Rs = Sdc × Rangedc – Rm = 1k × 0.45E rms 1 - Rm = 1k × 0.45(10) – 300 = 4.2k Chap 4: AC Meters 18 Con’t Method 2 The AC sensitivity for half way rectifier Sac = 0.45Sdc = 0.45(1k) = 450/V Rs = Sac × Rangeac – Rm = 450 × 10 –300 = 4.2k Chap 4: AC Meters 19 D’Arsonval meter movement used with full wave rectification Electrodynamometer, Iron-vane meter, thermocouple meter Loading effects of AC Voltmeter Chap 4: AC Meters 20 D’Arsonval Meter Movement Used With Full Wave Rectification Full bridge rectifier used in an ac voltmeter circuit During the positive half cycle, currents flows through diode D2, through the meter movement from positive to negative, and through diode D3. The polarities in circles on the transformer secondary are for the positive half cycle. Since current flows through the meter movement on both half cycles, we can expect the deflection of the pointer to be greater than with the half wave cycle, which allows current to flow only on every other half cycle; if the deflection remains the same, the instrument using full wave rectification will have a greater sensitivity. Chap 4: AC Meters 21 Consider the following circuit: AC voltmeter using full wave rectification Chap 4: AC Meters 22 Con’t When the 10Vrms of AC signal is applied to the circuit above, where the peak value of the AC input signal is E p 2 xE rms 1.414x (10) 14.14V And the average full wave output signal is E ave E dc 0.636xE p 0.636x14.14 9V Therefore, we can see that a 10Vrms voltage is equivalent to 9Vdc for full-scale deflection. Chap 4: AC Meters 23 Con’t Or E avg 0.636E p 0.636( 2 xE rms ) 0.9E rms This means an ac voltmeter using full wave rectification has a sensitivity equal to 90% of the dc sensitivity Sac = 0.9 Sdc Chap 4: AC Meters 24 Example 3.2 Compute the value of the multiplier resistor for a 10Vrms ac range on the voltmeter in Figure 1-2. AC voltmeter circuit using full wave rectification Chap 4: AC Meters 25 Solution The dc sensitivity is: 1 1 Sdc 1k / V I fs 1mA The ac sensitivity is: Sac = 0.9Sdc = 0.9 (1k) = 900 /V Chap 4: AC Meters 26 Con’t Therefore the multiplier resistor is: Rs = Sac x Range – Rm = 900 x 10Vrms – 500 = 8.5k Chap 4: AC Meters 27 Assignment AC Meters RS Ein = 10Vrms Ifs = 1mA Rsh = 0.5kΩ Rm = 0.5kΩ Each diode in full-wave rectifier circuit above has an average forward resistance of 50Ω and is assumed to have an infinite resistance in the reverse direction. Calculate: a) Multiplier resistance, RS b) AC sensitivity c) The equivalent dc sensitivity. Chap 4: AC Meters 28 Notice Note: Voltmeters using half wave and full wave rectification are suitable for measuring sinusoidal ac voltages only. Chap 4: AC Meters 29 Electrodynamometer Movement Source Fixed Coil Moving Coil Fixed Coil Most fundamental and versatile meter use today. Is a current-sensitive device – the pointer deflects up scale because of current flow through moving coil. Most important applications: voltmeter and ammeter standard. Chap 4: AC Meters 30 Electrodynamometer Movement The single-coil electrodynamometer movement consists of a fixed coil divided into two equal halves. Both halves of the split fixed coil and the moving coil are connected in series – current from the circuit being measured passed through all the coils causing magnetic field around the fixed coils. The moving coil rotates in this magnetic field. The electrodynamometer – handle much more current than d’ Arsonval movement. It can handle ~ 100mA. The electrodynamometer – have a very low sensitivity rating of ~ 20 to 100 Ω/V. Most extensive application: Wattmeter. The magnetic torque that cause pointer deflect up scale: m K m El cos Θm – angular deflection of the pointer Km – instrument constant (degrees/watt) cos θ – power factor E – rms value of source voltage l – rms value of source current Chap 4: AC Meters 31 Iron-Vane Meter Movement • The iron-vane meter movement consists of a fixed coil of many turns and two iron vanes placed inside the fixed coil. • it is widely used in industry. I • the current can be measured passes through the winding of the fixed coil setting up a magnetic field that magnetized the two iron vanes with the same polarity. Chap 4: AC Meters 32 Iron-Vane Meter Movement If one iron vanes is attached to the frame of a fixed coil – the other iron vane will then be repelled by amount related to the square of current. Although it is responsive to direct current (the hysteresis) – the iron vanes causes appreciable error. (used only for a very inexpensive indicators, i.e charge-discharge indicators on automobiles). It is used extensively in industry for measuring ac when errors on the order of 5% to 10% are acceptable. Iron-vane movement very sensitive to frequency change (25 – 125 Hz) - it is because the magnetization of the iron vane is nonlinear. Chap 4: AC Meters 33 Thermocouple Meter Basic thermocouple meter Usually consists a heater element – fine wire, a thermocouple, and d’Arsonval meter movement. To measure a very high-frequency ac (very accurate well > 50Hz). Chap 4: AC Meters 34 Loading Effect of AC Voltmeter The sensitivity of ac voltmeters, using either half wave or full wave rectification, is less than the sensitivity of dc voltmeters. Therefore, loading effect of an ac voltmeter is greater than that of a dc voltmeter. Sac = 0.45Sdc Sac = 0.9Sdc Chap 4: AC Meters 35 Voltage and Current Transformer Applications Calibrating AC voltmeters and ammeters for different fullscale ranges of operation is much the same as with DC instruments: series "multiplier" resistors are used to give voltmeter movement a higher range, and parallel "shunt" resistors are used to allow ammeter movements to measure currents beyond their natural range. However, we are not limited to these techniques as we were with DC: because we can use transformers with AC too. Chap 4: AC Meters 36 Summary For general purposes, the d’Arsonval movement – either half-wave or full-wave rectifier, is widely used. Meter Movement App. Voltage & Freq. Reading Obtained D’Arsonval 10Vrms, 60 Hz 0V Iron vane 10Vrms, 60 Hz 10V Electrodynamometer 10Vrms, 60 Hz 10V Thermocouple 10Vrms, 60 Hz 10V D’Arsonval with halfwave rectifier 10Vrms, 60 Hz 4.5V D’Arsonval with fullwave rectifier 10Vrms, 60 Hz 9.0V Iron vane 10VDC 10V Electrodynamometer 10VDC 10V Thermocouple 10VDC 10V Chap 4: AC Meters 37 Success is the ability to go from one failure to another with no loss of enthusiasm. - Sir Winston Churchill Chap 4: AC Meters 38