MetrLab4MEng17
TTÜ
MEHHATROONIKAINSTITUUT
KVALITEEDITEHNIKA JA METROLOOGIA ÕPPETOOL
MHT0014
MEASUREMENT IN MECHATRONICS
Laboratory works 4M
Title
Electricity current, voltage, frequency and resistance measurement.
Calibration of multimeter. Measurements using occilloscope.
Uncertainty estimation. Using PC by measurements
Student
Group
Work performed
Report was issued
Accepted
Lecturer
1. Aim of work:
1.1 Learning of calibration principles and results reporting using multimeter.
1.2 Learning of measurement principles of electrical parameters and results reporting.
2. Tasks:
2.1 To perform measurement of electrical parameters.
2.2 Carring out calibration of multimeter.
2.3 Estimation of measurement uncertainty.
2.4 Work up the calibration certificate.
3. Reports content:
3.1 Short description of work
3.2 Data of used standards and measuring instruments and its condition
3.3 Detailed data in calibration report of multimeter
- visual examination;
- pre-calibration checks;
- measurement results in calibration points.
3.4 Detailed data in measurement report
3.5 Results calculation – corrections and calculated values
3.5 Estimation of measurement uncertainty
3.6 Calibration certificates
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Measurements of electricity parameters
Object. More often are measured electrical parameters current and voltage, resistance, capacity
and inductivity and electrical power.
Alternated current AC:
- active resistance makes active power and current ant voltage vectors have no bias;
- capacity resistance makes reactive power and current ant voltage vectors have bias, current is
after voltage andthey have 90 o angle;
- inductive resistance makes reactive power and current ant voltage vectors have bias, current is
before voltage and they have 90 o angle;
Direct current DC makes only active power:
Measurement devices.
Electronical multimeters
Current clamp
Ocsilloscope
Voltage gauge
Resistance decade
LCR measuring devices
Capacitance decade,
100 pF…11.111 µF.
Inductivity decade 1 µH…11.111 H
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CALIBRATION OF MULTIMETER AND POWER MEASURING INSTRUMENT
1. Object. Object of this procedure is multimeter calibration.
2. Scope of use. Procedure can be used for calibration of multimeter electrical parameters AC
and DC current and voltage and resistance, capacity, frequency and temperature indications.
3. Terminilogy
3.1 Multimeter Measuring instrument with digital or analog indication for direct measurement
of AC and DC electrical parameters.
Pocket multimeters
Calibrator
3.2 Calibrator Measuring device with one value in output.
3.3 Internal impedance. Measurement should not alter the value of the measured signal. The
higher the value of the internal impedance, the higher the quality of the voltmeter, since it does
not significantly modify the status of the electric circuit under test. Any such alteration is a
loading error. Loading errors can occur at any junction along the signal chain but can be
minimized by impedance matching of the source with the measuring instrument. The
measuring instrument input impedance controls the energy that is drawn from the source, or
measured system, by a measuring instrument. The power loss through the measuring
instrument is estimated by P = E2/Z2, where Z2 is the input impedance of the measuring
instrument and E is the source voltage potential being measured. To minimize the power loss,
the input impedance should be large. See Fig in which the output signal from one instrument
provides the input signal to a subsequent device in a signal chain. The open circuit potential,
E1, is present at the output terminal of source device 1 having output impedance, Z1. Device 2
has an input impedance Z2 at its input terminals. Connecting the output terminals of device 1 to
the input terminals of device 2 creates the equivalent circuit also shown in Fig. The potential
actually sensed by device 2 will be E E Z Z 2 1 1 2 1
The difference between the actual potential E1 at the output terminals of device 1 and the
measured potential E 2 is a loading error brought on by the input impedance of measuring
device 2. A high input impedance Z2 relative to Z1 minimizes this error. A general rule is for
the input impedance to be at least 100 times the source impedance to reduce the loading error
to 1%.
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In general, null instruments and null methods will minimize loading errors. They provide the
equivalent of a very high input impedance to the measurement, minimizing energy drain from
the measured system. Deflection instruments and deflection measuring techniques will derive
energy from the process being measured and therefore require attention to proper selection of
input impedance.
