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AC Measurements and DMMs
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Digital Multimeters&
AC measurements
Politecnico di TorinoThis material freely available to Politecnico di Torino students forpreparation to the exam. Any other either commercial ornon-commercial use expressly prohibited without written consentof the author
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Time-varying quantities are usually characterized bymeans of few parameters
The first electricity use was to transfer energy andemployed DC supplies
Many equations used in DC can be used in AC if RMSvalues are used
The most important parameter (from this point of view!)is therefore the RMS value
AC voltmeters
!=T
dttv
0
2eff )(
T
1V
Measuring RMS values is not easy since it involves non-linear operations and circuits
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AC Measurements and DMMs
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IFthe signal has a defined and known shape, the RMSvalue can be computed starting from other quantities.
Historically the signals were (only) sinusoidal thussomeone started to produce voltmeters that do not
measure the RMS value, but nonetheless do display it:
Voltmeters calibrated in RMS value, i.e. voltmeterscapable of displaying the RMS value IFthe signal is
sinusoidal
There are three basic types of AC voltmeters calibrated in
RMS
! (True) Root Mean Square (TRMS)! (rectified) average (AVG)! Peak
Voltmeters calibrated in RMS values
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Basic equations for sine signals
A peak voltmeter displays the RMS value if its output ismultiplied by 0.707
A (rectified) average voltmeter displays the RMS value ifits output is multiplied by 1.11
2V
eff
PV
= ! ==T
0
PPm
2Vdtt)sin(V
T
1V
"
#
m
m
effV11.1
22
VV !=
"
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AC Measurements and DMMs
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Sine signal with peak value10V (RMS value 7.07V)
Type Measurement Multiplier Display
VRMS
7.07 7.07
VAVG
6.366 1.11 7.07
Vp
10 0.707 7.07
BEWARE it works only with sine signals!
Square signal with peak value10V (RMS value 10V)
Type Measurement Multiplier Display
VRMS 10 10
VAVG
10 1.11 11.1
Vp
10 0.707 7.07
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Each instrument actually measures (correctly) thequantity it is designed for
It is always possible to back-correct the output(decalibration) getting the (correct) original value
From average voltmeter it is possible to get the(real) average value by dividing by 1.11
From a peak voltmeter it is possible to get the(real) peak value by dividing by 0.707
NOTE: if the signal shape is known, from average/peakvalues it is easy to compute the RMS value
Decalibration
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AC Measurements and DMMs
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(rectified) Average voltmeters
A rectifier + a DC voltmeter
Two possibilities based on the rectifier type:
Half-wave Full-wave
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Half-wave
Vi Vo
! ==
2/
0
)(1 T p
Pss
Vdttv
TV
"
ssssp
eff VVV
V 22.222
!==
"
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AC Measurements and DMMs
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Full-wave
Graetz bridgeVi Vo
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Vi Vo
Full-wave
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AC Measurements and DMMs
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Vi Vo
Full-wave
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T
0
p
Pds
V2dt)t(v
T
1V
mdsp
eff VVV
V 11.1222!==
"
VDC
ViV0
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AC Measurements and DMMs
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Half-wave or full-wave?
Full-wave:
Reduced ripple i.e.more steady readings
Increased voltage dropon the diodes, thus
greater problems at
low amplitudes
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Example: the tester
The diode voltage dropturns out in a non-linearscale at low voltages
The manufacturer changesthe ticks to correct for thisnon-linearity
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AC Measurements and DMMs
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Peak voltmeters
The capacitor charges to the peak value, and neverdischarges
A discharge resistor is added in parallel to thecapacitor
Vi
Vo
!A diode in series to a capacitor
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Vi VDC
RC>>T
A DCcomponenton the
signalalters theoutput
A galvaniccoupling isrequired for therectifier to work
!Two problems
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AC Measurements and DMMs
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AC coupled peak voltmeter a.k.a zero
fix peak voltmeter
Vi Vo
VC
IC Vi
IC
VC
V0
The diode direction canbe reversed
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Vi VDC
The signal is shifted to have itsminimum value at zero
For a sine signal the shiftequals the peak value (withouttaking into account any DCcomponent)
A DC voltmeter is connected tothe output
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AC Measurements and DMMs
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Advantages of the AC coupled peak
voltmeter
Does not require galvaniccoupling
DC components do not affectthe output
Can be easily arranged in theform of probe
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AC coupled Peak probe
2
1
21
2!
