AC VOLTMETERS
Electronic 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: massimo.ortolano@polito.it
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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 generator board.
(Preliminaries)
Figure 3: A BNC male con-
Figure 4: A BNC male to
Figure 5: A crocodile (al-
nector.
BNC male cable.
ligator in the US) clip.
Figure 6: A BNC T adaptor.
(Preliminaries)
1.1
DC measurements
Given a periodic voltage waveform v(t) with period T , its direct component (DC component) is the mean value of v(t) over a period,
1
Vdc =
T
def
Z
t 0 +T
v(t) dt,
(1)
t0
where t 0 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.,
1
τ
when τ T .
Z
t 0 +τ
t0
1
v(t) dt ≈
T
Z
t 0 +T
v(t) dt,
t0
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 ACcoupled, 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
v Z
u
t 0 +T
def t 1
2 (t) dt.
Vac,rms =
vac
T t
(2)
0
1.2.2
Metrix MX1 average responding voltmeter
Set for AC voltage measurements, the Metrix MX1 analogue multimeter is an averageresponding voltmeter. Voltmeters of this type measure the average rectified value
1
Vav =
T
def
Z
t 0 +T
|v(t)| dt,
(3)
v± (t) dt,
(4)
t0
for a full-wave rectifying voltmeter, or
def
Vav± =
1
T
Z
t 0 +T
t0
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 = Kav Vav , where
Kav =
 π

≈ 1.11

 2p2
for a full-wave rectifying voltmeter,

π

 p ≈ 2.22
2
for a half-wave rectifying voltmeter
is an appropriate scale factor (you will discover in §4 whether your voltmeter is half- or fullwave 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 (figures 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 component is removed by the series capacitor) and the voltmeter reading is Vread = Kp Vp , with
p
Kp = 1/ 2. Also for peak-responding voltmeters, the voltmeter reading corresponds to
the RMS value for a sinusoidal input waveform, only.
Peak probe
DC Voltmeter
4.1 MΩ
HI
v(t)
10 MΩ
+
V 0.707Vp
−
LO
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 signal 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 oscilloscope’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 (positive 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 exchanging 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 oscilloscope’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 uncertainty.
5 Measure the voltage with the digital multimeter and evaluate the associated uncertainty.
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 correspond to the expected reading calculated in point 2?
4 Measure the voltage with the analogue multimeter. Does the measured value correspond to the expected reading calculated in point 2?
5 Measure the voltage with the peak probe (connected as in figure 8). Does the measured 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 measurement 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 correspond to the expected reading calculated in point 2?
4 Measure the voltage with the analogue multimeter. Does the measured value correspond to the expected reading calculated in point 2?
5 Measure the voltage with the peak probe (connected as in figure 8). Does the measured 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 measurement 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 values: 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.