Note-4 1
Half-wave Rectifier AC Meters Disadvantages: 1. In negative half-cycle, reverse current flows through the circuit reduces average value of current meter reads lower than actual. 2. High peak inverse voltage (PIV) rating of Diode may be required 2
Solution to these problems: 1. In negative half-cycle, D 2 conducts no negative current flows through the meter movement. 2. PIV rating requirement is much less than the large peak input voltage (V p ). 3
Sensitivity of the voltmeter Input resistance of this circuit - R s +R m (during the positive half-cycle) - R s (during the negative half-cycle) Generally, R s >> R m And, we know that: So, I fsd is the full-scale deflection current of the movement V fsd is the full-scale range (rms) voltage. S ac is the AC sensitivity of the voltmeter and is defined as: So, S ac < S dc 4
Non-linearity in the lower rms ranges - Diode I-V characteristics is non-linear - This non-linearity is maximum at low values of current - Effect of non-linearity can be reduced by operating the diode at relatively higher current Improving the linearity 5
If R sh = R m, the current through diode D 1 doubles to 2I av. So, we can write: The AC sensitivity is now: So, S ac is further reduced. 6
Full-Wave Rectifier Based Meter The average current is given by, It can be shown that R s is given by, Now, the AC sensitivity becomes: This is double that of a half-wave rectifier-based meter. 7
Electrodynamic Meter Movement The main constructional difference with PMMC meter: PMMC meter: uses permanent magnet Electrodynamic meter: uses electro-magnet Three coils two stationary field coils and one moving coil Connected in series; So same current flows through each coil 8
Deflecting Torque: If i 1 is current through the fixed coils. B = K 1 i 1 Wb/m 2 If i 2 is current through the moving coil, Force applied, f = NBi 2 L newton N number of turns in the moving coil; L length of moving coil t D = NBi 2 Lb, So, t D = NK 1 i 1 i 2 Lb b breadth of moving coil For i 1 = i 2 = i, t D = K 1 ANi 2, A effective area of moving coil So, t D α i 2 For a rapidly varying current, the moving system responds to the average value of current. So, t D α (i 2 ) av 9
Controlling Torque: If controlling torque is provided by a spring: t C = K 3 θ Steady-State Deflection: t C = t D θ α (i 2 ) av 10
Calibration: Meter deflection takes the position of average of the squared current. However, the scale is calibrated in terms of the rms value of the sinusoidal signal. As the rms value of a DC signal is its DC value itself, the same scale can be used for both DC and AC signal. So, electrodynamometer type instruments can be calibrated with DC and used for measuring AC rms values 11
Advantages: 1. Can be used for both DC and AC 2. Can be calibrated for rms reading irrespective of voltage waveforms Disadvantages: 1. Low torque/weight ratio, so low sensitivity 2. Non-uniform scale 12
Voltmeter Construction: Similar to PMMC voltmeter, multiplier resistors are connected in series with the coils to limit the current through the meter Ammeter Construction: Similar to PMMC ammeter, shunts are connected in parallel with the moving coil to increase the current measuring range. 13
Why Electronic Analog Meters? Disadvantages of non-electronic meters: - low sensitivity ; low input impedance (for voltmeters) - large power consumption (for low power electronic circuit applications) - accuracy is very low at lower ranges 14
Solutions to these problems: - An amplifier is necessary for sensitive low current, voltage measurement - the amplifier must have very large input impedance so that it draws minimum current from the electronic circuit These can be achieved by electronic meters 15
Electronic DC Voltmeters - The circuit to the right side of A-B is the same as that of a non-electronic DC voltmeter - A single multiplier resistor is used for a fixed maximum voltage across A-B, V A-B = I m (R s +R m ) 16
A Typical Range Selection and Amplifier Circuit - Let the multiplier resistor be designed for a 1 V input at A-B. So the maximum voltage across A-B is 1 V - The meter voltage range selection is done by a combination of input switching and amplifier gain selection - Input switching: two switches, S 1 and S 2 (mutually exclusive). - S 1 : for lower than 1V range - S 2 : for greater than 1V range 17
For input voltages less than 1 V: - S 1 and S 3 are closed - Gain of the non-inverting amplifier is chosen such that the voltage across A-B does not exceed 1 V. - Recall the gain equation for non-inverting amplifier, Gain 1 - For 10 mv range, the gain should be 100, i.e. switch S 7 shall be closed (R i =R 6 = 1k and R f =R 4 +R 5 = 90k +9k =99k ) R R f i - For 100 mv input range, the gain should be 10, i.e. switch S 6 shall be closed (R i =R 5 +R 6 = 9k +1k = 10k and R f =R 4 = 90k ) 18
- For input voltage greater than 1 V: - As the input voltage is greater than 1V, it must be attenuated. - S 2 and S 4 are closed - Resistors R 2 and R 3 provide an attenuation of 100. - Then the gain of the amplifier is selected for appropriate range by closing S 5, S 6 or S 7. - For example, for a 10 V range, first divided by 100 in the voltage divider stage. Then the gain of 10 is selected by closing S 6 which maintains a maximum of 1V across A-B. Input impedance: - R in 10 G (for input ranges less than 1V) - ( R ) 2 R 10 M (for input ranges greater than 1V) 3 R in 19
Electronic DC Ammeter Shunt-type circuit (Fig. a) - Current is converted into voltage by passing through a precision resistor, R S. - This voltage (which is proportional to input current) is measured by an electronic voltmeter. - The scale is calibrated in units of current. - R S should be as low as possible for low input resistance of the ammeter 20
To measure very low currents (i.e. Pico-amperes), this circuit can be employed. - The op-amp is used as the current to voltage converter (voltage = R F I in ). - The resistor, R F, does not need to be very small, as the input resistance of this current to voltage converter circuit is equal to 0, irrespective of the value of R F. - The current which is converted to voltage is then measured by using the electronic voltmeter. - The meter is calibrated in units of current directly. 21
Electronic AC Meters AC Voltmeter: -A rectifier (half-wave or full-wave) is used to convert AC to DC. AC Ammeter: Shunt-type arrangement similar to the DC ammeter is used in these meters 22
Problem Exercise 1 An ac voltmeter is used to measure voltage V across 60 kω resistor in the following circuit. What is the minimum voltage reading that can be indicated by this meter? The specifications of the ac voltmeter are: Meter Specs: - Full-wave rectification - 100 µa meter movement - 15V range - Accuracy = ± 3% fsd 23