+ RR
R
Vi
Vm
Rs R
i
DMMProbe
IF Rs=0.4Ri , the DMM displaysthe RMS value (with sinesignals!)
With other signals thedecalibration must be used
BEWARE: if the signal is notsymmetric the output dependson the polarity
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AC Measurements and DMMs
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(True) RMS voltmeters
Perform dttVT
V
T
eff !=2)]([
1
Useful for distorted signals and noise measurements.
Three basic types:
Electrothermal Digital Analogue
!Electrothermal Take advantage of the the thermal effect (V2/R)
connected to the signal
Usually by comparing thermal effects of theunknown AC signal with a DC aux signal
Slow, but extremely accurate
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Digital
An ADC is used to sample the singnal The RMS is computed by summation For good results:
Synchronous sampling and/or High sampling frequency
Good accuracy
!"
=
""=T
T
k
eff TkvTTV
1
2)]([
(True) RMS voltmeters
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AC Measurements and DMMs
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Analogues
Employ non-liner circuits (usually log type) to perform: product v(t)v(t) average Square root
Available as integrated circuits Medium accuracy
Technology Uncertainty
Electrothermal 0.003%
Digital 0.01%
Analogue 0.05%
(DC) 0.0003%
(True) RMS voltmeters
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In brief
The different voltmeter types give the same resultsonly if the signal is of sine type
It is always- possible to decalibrateto getthe actual measured value
IF the signal shape is knownit is possible tocompute the RMS value
IF the signal shape is known it is possible topreview what every voltmeter should display
If the signal has DC components, the actualdisplayed value depends on the voltmeter coupling
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AC Measurements and DMMs
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Inputfront-end
Based on Analog to Digital Converter
ADCProcessing
Display
Interface
Digital Multi Meters
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DMM resolution
Different ways of express the resolution
Maximum figure on the display NMAXDimensionless valueNumber of (equivalent) digitsusually computed as :
IF b=2 bits,
IF b=10 (fractional) number of digits
usually rounded according to the most
significant digit value:
0-1 0.5
0-3 0.75
0-9 1
MAXbNlog=!
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AC Measurements and DMMs
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NMAX=9999 4 (4)
3.75
3.75
3.5
(3.6)
(3.5)
(3.3)
NMAX=3999
NMAX=3100
NMAX=1999
NMAX=1299 3.5 (3.1)
The net effect can be an abrupt resolutionchange
Examples
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ADC
Display CPU
Currentgenerator
Ampl. AC/DC
Swithc
Referencevoltage
In
Referencethe DMM cannot be better than itsreference
Usually a special zener of 1-10V Other internal standard can be present
Switch:to select different functions (V, I, R,..) Usually 2 to 5 inputs
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AC Measurements and DMMs
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Switch and inputs
You may find
2 main inputs 2 sense inputs 1 current input A guard input
In simpler DMM the guard ismissing and often also the
sense inputs are missing
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Voltage
Only the main inputs are used
Atten.
Gen.IHI-S
HI
LO
LO-S
I Typical input
impedance 10M!
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AC Measurements and DMMs
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The input impedance isrelated to the input
divider
On ranges up to 10 Vthe divider is not
required
Some DMMs allow thedivider to be
disconnected on these
ranges raising the input
impedance to >10 G!
