### AC Voltmeter using Rectifiers

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.