The PMMC movement used in d.c. voltmeters can be effectively used in a.c. voltmeters. The rectifier is used to convert a.c. voltage to be measured, to d.d. This d.c., if required is amplified and then given to the PMMC movement. The PMMC movement gives the deflection proportional to the quantity to be measured.
It
is important to study some basic definitions related to the a.c. quantities,
before studying the operation of the a.c. voltmeters. The a.c. meters are
usually calibrated to read r.m.s. value of an alternating quantity to be
measured.
The
r.m.s. value of an alternating quantity is given by the steady current (d.c.)
which when flowing through a given circuit for a given time produces the same
amount of heat as produced by the alternating current which when flowing
through the same circuit for the same time. The r.m.s. value is calculated by
measuring the quantity at equal intervals for one complete cycle. Then squaring
each quantity, the average of squared values is obtained. The square root of
this average value is the r.m.s. value. The r.m.s. means root-mean square i.e.
squaring, finding the mean i.e. average and finally root.
If
the waveform is continuous then instead of squaring and calculating mean, the
integration is used. Mathematically the r.m.s. value of the continuous a.c.
voltage having time period T is given by,
The 1/T term indicates the mean value or average
value.
For purely sinusoidal quantity
Vrms = 0.707 Vm
Where Vm = peak value of the sinusoidal quantity
Most of the a.c. voltmetrs are r.m.s.
responding or average responding type, with scale calibrated interms of the
r.m.s. value of a sine wave.
The avearge value of an a.c. quantity is
another important parameter. The avearge value is defined as that value which
is obtained by averaging all the instantaneous value over a period of a half
cycle. For the symmetrical a.c. quantity, the avearge value over a complete
cycle is zero as both positive and negative half cycles exactly identical. Hence
average value can be expressed mathematically using an integration as,
The interval T/2 indicates the everage over half
a cycle.
For purely sinusoidal quantity,
As mentioned earlier, the average responding
meter scale is also calibrated in terms of r.m.s. values. To achieve such
calibration, a pure sine wave with r.m.s. value of 1 V is applied. Then the
deflection of meter is adjusted to 1 V reading. For this, a particular factor
is required to be considered. This factor is called form factor.
The form factor is the ratio of r.m.s. value to
the average value of an alternating quantity.
For purely sinusoidal waveform the form factor
is 1.11. Thus while calibrating average responding meter interms of r.m.s.
values the markings are actually corrected by a factor of 1.11.
Some meter scales are calibrated in terms of
peak values of the input. In such cases another factor relating peak value and
the r.m.s. value becomes important. This factor is called peak factor or Crest
Factor.
The peak factor or crest factor is the ratio of
peak (maximum) value of the r.m.s. value of an alternating quantity.
For purely sinusoidal a.c. quantity the crest
factor is 1.414
The question is, why to use these factors to
correct the reading by measuring average and peak values, when the true r.m.s.
voltmeter can give direct r.m.s. reading. The reason behind this is that the
average and peak responding meters are less in cost and very simple in
construction as compared to true r.m.s. voltmeters.
A.C. voltmeters can be designed in two ways:
i) First rectifying the a.c. signal and then
amplifying
ii) First amplifying the a.c. signal and the
rectifying.
1.1) First rectifying the a.c. signal and then
amplifying
In this arrangement simple diode rectifier
circuit preceds the amplifier and the meter. This is shown in the Fig 1.
 |
| Fig 1 |
The a.c. input voltage if irst rctified using
the diode D. This rectified signal is then applied to the amplifier of gain A.
The amplified siganl is then given to the basic PMMC meter to obtain the
deflection.
This approach ideally requires a d.c. amplifier
with zero drift characteristics and a d.c. meter movement with high
sensitivity. The resistance Rin indicates input resistance of the meter.
1.2) First amplifying the a.c. signal and the
rectifying.
In this approach, the a.c. input signal which
is a small signal is amplified first and then rectified after the sufficient
amplification. The a.c. signal is applied to an amplifier and hence amplifier
is necessarily an a.c. amplifier. This type of approach is shown in the Fig.2
The a.c. amplifier requires a high open loop
gain and the large amount of negative feedback to overcome the nonlinearity of
the rectifier diodes.
The amplifier output is then applied to full
wave rectifier consisting of diodes D1 and D2.
The diodes are nonlinear devices, particularly
at the low values of the forward current. This is shown in the Fig. 3.
 |
| Fig 3 forward characteristics of a diode |
Due to this nonlinear behaviour of the diodes,
the meter scale is also nonlinear and is crowded at the lower end of a low
range voltmeter.
In this region, the meter sensitivity is also
very low because of high forward resistance of the diode. Dependence of diode
characteristics on temperature is also an important factor in a.c. voltmeters. The
rectifier shows the capacitance properties under reverse biased and tends to
bypass high frequencies. The meter reading may have error due to such effect of
the order of 0.5 % decrease of every 1 kHz rise in the frequency.