Gen.IHI-S
HI
LO
LO-S
I
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Current
The measurement is performed byusing an internal shunt using the
auxiliary current input and the the
main input LO
Safer solution than inserting theshunt between the inputs
Gen.IHI-S
HI
LO
LO-S
I
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AC Measurements and DMMs
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Resistance
An internal current generator isused and the voltage drop onthe unknown resistor measured
Current adjusted to havevoltage drops of few hundreds
of millivolts
The cable resistance affects theresults
Gen.IHI-S
HI
LO
LO-S
I
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4 Wire resistance
Employs main and senseinputs:
2 cables for current 2 cables for voltage
The cable resistance does notaffect the result
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AC Measurements and DMMs
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Amplifier ADC with typical input range 10V The amplifier extends the input range to
10 - 100mV Noise and pass-band possible problems
ADC
Display CPU
Current
generator
Ampl. AC/DC
Swithc
Reference
voltage
In
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For AC voltage and current the AC/DC converter canbe
AVG TRMS
With coupling AC+DC AC only
ADC
Display CPU
Currentgenerator
Ampl. AC/DC
Swithc
Referencevoltage
In
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AC Measurements and DMMs
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AC coupling
2
DC
2
DCeffACeffAC VVV
The AC coupling removes any DC component and
makes easier to arrange the circuits.
Two problems:
The measured RMS in the case of signals withDC component is
The AC coupling may add errors due to the highpass filtering action
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5ms/div 0.2V/div
Example: AC+DC
VVeff
4.0=
The RMS value does notdepend on ducy-cycle
VVdc
2.0)34.014.0(41 !="!"=
Example: AC
5ms/div 0.2V/div
The RMS value is connectedto the duty cycle
VVeffAC
35.02.04.0 22
!"=
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AC Measurements and DMMs
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The crest factor
Signals with the same RMS value
eff
p
fV
Vk =Crest factor
The input analogue circuits must handle thesignals without distortion
From RMS it is not possible to compute the peakvalue
DMMs can handle only signals with limited crestfactor (e.g. 5-7)
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Two basic types on ADCs: SPOT Integrating ADC
ADC
Display CPU
Currentgenerator
Ampl. AC/DC
Swithc
Referencevoltage
In
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SPOT ADC The converted value is connected to a specific
signal value at a specific (very small) sampling
time
Integrating ADC The converted values is connected to the average
value in a certain (usually large) time interval
The aperture time (a.k.a. integration time) islarge by design
Used due to their properties: Low cost High accuracy (20-24bit) Reduce the differential mode noise at mains
frequency
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Frequency responseof the ADC forintegration time20ms
The integration acts as a low pass filter and reducethe noise: easy to obtain 20-24 bits
The integration nullifies components with periodequals to the integration time The integration time is expressed in PLC (periods of
mains)
50 100 150
0.2
0.4
0.6
0.8
1
Hz
A m p
i e z z
a
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AC Measurements and DMMs
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Guard
connection
Some DMMs have a guardinput
Useful for noisereduction
Difficult to use The guard is connected to
the shield
It is not a groundconnection
HI
LO
G
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Example: measurement in the presenceof a common mode noise Vcm
The Vcm is attenuated by the differentialinput front-end
A connection LO - guard eliminated theVcm
Vd
Vcm
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AC Measurements and DMMs
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Vd
If the cables have a not negligible impedance thecurrent which flows through the parasitic capacitance
may lead to errors The connection LO-guard makes thing worsen as it
increases the stray capacitances
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Vd
This connection removes the problem since the noisecurrent flows through the guard cable
In other cases a different approach has to be used
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AC Measurements and DMMs
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Revision questions
Why the RMS value is often used for AC measurements? Why average and peak voltmeters are used, how are they
calibrated, what they measure?
What is the decalibration when and how can it be used? What does it means half-wave full-wave, how the circuits are
arranged, what are pros and cons of each circuit?
How a peak voltmeter is arranged? What are the differencesbetween AC and DC coupling, what are pros and cons of eachcircuit?
How a DMM is arranged, what does it means a resolution indigits?
How the front end is arranged, how may inputs can be found ona DMM, how are they connected during the use?
What is the typical input impedance, how can be increased issome cases, what is a 4 wires connection, where is it used andwhy?
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Revision questions
What does it means AC coupling for RMS measurements whatare the effects, why is it used?
What is the crest factor, how it affect the converted value? What does it means SPOT ADC /Integrating ADC what are pros
and cons of the two technologies?
What is the guard connection, how is it used?