ALTERNATING CURRENT METERS

Part 2

2

Objectives

• Ability to know the operation & Analyzed D’Arsonval meter movement used with half wave rectification

• Abilty to know the operation & analyzed D’Arsonval meter movement used withfull wave rectification

• Types of meter movement and application for each meter movement.

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Alternating Current Waveform

Sinusoidal wave

Square wave

Triangle wave

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Alternating Current Waveform

Erms= E(root mean square), Ep-p= E peak-peak, Ep= E peak

5

Vavg = 0Vrms = 0.707Vp

Vavg = 0.636Vp

Vrms = 0.707Vp

Vavg = 0.318Vp

Vrms = 0.5Vp

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Vavg = 0

Vrms = 0.707Vp

Average and RMS Value

Sine Wave

Full Wave

Vavg = 0.636Vp

Vrms = 0.707Vp

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Vavg = 0.318Vp

Vrms = 0.5Vp

Cont..

Half Wave

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Five principal meter movements used in ac instrument

1. Electrodynamometer2. Iron Vane3. Electrostatic4. Thermocouple5. D’Arsonval with rectifier

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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

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• 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

PMMC Instrument on AC

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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

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1. Half wave rectification2. Full wave rectification

Two types of PMMC meter used in AC measurement :

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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”.

pVV

V Prms 5.0

2

rmsrmsp

ave VVV

V 45.02

pdcave V318.0VV

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• 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.

Cont…

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•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.

Cont…

mdc

rmsm

dc

dcs R

I

E45.0R

I

ER

Sac = 0.45Sdc

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Commercially produced ac voltmeters that use half wave rectification also has an additional diode and a shunt as shown in Figure below:

Cont..

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•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.

Cont…

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Example 1-1

Compute the value of the multiplier resistor

for a 15Vrms ac range on the voltmeter

shown in Fig. 1.

Fig. 1: AC voltmeter using half wave rectification

RS

Ein = 15Vrms

Ifs = 1mA

Rm = 300Ω

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Solution:

Method 1

The sensitivity of the meter movement,

V/k1m1

1

I

1S

fsdc

Rs = Sdc × Rangedc – Rm

= 1k × 1

E45.0 rms - Rm

= 1k × 0.45(10) – 300

= 4.2k

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Cont.

Method 2

The AC sensitivity for half wave rectifier,

Sac = 0.45Sdc = 0.45(1k) = 450/V

Rs = Sac × Rangeac – Rm

= 450 × 10 –300

= 4.2k

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Cont.

Rs = mfs

rms RI

E45.0

300m1

1045.0

= 4.2k

=

Method 3

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Example 1-2

Calculate the ac and dc sensitivity and the value of the multiplier resistor required to limit the full scale deflection current in the circuit shown in Fig above.

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D’Arsonval meter movement used with full wave

rectification

Fig. 2: 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.

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Consider the circuit shown in Fig. 1-2

Fig. 1-2: AC voltmeter using full wave rectification

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Cont.When the 10Vrms of AC signal is applied to the circuit above, where the peak value of the AC input signal is

V14.14)10(x414.1xE2E rmsp

And the average full wave output signal is

V914.14x636.0xE636.0EE pdcave

Therefore, we can see that a 10Vrms voltage is equivalent to 9Vdc for full-scale deflection.

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Cont.

Sac = 0.9 Sdc

rmsrmspavg E9.0)xE2(636.0E636.0E

Or

This means an ac voltmeter using full wave rectification has a sensitivity equal to 90% of the dc sensitivity

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Example 1-2Compute the value of the multiplier resistor for a 10Vrms ac range on the voltmeter in Figure 1-2.

Fig. 1-2: AC voltmeter circuit using full wave rectification

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Solution 1-2

The dc sensitivity is

V/k1mA1

1

I

1S

fsdc

The ac sensitivity is

Sac = 0.9Sdc = 0.9 (1k) = 900 /V

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Cont.

Therefore the multiplier resistor is

Rs = Sac x Range – Rm

= 900 x 10Vrms – 500

= 8.5k

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Cont.

Note: Voltmeters using half wave and

full wave rectification are suitable for measuring only sinusoidal ac voltages.

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Electrodynamometer Movement

Fixed CoilMoving Coil

Fixed Coil

Source

• 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.

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Electrodynamometer (Cont..)• 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:

cosElKmm Θm – angular deflection of the pointer E – rms value of source voltageKm – instrument constant (degrees/watt) l – rms value of source currentcos θ – power factor

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Iron-vane Meter Movement

I

• 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.

• 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.

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Iron-vane Meter (Cont…)• 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.

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Thermocouple Meter

d’ Arsonval meter

movement

Heater

Insulating bead

Thermocouple

Source

I

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).

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Loading effects 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

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Calibrating AC voltmeters and ammeters for different full-scale 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.

Voltage and Current Transformer Applications

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SUMMARY

• The D’Arsonval Meter Movement - Current-sensitive device capable of directly measuring only very small currents.

• D’Ársonval Meter Movement Used In A DC Ammeter : This done by placing a low resistance called a shunt (Rsh) in parallel, and its function is to provide an alternate path

• The Ayrton Shunt- The purpose of designing the shunt circuit is to allow to measure current I that is some number n times larger than Im.

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SUMMARY

• D’Ársonval Meter Movement Used In A DC Voltmeter: The basic d’Ársonval meter movement can be converted to a dc voltmeter by connecting a multiplier Rs in series with the meter movement

• Voltmeter Loading Effects: is used to measure the voltage across a circuit component

• 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

40

SUMMARY

D’Arsonval meter movement used with full wave rectification: deflection of the pointer to be greater than with the half wave cycle, which allows current to flow only on every other half cycle

Loading effects of AC Voltmeter: loading effect of an ac voltmeter is greater than that of a dc voltmeter