AC VOLTMETERSElectronic Measurements Lab
Massimo Ortolano
POLITECNICO DI TORINO
c© 2011–2016 Massimo Ortolano
Dipartimento di Elettronica e Telecomunicazioni (DET)
Politecnico di Torino
Corso Duca degli Abruzzi, 24
10129 Torino
Italy
Email: [email protected]
This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported
License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 444 Castro Street, Suite 900, Mountain View, California, 94041,
USA.
1 Preliminaries
The objective of this lab is to study the response of different types of AC voltmeters to
sinusoidal and non-sinusoidal input waveforms.
Equipment (instrument specifications):
• Bench DC power supply
• Signal generator board (LED product)
• Digital oscilloscope
• Handheld analog multimeter (tester) (Metrix MX1 or ICE 680)
• Bench digital multimeter (Agilent/Hewlett-Packard HP34401A)
• ER-15 Peak probe (LED product)
• 1 banana plug to banana plug cable (figure 1)
• 1 three-wire power cable (figure 2)
• 2 BNC male to BNC male cables (figures 3 and 4)
• 1 BNC male to banana plug cable
• 1 crocodile clips to BNC male cable (figure 5)
• 1 BNC T adaptor (figure 6)
Figure 1: A banana plug. Figure 2: Three-wire power cable for the signal gen-
erator board.
(Preliminaries)
Figure 3: A BNC male con-
nector.
Figure 4: A BNC male to
BNC male cable.
Figure 5: A crocodile (al-
ligator in the US) clip.
Figure 6: A BNC T ad-
aptor.
(Preliminaries)
1.1 DC measurements
Given a periodic voltage waveform v(t) with period T , its direct component (DC compon-
ent) is the mean value of v(t) over a period,
Vdcdef=
1T
∫ t0+T
t0
v(t)dt, (1)
where t0 is an arbitrary time instant.
When a periodic voltage waveform is applied to the input of a DC voltmeter, and the
waveform period is much less than the voltmeter integration time, the voltmeter reading
corresponds approximately to the DC component, i.e.,
1τ
∫ t0+τ
t0
v(t)dt ≈1T
∫ t0+T
t0
v(t)dt,
when τ T .
1.2 AC measurements
You can find on the workbench three different types of AC voltmeters.
1.2.1 HP/Agilent 34401A RMS-responding voltmeter
Set for AC voltage measurements, the HP/Agilent 34401A digital multimeter is an AC-
coupled, RMS-responding voltmeter (also called true RMS voltmeter). Whatever the
waveform, the voltmeter reading Vread equals the root-mean-square (RMS) value of the
AC component vac(t) = v(t)− Vdc (the voltmeter is AC-coupled and thus removes the DC
component): Vread = Vac,rms, with
Vac,rmsdef=
√
√
√ 1T
∫ t0+T
t0
v2ac(t)dt. (2)
1.2.2 Metrix MX1 average responding voltmeter
Set for AC voltage measurements, the Metrix MX1 analogue multimeter is an average-
responding voltmeter. Voltmeters of this type measure the average rectified value
Vavdef=
1T
∫ t0+T
t0
|v(t)|dt, (3)
for a full-wave rectifying voltmeter, or
V±avdef=
1T
∫ t0+T
t0
v±(t)dt, (4)
for a half-wave rectifying voltmeter, where v+(t) and v−(t) respectively denote the positive
and the negative parts of the waveform.
The voltmeter reading is Vread = KavVav, where
Kav =
π
2p
2≈ 1.11 for a full-wave rectifying voltmeter,
πp
2≈ 2.22 for a half-wave rectifying voltmeter
is an appropriate scale factor (you will discover in §4 whether your voltmeter is half- or full-
wave rectifying). In average-responding voltmeters, the voltmeter reading corresponds to
the RMS value for a sinusoidal input waveform, only.
1.2.3 Peak responding voltmeter
The ER-15 Peak probe connected to a DC voltmeter with an input resistance of 10 MΩ (fig-
ures 7 and 8) realizes a peak-responding voltmeter. For a symmetric input waveform,
this probe measures the peak voltage Vp of the input signal AC component (the DC com-
ponent is removed by the series capacitor) and the voltmeter reading is Vread = KpVp, with
Kp = 1/p
2. Also for peak-responding voltmeters, the voltmeter reading corresponds to
the RMS value for a sinusoidal input waveform, only.
4.1MΩ
Peak probe
HI
10 MΩ
LO
V+
0.707Vp
−
DC Voltmeter
v(t)
Figure 7: ER-15 peak probe connected to a DC voltmeter: equivalent circuit diagram. The
Schottky diode guarantees a lower voltage drop with respect to a silicon one.
Figure 8
2 Powering the signal generator board
The signal generator board requires a 12 V dual symmetrical power supply.
