AC meters and Instruments

The d'Arsonval movement employed in dc meters can also be used to measure sinusoidal voltages and currents if the bridge rectifier of [Fig. 1] is placed between the signal to be measured and the average reading movement.
Full-wave bridge rectifier
Fig. 1: Full-wave bridge rectifier
The bridge rectifier, composed of four diodes (electronic switches), will convert the input signal of zero average value to one having an average value sensitive to the peak value of the input signal. The conversion process is well described in most basic electronics texts. Fundamentally, conduction is permitted through the diodes in such a manner as to convert the sinusoidal input of [Fig. 2(a)] to one having the appearance of [Fig. 2(b)]. The negative portion of the input has been effectively flipped over by the bridge configuration. The resulting waveform of [Fig. 2(b)] is called a full-wave rectified waveform.
full-wave rectified waveform
Fig. 2: (a) Sinusoidal input; (b) full-wave rectified signal.
The zero average value of [Fig. 2(a)] has been replaced by a pattern having an average value determined by
$$G = {2V_m + 2V_m \over 2\pi} = {4V_m \over 2\pi}= 0.637Vm$$
The movement of the pointer will therefore be directly related to the peak value of the signal by the factor $0.637$.
Forming the ratio between the rms and dc levels will result in
$$ {V_{rms} \over V_{dc}} = {0.707Vm \over 0.637Vm}= 1.11$$
revealing that the scale indication is $1.11$ times the dc level measured by the movement; that is,
$$\text{Meter indication(full-wave)} = 1.11 (dc or average value)$$
Some ac meters use a half-wave rectifier arrangement that results in the waveform of [Fig. 3], which has half the average value of [Fig. 2(b)] over one full cycle. The result is
$$\text{Meter indication(full-wave)} = 2.22 \text{(dc or average value)}$$
Half-wave rectified signal
Fig. 3: Half-wave rectified signal.
Electrodynamometer movement
Fig. 4: Electrodynamometer movement.
A second movement, called the electrodynamometer movement ([Fig. 4]), can measure both ac and dc quantities without a change in internal circuitry. The movement can, in fact, read the effective value of any periodic or non-periodic waveform because a reversal in current direction reverses the fields of both the stationary and the movable coils, so the deflection of the pointer is always up-scale.
The VOM, introduced before, can be used to measure both dc and ac voltages using a d'Arsonval movement and the proper switching networks. That is, when the meter is used for dc measurements, the dial setting will establish the proper series resistance for the chosen scale and will permit the appropriate dc level to pass directly to the movement. For ac measurements, the dial setting will introduce a network that employs a full- or half-wave rectifier to establish a dc level. As discussed above, each setting is properly calibrated to indicate the desired quantity on the face of the instrument.
Example 1: Determine the reading of each meter for each situation of [Fig. 5(a)] and [(b)].
Fig. 5Example 1.
For [Fig. 5(a)], situation (1): By Eq. (1),
$$\text{Meter indication} = 1.11(20 V) = 22.2 V$$
For [Fig. 5(a)], situation (2):
$$V_{rms} = 0.707V_m = 0.707(20 V) = 14.14 V$$
For [Fig. 5(b)], situation (1):
$$V_{rms} = V_{dc} = 25 V$$
For [Fig. 5(b)], situation (2):
$$V_{rms} = 0.707Vm = 0.707(15 V) = 10.6 V$$

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