3.4 Phasor. A phasor is a constant complex number, usually expressed in exponential form,
representing the complex amplitude (magnitude and phase) of a sinusoidal function of time.
The impedance of a circuit element can be defined as the ratio of the phasor voltage across the
element to the phasor current through the element, as determined by the relative amplitudes and
phases of the voltage and current. This is identical to the definition from Ohm’s law,
recognising that the factors of
cancel. Phasor (a portmanteau of phase vector), is a complex
number representing a sinusoidal function whose amplitude (A), frequency (ω), and phase (θ)
are time-invariant. It is also known as complex amplitude.
3.5 Complex impedance. It is the complex ratio of the voltage to the current in an alternating
current AC circuit. Impedance extends the concept of resistance to AC circuits, and possesses
both magnitude and phase, unlike resistance, which has only magnitude. When a circuit is
driven with direct current DC, there is no distinction between impedance and resistance.
Impedance is represented as a complex quantity Z and the term complex impedance may be
used interchangeably; the polar form conveniently captures both magnitude and phase
characteristics,
Z=|𝑍|ejargZ
where the magnitude
represents the ratio of the voltage difference amplitude to the current
amplitude and the argument argZ, commonly given the symbol φ or Θ gives the phase
difference between voltage and current, j is the imaginary unit, and is used instead of i in this
context to avoid confusion with the symbol for electric current.
In Cartesian form,
Z=R+jX,
where the real part of impedance is the resistance R and the imaginary part is the reactance X.
A purely reactive component is distinguished by the sinusoidal voltage across the component
being in quadrature with the sinusoidal current through the component. This implies that the
component alternately absorbs energy from the circuit and then returns energy to the circuit. A
pure reactance will not dissipate any power.
Z  R2  X 2
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The impedance of an ideal resistor is purely real and is referred to as a resistive impedance:
For ordinary currents and frequencies the behavior of a resistor is that of a dissipative element which
converts electrical energy into heat. It is independent of the direction of current flow and
independent of the frequency. So we say that the AC impedance of a resistor is the same as its DC
resistance. For calculations shall be used the rms or effective values for the current and voltage in
the AC case.
Reactance is the imaginary part of the impedance; a component with a finite reactance induces a
phase shift between the voltage across it and the current through it.
A purely reactive component is distinguished by the sinusoidal voltage across the component being
in quadrature with the sinusoidal current through the component. This implies that the component
alternately absorbs energy from the circuit and then returns energy to the circuit. A pure reactance
will not dissipate any power.
Ideal inductors and capacitors have a purely imaginary reactive impedance.
The impedance of capacitors decreases as frequency increases. A capacitor has a purely reactive
impedance which is inversely proportional to the signal frequency. A capacitor consists of two
conductors separated by an insulator, also known as a dielectric.
At low frequencies a capacitor is open circuit, as no charge flows in the dielectric. A DC voltage
applied across a capacitor causes charge to accumulate on one side; the electric field due to the
accumulated charge is the source of the opposition to the current. When the potential associated with
the charge exactly balances the applied voltage, the current goes to zero.
Driven by an AC supply, a capacitor will only accumulate a limited amount of charge before the
potential difference changes sign and the charge dissipates. The higher the frequency, the less
charge will accumulate and the smaller the opposition to the current.
Phasor diagram
Capacitor load.
Current before voltage,
for loading of capacitor
is needed time
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The voltage across a capacitor lags the current because the current must flow to build up the charge,
and the voltage is proportional to that charge which is built up on the capacitor plates.
Inductive reactance
is proportional to the signal frequency and the inductance .
An inductor consists of a coiled conductor. Faraday’s law of electromagnetic induction gives the
back emf (voltage opposing current) due to a rate-of-change of magnetic flux density through a
current loop. For an inductor consisting of a coil with loops this gives.
The back-emf is the source of the opposition to current flow. A constant direct current has a zero
rate-of-change, and sees an inductor as a short-circuit (it is typically made from a material with a
low resistivity). An alternating current has a time-averaged rate-of-change that is proportional to
frequency, this causes the increase in inductive reactance with frequency.
Inductive load.
