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This result is noticeably less than the above solution. The development
of Eq. (13.37) can be found in Chapter 25.
Instrumentation
It is important to note whether the DMM in use is a true rms meter or
simply a meter where the average value is calibrated (as described in
the next section) to indicate the rms level. A true rms meter will read
the effective value of any waveform (such as Figs. 13.49 and 13.61)
and is not limited to only sinusoidal waveforms. Since the label true
rms is normally not placed on the face of the meter, it is prudent to
check the manual if waveforms other than purely sinusoidal are to be
encountered. For any type of rms meter, be sure to check the manual for
its frequency range of application. For most it is less than 1 kHz.
13.8 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.
13.62 is placed between the signal to be measured and the average reading
movement.
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. 13.63(a) to one having the
appearance of Fig. 13.63(b). The negative portion of the input has been
effectively “flipped over” by the bridge configuration. The resulting
waveform of Fig. 13.63(b) is called a full-wave rectified waveform.
V m
–V m
v i
0 � 2� �
0 � 2� �
(a)
V m
v movement
(b)
FIG. 13.63
(a) Sinusoidal input; (b) full-wave rectified signal.
V dc = 0.637V m
The zero average value of Fig. 13.63(a) has been replaced by a pattern
having an average value determined by
2Vm � 2Vm 4Vm 2Vm G ��� �����0.637Vm 2p
2p p
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
� Vdc
0.707Vm �� � 1.11
0.637Vm
ac METERS AND INSTRUMENTS ⏐⏐⏐ 551
+
v i
–
v movement
–
+
FIG. 13.62
Full-wave bridge rectifier.