1 Turn on the DC power supply (do not connect the signal generator board). Set the
switches on the front panel to select the tracking/series mode of operation: in this
mode of operation the output voltage of the slave section matches that of the master
section, and the two main outputs are connected in series internally.
2 Adjust the master output voltage to 12 V.
3 Turn off the DC power supply. Using the three-wire power cable, connect the sig-
nal generator board to the power supply: red, 12 V; black, −12 V; and green, 0 V.
Warning: Do not connect the green cable to the power supply’s earth ground! The
green cable must be connected to the common point between the two main power
outputs (fig. 9).
4 Turn on the power supply: you should read 0 on the board display. Press the UP and
DOWN keys: the displayed digit should change.
0 30 0 30
++− −
Figure 9: Powering the signal generator board: at the end of §2, the power-supply set-up
should look like the above.
3 DC component
1 Connect, by means of a BNC T adaptor and a BNC-terminated cable, the oscillo-
scope’s input to signal B4. With the adaptor, you can always check the signal on the
oscilloscope’s display while making measurements with a voltmeter.
2 Set the oscilloscope’s input coupling to DC. Measure the waveform parameters (pos-
itive peak value, negative peak value and duty factor) and determine the signal DC
component by means of definition (1).
3 Set the oscilloscope’s input coupling to AC: this removes the DC component and the
trace on the oscilloscope’s display should shift accordingly. From the measurement
of the vertical displacement, determine the DC component.
4 Measure the DC component by means of the analogue multimeter. Do not disconnect
the oscilloscope.
5 Measure the DC component by means of the digital multimeter.
6 Evaluate the uncertainties of the above measurements and check the agreement
between them.
4 Average-responding voltmeter: half- or full-wave?
1 Connect the analogue multimeter, set for AC voltage measurements, to a DC voltage
source (for instance, to a power supply output). Make two measurements by ex-
changing the polarity of the test leads: what do you deduce?
2 Knowing the value of the DC voltage, can you determine the scale factor Kav?
5 Sine wave
1 Connect, by means of a BNC T adaptor and a BNC-terminated cable, the oscillo-
scope’s input to signal A0. With the adaptor, you can always check the signal on the
oscilloscope’s display while making measurements with a voltmeter.
2 By means of the oscilloscope, measure the peak-to-peak amplitude of the selected
signal. Evaluate the associated uncertainty. Is there any DC component?
3 From the above measurement, determine the RMS value and evaluate the associated
uncertainty. Can you think of a source of uncertainty other than the oscilloscope?
4 Measure the voltage with the analogue multimeter and evaluate the associated un-
certainty.
5 Measure the voltage with the digital multimeter and evaluate the associated uncer-
tainty.
6 Measure the voltage with the peak probe (connected as in figure 8) and evaluate the
associated uncertainty.
7 Since the waveform is sinusoidal, all voltmeters should indicate the same value. Are
all of the above measurements compatible? If not, can you think of possible causes
of error?
6 Triangle wave
1 Select the signal A3 from the signal generator board.
2 From the waveform represented on the oscilloscope’s display, determine the expected
readings of the three AC voltmeters.
3 Measure the voltage with the digital multimeter. Does the measured value corres-
pond to the expected reading calculated in point 2?
4 Measure the voltage with the analogue multimeter. Does the measured value cor-
respond to the expected reading calculated in point 2?
5 Measure the voltage with the peak probe (connected as in figure 8). Does the meas-
ured value correspond to the expected reading calculated in point 2?
6 Determine the errors of the measurements at point 4 and 5 with respect to the meas-
urement at point 3.
7 Pulse wave
1 Select the signal B4 from the signal generator board.
2 From the waveform represented on the oscilloscope’s display, determine the expected
readings of the three AC voltmeters.
3 Measure the voltage with the digital multimeter. Does the measured value corres-
pond to the expected reading calculated in point 2?
4 Measure the voltage with the analogue multimeter. Does the measured value cor-
respond to the expected reading calculated in point 2?
5 Measure the voltage with the peak probe (connected as in figure 8). Does the meas-
ured value correspond to the expected reading calculated in point 2?
6 Determine the errors of the measurements at point 4 and 5 with respect to the meas-
urement at point 3.
8 A closer look at the peak probe
The peak probe represented in figure 7 is actually a diode clamper (so called because it
“clamps” the waveform negative peak to 0 V; it is also —improperly— called DC restorer).
To verify this fact:
1 Connect the probe input to signal A0.
2 Connect the oscilloscope’s input to the probe output by means of a 1:10 oscilloscope
probe (disconnect any voltmeter from the probe) to obtain a 10 MΩ input resistance.
Set the oscilloscope’s input coupling to DC.
3 Look at the output waveform. Determine the minimum and the average signal val-
ues: are they compatible with what you know about the diode clamp circuit?
4 Connect the probe input to signal B4. Discuss what you observe on the oscilloscope’s
display.