Voltage before current,
current has resistance
from EMField
The voltage across an inductor leads the current because the Lenz’ law 6ehaviour resists the buildup
of the current, and it takes a finite time for an imposed voltage to force the buildup of current to its
maximum.
The total reactance is given by X=XL+XC , so that the total impedance is
The phase angles in the equations for the impedance of inductors and capacitors indicate that the
voltage across a capacitor lags the current through it by a phase of
, while the voltage across an
inductor leads the current through it by
. The identical voltage and current amplitudes indicate
that the magnitude of the impedance is equal to one.
Resistance and reactance together determine the magnitude and phase of the impedance:
In many applications the relative phase of the voltage and current is not critical so only the
magnitude of the impedance is significant.
Measurement of impedance. The impedance may be measured or displayed directly in ohms, or
other values related to impedance may be displayed; for example in a radio antenna the standing
wave ratio or reflection coefficient may be more useful than the impedance alone. Measurement of
impedance requires measurement of the magnitude of voltage and current, and the phase difference
between them.
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Impedance is often measured by “bridge” methods, similar to the direct-current Wheatstone bridge;
a calibrated reference impedance is adjusted to balance off the effect of the impedance of the device
under test. Impedance measurement in power electronic devices may require simultaneous
measurement and provision of power to the operating device.
The impedance of a device can be calculated by complex division of the voltage and current. The
impedance of the device can be calculated by applying a sinusoidal voltage to the device in series
with a resistor, and measuring the voltage across the resistor and across the device. Performing this
measurement by sweeping the frequencies of the applied signal provides the impedance phase and
magnitude.[10]
The use of an impulse response may be used in combination with the fast Fourier transform (FFT) to
rapidly measure the electrical impedance of various electrical devices.
The LCR meter (Inductance (L), Capacitance (C), and Resistance (R)) is a device commonly used to
measure the inductance, resistance and capacitance of a component.
Root-mean-square (RMS) and effective values. Circuit currents and voltages in AC circuits are
generally stated as root-mean-square or rms values rather than by quoting the maximum values. The
root-mean-square for a current is defined by
When this process is carried out for a sinusoidal current
Since the AC voltage is also sinusoidal, the form of the rms voltage is the same. These rms values
are just the effective value needed in the expression for average power to put the AC power in the
same form as the expression for DC power in a resistor. In a resistor where the power factor is equal
to 1:
Since the voltage and current are both sinusoidal, the power expression can be expressed in terms of
the squares of sine or cosine functions, and the average of a sine or cosine squared over a whole
period is = 1/2.
3.6 Electric power measurement
Electric power P dissipated by a load L fed by a dc power supply E is the product of the voltage
cross the load VL and the current flowing in it IL.
Therefore, a power measurement in a dc circuit can be generally carried out using a voltmeter (V)
and an ammeter (A)
Electric energy meters measure the active or reactive component E= Uit. Active energy meter can
measure AC with prescribed accuracy in range of cos φ= -0,5 (inductive) or cos φ=0,8
(capacitance).
U  IZ  I Z e j
PACT  IU cos 
PREAC  IU sin 
4. Object handling before calibration
Presented for calibration multimeter shall be cleaned and be in working condition according to
producers instructions.
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5. Method principle
By calibration is used comparison of multimeter indication with standards values. For calibration
result is estimated measurement uncertainty.
Environment conditions shall be as next:
- temperature (20 ± 3) oC;
- temperature shall not change during calibration over 1 oC per 1 hour;
- humidity shall be less than 80 %rel.
Before calibration the measurement instruments, standards and equipment shall be kept in above
environment conditios allowing them to have the same temperature as environment.
Safety. Exists danger from electricity. Shall be not measured AC voltage over 24 V and DC voltage
over 32 V.
6. Equipment
For calibration shall be used next standards and devices:
- standard multimeter, which has AC and DC voltage, current and frequency measurement range;
- watt- ja varmeters;
Digital TRMS power meter for AC and DC networks. For 1-phase (PX 110) or symmetrical threephase networks (PX 120). Versatile measurements: U, I, W, VA, Var, PF.
