AC voltmeters, Electronic Measurements Lab - polito.itled.polito.it/material/ortolano/lab_ac_voltmeters.pdf · The objective of this lab is to study the response of different types

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]

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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.