Electrical power meter
Functiongenerator
- AC and DC power sources;
- frequency generator. Function generator
Frequency range 0,2 Hz…20 MHz; 10 mV…20 Vss (50 Ω Last). Sweep Input impedance: 82 Ω,
sweep rate: >20:1; max. rise time: 0.1 V/µS. Attenuator -20 dBx 2. Amplitude 10 mV…20 Vss (50
Ω Last). Signal shapes: Sine, triangle, square, DC Variable symmetry
- standard resoistance, capacitance and inductivity decades.
Resistance decade
Capacitance decade, 100 pF…11.111 µF.
Inductivity decade 1 µH…11.111 H
- thermometer for environment temperature measurement,scale interval at least 1 oC.
7. Visual inspection
Suitability for calibration shall be estimated initially visually which involve next steps:
- multimeters parts and insulation shall be without damages and corrosion;
- descriptions, scale lines and figures shall be easily read;
- movement of switches shall be without jumping and be smooth;
- fixing parts (contacts) shall allow firmly fix electric circuits.
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8. Pre-calibration works
Multimeter, standards and auxiliary equipment shall be prepared according producers instuctions.
- multimeter shall be switch to scheme and given load before calibration during required time period
so as prescribed by producer;
- by calibration of minimal values shall be safeguard from emc fields and leakage current;
- if required shall be followed earth magnetic field direction;
- the vertical (as rule max deviation ±1o) or horisontal (as rule max deviation ±5o) placement of
multimeter shall meet the producers requirements,
9 Calibration
During calibration shall be compared standards and multimeter indications. Calibration shall be
carried out over all multimeter measurement range, beginning from Min indication up to Max
indication. Between them shall be taken 3...5 points with constant step.
9.1 Voltage range calibration
As standards is used high accuracy multimeter.
Shall be taken and documented standard E and multimeter U readings.
If needed, the indications shall be taken when voltage is increasing and decreasing.
If needed, shall be estimated deviation from zero value after max U was given to multimeter. After
that the standards indication shall be set on zero value and taken multimeter indication Uzero.
V
R
Stabilised AC or
DC voltage
(0…30) V
A
Fig. 1. Measurement scheme for voltage and current values calibrations
9.2 Current range calibration
As standards is used high accuracy multimeter.
Shall be taken and documented standard E and multimeter I readings.
If needed, the indications shall be taken when current is increasing and decreasing.
If needed, shall be estimated deviation from zero value after max I was given to multimeter. After
that the standards indication shall be set on zero value and taken multimeter indication Izero.
9.3 Electrical resistance range calibration
The electrical resistivity of a material is a number describing how much that material resists the flow
of electricity.
As standard is used resistance decade.
Shall be taken and documented standard E and multimeter R readings.
Stabilised
F
R
C
1 Ω ÷ 1 GΩ
1 Hz ÷ 1 GHz
1 pF ÷ 30 µF
Fig 2. Measurement scheme for electrical resistance, capacity and frequency values calibration
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9.4 Electrical capasitance range calibration
A capacitor is a system of two conducting electrodes, having equal and opposite charges separated
by a dielectric. The capacitance C of this system is equal to the ratio of the absolute value of the
charge Q to the absolute value of the voltage between bodies as:
Practical capacitors have increases in losses at very low and very high frequencies. At low
frequencies, the circuit becomes entirely resistive and the DC leakage current becomes effective. At
very high frequencies, the current passes through the capacitance and the dielectric losses become
important.
As standard is used capasitance decade.
Shall be taken and documented standard E and multimeter C readings.
9.5 Electrical inductance range calibration
Inductance is an electrical parameter that characterizes electric circuit elements (two- or fourterminal networks) that become magnetic field sources when current flows through them. They are
called inductors, although inductance is not a unique property of them. Electric current i (A) and
magnetic flux (Wb) are interdependent; that is, they are coupled. Inductance is a measurable
parameter; therefore, it has a physical dimension, a measurement unit (the henry), as well as
reference standards. Inductance is a property of all electrical conductors.
As standard is used inductance decade.
Shall be taken and documented standard E and multimeter L readings.
9.6 Frequency range calibration
As standard is used high accuracy multimeter or frequency meter.
Shall be taken and documented standard E and multimeter F readings.
9.7 Thermometer calibration
As standard is used high accuracy thermometer. Comparison shall be performed in stabilised
environment (as rule in thermostat).
Shall be taken and documented standard E and multimeter T readings.
10. Results calculation
As measurements results are found next parameters and its values:
-standard E and multimeter A indications and calculated shall be correction K to multimeter
indication Ki = Ast – Ami;
- measurement estimation in probability level 0,95.
Results are documented in calibration certificate.
11. Measurement of impedance
As standard is used high accuracy multimeter and capacitance and inductance decades.
Shall be taken and documented standard E and multimeter Z readings.
Shall measured AC frequency f and voltage U and current I.
Reactive resistance components are calculated by equations:

1 
1
X

and
C

C2

fC
X

L
2

fL
L
Impedance is calculated by Z = R2 X2 .
L
C
V
R
A
Stabilised el.
AC
(0 ÷ 30) V
Fig. 3. Measurement scheme for impedance
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13. Estimation of measurement uncertainty
Calibration result has uncertainty which are caused by various influence factors. Uncertainty
estimation shall be calculated on a standard deviation level and are summarised to have combined
uncertainty u. Combined uncertainty can have statistically calculated component uA (so called A
component) and experimentally estimated component uB (so called B component), then
u = u 2A  u B2 .
If calibration results have normal distribution then
uA =
n
1
 (x  x)2 ,
n(n  1) i 1 i
where n is quantity of measurements, xi are separate results values and x is arithmetical average.
Experimentally calculated combined uncertainty uB has next main components:
1. Standards uncertainty uST. Uncertainty is given in calibration certificate of standard as expanded
uncertainty U, then
uST = U/2.
2. Uncertainty from electrical scheme influence uSCH..
3. Uncertainty from applied current value influence uCUR.
4. Uncertainty from applied frequency value influence uFREQ.
5. Standards and multimeter warming influence uTEMP.
6. Uncertainty from earthing influence uNEU.
7. Uncertainty from few repeated measurements uREP. If results range is xt=xmax-xmin, then
uREP = x t / 2 3 .
8. Uncertainty from indication reading uRES, which include paralax deviation and reading rounding.
For analog indication uRES= 1 / 2Scale interval and for digital indication uRES= Scale interval
3
3
9. Internal resistance influence uIR.
10. Environment uENV
11. Digitalisation influence uDIG. Measured length is measured with sensor. As rule sensor gives in
output already electrical signal. Electrical output signal is given to ADC convertor which converts
its to coded IT values. Convertation capability depends on ADC bits, as rule exists 8 or 10 or 12 bits
ADC.
8 bits ADC has capability to sens 28=256 different levels. If measured range is as electrical signal
from 0 V up to 10 V, then sensed different electrical values are with step 10/256 = 0,04 V. Required
is to have stabilised reference voltage for ADC and rapid repeated measurements cycle.
Example. If required is for length measures measurement expanded uncertainty U=0,01 mm which
allows to have minimal scale interval ScI=0,01 mm. Then 8 bits ADC gives possibility for max
measured range 0,01 .256 = 2,56 mm. Expected is that sensor has measurement capability at least
1/3 from U value and conversation capability of length values to electrical signal is 1/5 from U
value.
12. Combined uncertainty uB is calculated by formula uB =  ui2 .
13. Expanded uncertainty U is calculated by formula U = k . u,
where k is coverage factor, where k = 2 gives probability level ca 95 %.
Calibration result is expressed as next:
(Li + K) measuring unit and U measuring unit and covarage factor k =2
14. Summary
Calibration results are summarised in calibration report and in calibration certificate.
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12. MEASUREMENTS USING OSCILLOSCOPE
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Measurements of impulsses
Example: Program PicoScope 6 Automotive. Väntvõlli ja nukkvõlli Halli andur
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Hall Effect Sensors are devices which are activated by an external magnetic field. We know that a
magnetic field has two important characteristics flux density, (B) and polarity (North and South
Poles). The output signal from a Hall effect sensor is the function of magnetic field density around
the device. When the magnetic flux density around the sensor exceeds a certain preset threshold, the
sensor detects it and generates an output voltage called the Hall Voltage, VH.
Hall Effect Sensors consist basically of a thin piece of rectangular p-type semiconductor material
such as gallium arsenide (GaAs), indium antimonide (InSb) or indium arsenide (InAs) passing a
continuous current through itself. When the device is placed within a magnetic field, the magnetic
flux lines exert a force on the semiconductor material which deflects the charge carriers, electrons
and holes, to either side of the semiconductor slab. This movement of charge carriers is a result of
the magnetic force they experience passing through the semiconductor material.
Example.
MULTIMEETER DVM1200 VELLEMAN USE BY MEASUREMENT WITH PC
1. Swtch on multimeter and press the button Hz/Duty. Indicated will be PC-LINK.
2. Connect the multimeter optical port with PC USB port.
3. Start PC-LINK SOFT. Indicated will be PC-LINK SOFT.
4. Adjust the PC port to the transmition frequency. Select:
- Control panel
- System
- Hardware
- Device manager
- Ports (COM&LPT)
- Sunplus USB Serial COM Port (COM x, where x is port ID)
- Port Setting, take Bits per second 2400 and OK.
5. Select from PC-LINK SOFT:
- Set ass Stop
- System Set take Port Selected, same port, what was in Device manager’is and Apply.
- Start, shall be seen multimeter indication and on the graph the results.
6. Graph saving:
- File → Export Graph → file place.
7. Results saving:
- File → Save → file place.
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2. Thermometer, software Logger Lite
Program gives windows.
Shall be set up measurement parameters through → Experiment → Data collection
DIGITALISATION OF MEASUREMENT RESULTS
Digitalisation of electrical parameters
Measured length is measured with sensor. As rule sensor gives in output already electrical
signal. Electrical output signal is given to ADC convertor which converts its to coded IT
values. Convertation capability depends on ADC bits, as rule exists 8 or 10 or 12 bits ADC.
8 bits ADC has capability to sens 28=256 different levels. If measured range is as electrical
signal from 0 V up to 10 V, then sensed different electrical values are with step 10/256 = 0,04
V. Required is to have stabilised reference voltage for ADC and rapid repeated measurements
cycle.
Example. If required is for length measures measurement expanded uncertainty U=0,01 mm
which allows to have minimal scale interval ScI=0,01 mm. Then 8 bits ADC gives possibility
for max measured range 0,01 .256 = 2,56 mm. Expected is that sensor has measurement
capability at least 1/3 from U value and conversation capability of length values to electrical
signal is 1/5 from U value.
Measuring
instrument
indication
Measurement range
Scale interval
Δindication
ADC
Coded output
Standard value Ast
Input A (measured value)
Fig. 4. Principal scheme for digitalising electrical values using time of loading of the capasitor.
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Digitalisation of length parameters
Digital measuring instrument has LCD
read out and a serial output.
Digital calipers and micrometers are
accurate measuring instruments. They
have a resolution of (1…50) µm with an
accuracy up to of 5 µm. This high
performance is achieved with the use of multiplate
capacitive sensors.
Capacitive sensors are rugged and simple to build.
They are highly linear and immune to mechanical
and electronic noise. However, since they rely on
capacitance, they are sensitive to liquids. Any
liquid that bridges the capacitive plates increases
the capacitance. A drop of oil can increase the
capacitance by a factor of 80. Digital calipers use
multiple plates to form a capacitive array that can
senses motion accurately. There is a stator and
slider (“rotor”) plates in a digital caliper. The stator
is embedded in the metallic ruler on which
electronic housing slides. The electronic housing
contains the slider.
Fig 1 Multiplate electrodes stator and electrodes etched on PCB of a digital caliper
The stator pattern is fabricated on the top copper layer of a standard glass-epoxy laminate and glued
to the stainless steel bar of the caliper. The slider pattern shown is similarly fabricated on PC
laminate, drives a 100 kHz signal through the sin/cos plates to the stator electrodes, and picks up AC
voltages at the two central pickup plates which describe sin(displacement) and cos(displacement)
signals.
Separate sin and cos signals are needed to determine direction of motion. The combination of platecounting digital circuits and analog interpolation between plates yields 0.0002” accuracy over 6”
with standard PC fabrication methods. This application uses a small watch battery, and shows the
microamp-level current consumption possible with the technology.
Parallel multiplates can to increase the sensor capacitance in a small volume
Figure 2 Multiplate electrodes
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Fig. shows the electrode structure of Analog Devices’ surface-machined silicon accelerometer, the
ADXL50, with an overall size of (500 x 625) μm. Its 42 silicon fingers are 100 μm in length with a
2 μm gap and a total capacitance of 0,1 pF. The H-shaped piece is elastically mounted using the
good spring characteristics of silicon, and responds to acceleration in the x direction with a small
displacement. With a displacement in the –x axis, the H picks up more of the 0 deg. drive signal,
and a demodulator (not shown) converts the displacement into acceleration.
As the limiting resolution of the sense amplifier is 20x10-18 pF, a beam displacement of 20x10-12
m can be measured.
Independent multiplates Despite the high accuracy of capacitance motion detection, system
imperfections such as mechanical tolerance, unwanted tilt sensitivity and residual analog circuit
accuracy limit the reasonable performance of a simple analog sensor to about 0.1 % accuracy. For
some applications, such as a digital vernier caliper manufactured by L.S. Starrett Co., an 0.0001”
resolution over 6” was needed. This multiplate pattern was used applied acceleration tether anchor
amp proof mass
Rotary motion sensors
The examples above all show linear motion transducers, but many capacitive sensors are used for
rotary motion. Rotary motion electrode design is simply done by wrapping the single-plate or
multiplate patterns around 360 degrees. Just as tilt and offset in a single-plate motion pickup must
be addressed with correct plate design (fig 8), tilt or runout in a rotary transducer is handled with the
same techniques.
The use of indepently addressed multiplates in rotary encoders is common. Very high accuracy
electrodes can be manufactured with thin film deposition on glass and precision photolithography,
with feature sizes down to 5 mm lines and spaces.
2D sensors A variety of two-dimensional capacitive sensors have been produced, including this
finger-position
sensor
References www.capsense.com/capsense-wp.pdf
Digitalisation of optical parameters
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CALIBRATION REPORT No ______ . ____ 201__ .a.
Page 1 (2)
Measuring instrument _______
______
, identif.No. ____________
Environment temperature ____ oC, humidity _____ rel %. MI warming _____ min.
Visual inspection: Correct
Yes No. Pre-testing: Correct
Yes
No
Nominal value
Multimeters
indication
Standards
indication
Indication
correction K
Combined uncertainty u
k=1
Direct (DC) voltage
0,2 V
15,0 V
30,0 V
15,0 V
0,2 V
Direct (DC) current
µA
... mA (360 Ω; 15,0 V)
mA
Alternating (AC) voltage
0,2 V
15,0 V
24,0 V
15,0 V
0,2 V
Alternating (AC) current
µA
... mA (360 Ω; 15,0 V)
mA
Resistance
Ω
kΩ
MΩ
kΩ
Ω
Capacity
pF
nF
µF
nF
pF
Temperature
o
C
Frequency, sinius wave
50 Hz
20 kHz
2 MHz
Frequency, rectangular wave
50 Hz
20 kHz
2 MHz
Uncertainty estimation for current:
I=U/R== 15,0 V/360,0 Ω =…………….;uI=
2
2
 I  2  I  2

 uU  
 uR
 U 
 R 
=……………………………..:
ELECTRICAL SCHEME
L
R1
R2
C
A
Stabilised AC (0 ... 30) V
V
MetrLab4MEng17
Page 2 (2)
U= 15,0 V
R= 360,0 Ω
Influence for
uncertainty
Sensitivity
coeficient
Distribu
tion
Sensitivity
coeficient
Value
Distributi
on
Value
Standard uST
Scheme uSCH
Current uCUR
Frequency uFREQ
Warming uTEMP
Earthing uNEU
Reading uRES
Digitalisation uDIG
Input resistance uIR
Repeated tests uR
Environment uENV
Combined uncertainty u
u
uR=
=
2
i
uU=
u
2
i
=
SCHEME IMPEDANCE Inital data: C= 0,1 μF; R=1,0 kΩ; U~=24,0 V; f = 50 Hz; L= 0,1 mH
1 =
2fC
.................. Ω;
2
2
= ……………….Ω
uXc=
 Xc  2  Xc  2

 uf 
 uC
 f 
 C 
X L  2πfL = .................. Ω.,
uXL=
 XL  2  XL  2

 uf 
 uL
 f 
 L 
X=XL+XC=................ kΩ,
uX=
Z = R 2  X 2 =............................. Ω,
uZ=
 = arctan (X / R) = ........................ ;
uφ=
XC 
2
2
2
2
 X  2
 X  2

 u XL  
 u XC
 XL 
 XC 
2
2
 Z  2  Z  2

 uR 
 uX
 R 
 X 
2
ELECTRICAL POWER
Active power P=UI cos φ = .................... W, uP=
=………………Ω
……………… Ω
=........................... Ω.
2
   2    2

 uX  
 uR
 X 
 R 
2
=..................................
2
2
 P  2  P  2  P  2
 u cos 

 u U    u I  
 U 
 I 
  cos  
=........... W.
For power P=UI cos φ = ................... needed current I:
without X resistance I = …………………….… ; with X resistance I=…………………….….
MEASUREMENT WITH OCSILLOSCOPE
Active resistance
Voltage U
After R1
Before R2
Before R1
After R2
Current I
Voltage
∆U
Resistance
R1
Uncertainty
uR1
Complex resistance
Voltage
U before
R1
Voltage
U
after R2
Resistance R
Voltage
∆U
Voltage
U before
C
Resistance XL
Voltage
U after C
Resistance XC
Voltage
∆U
Voltage
before
L
Resistance X
Voltage
U
after L
Voltage
∆U
Resistance Z
Current I
Frequency f
Uncertainty u
Impulsses
Quantity n/time period T
/ 60 s
/ 60 s
/ 60 s
/ 60 s
Uncertainty un=
Uncertainty
2
Frequency
2 kHz
2 kHz
2,0 MHz
2,0 MHz
 n  2  n  2
  u f    uT
 T 
 f 
Voltage U
Wave form
Sinusoidal
Rectangular
Sinusoidal
Rectangular
2
= ..............................Measurement performed by_______.
Phase
angle
φ
MetrLab4MEng17
Page 1 (1)
AS Metro
CALIBRATION CERTIFICATE No........
of standard
Measuring instrument: Digital multimeter APPA 207, nr
Calibrated:
11.04.2014
Used equipment and standards: standard resistance, standard termometer, standard frequency meter,
voltage calibrators.
Calibration method: Calibration was performed by comparison of indications of standard and
calibrated instrument.
Results:
Indication of calibrated
Indication of
Expanded uncertainty
measuring instrument
standard
U (k=2)
Direct voltage
(5...40) mV
0,06 % + 8 scales values
40 mV...1000 V
0,06 % + 2 scales values
Alterneting voltage
(40...400) mV
40 Hz...100 Hz
0,70 % + 5 scales values
100 Hz...1 kHz
1,00 % + 5 scales values
400 mV...40 V
40 Hz...100 Hz
0,70 % + 5 scales values
100 Hz...1 kHz
1,00 % + 5 scales values
1 kHz...10 kHz
2,00 % + 6 scales values
10 kHz...20 kHz
3,00 % + 7 scales values
20 kHz...50 kHz
5,00 % + 8 scales values
50 kHz...100 kHz
10,00 % + 10 scales values
Direct current
5 mA...10 A
0,20 % + 4 scales values
Alternating current
5 mA...10 A
40 Hz...400 Hz
0,80 % + 8 scales values
Frequency
40 Hz...400 Hz
0,01 % + 1 scales values
Resistance
5 Ω...400 kΩ
0,30 % + 2 scales values
400 kΩ...4 MΩ
0,30 % + 4 scales values
Capacity
400 pF...4 µF
0,90 % + 20 scales values
4 µF...400 µF
1,90 % + 20 scales values
Temperature
-50 oC... +1200 oC
1 oC + 1 scales values
Calibration results have traceability to International SI units through used standards, which were
calibrated in
accredited calibration laboratory
Calibration was performed