Testing, Measurement, and Troubleshooting

TerminologyAccuracy

Measure of an instrument's capability To approach a true or absolute value

BiasMeasure of how closely the mean value

In series of repeated measurementsApproaches true value

Golden UnitUnit whose behaviour is completely knownUsed as a standard

MeanMeasure of the central value of set of measurements

meanN

mii

N i

10

ResidualMeasured value minus the mean

ResolutionMeasure of ability to discern value of a measurement

Root Mean SquareSquare Root of average of the average of the squares of the values

rms valueyNi

N

2

Statistical Tolerance IntervalEstimate of amount of measurement variability

Due to test systemExcluding UUT variability

Test limits must be outside the STI limitsTest Limits

Upper and Lower physical limits of the measurementTrue Value

Actual value of variableUUT / DUT

Unit or device Under TestVariance

Also know as precisionHas no unit of measureIndication of relative degree of repeatability

How closely values within series of repeated measurementsAgree with each other

Basic NumbersTypically represented in binarySubject to word sizeConsider 4 bit word

Can view bits in several waysResolution

Decide resolution desired4 bits

Represent only integers0-15

3bits + 1 bitRepresent numbers

0-7.5

2bits + 2 bitsRepresent numbers

0-2.75To represent 2.3

Best is 2.5 or 2.25Error

0.2 or 0.5All that can be resolved is

± 0.25When working with numbers

Faced with TruncationRounding

Which is more / less accurateConsider

x = original numberN.n

XE

2-nX

Truncated

XE

2-nX

2-n/2

Rounded

Value of LSB

2-n

Let's plot error vs original number Truncated and Rounded numbers

ErrorER = XE - XET = XE - X

Truncation-2-n < ET £ 0

Rounding -½ 2-n < ER £ ½ 2-n

Observe:Full range of the error is the sameRounding

More evenly distributedMaximum error less

Propagation of ErrorLet's see how errors propagate under processingAssume two perfect numbers

N1 and N2Truncation

Implies ET < 1 LSB

AdditionWe have

N1E + E1

N2E + E2

(N1E + E1) + (N2E + E2) = N1E + N2E + E1+ E2

Thus2 *2-n < ET £ 0 Þ 21-n < ET £ 0

X XE ErrorTruncation 0 0 0

2-n 0 -2-n

Rounding 0 0 0½ 2-n - 0 -½ 2-n

½ 2-n + 2-n ½ 2-n

MultiplicationWe have

N1E + E1

N2E + E2

(N1E + E1) * (N2E + E2) = (N1E * N2E) + (N2E * E1 + N1E * E2 ) + (E1 * E2 )

Neglect E1 * E2

ThusError now depends upon the size of the numbers

Example:Let n = 3

AdditionMaximum error

21-n = 21-3 = 2-2 = 0.25

MultiplicationLet E1 = E2 = 2-n = 2-3

Let N1E = N2E = 25

Thus25 * 25 = 102425 * 2-3 + 25 * 2-3 = 8Almost 10% error

Maximum error21-n = 21-3 = 2-2 = 0.25

Common MeasurementsVoltage

Voltage measurement Fundamental Electrical Engineering measurementMethod generally involves comparing

Unknown value againstKnown reference

Done very accurately using bridge circuitsEarly analog meters used unknown voltage

Deflect meter movementAgainst calibrated dial

Calibration done by noting movementBy known reference

Contemporary digital metersAccomplish same thing

Using digital methodsWill discuss several

CurrentCurrent measured several ways

Current shuntPrecise resistor inserted in current path

Typical values 0.1W to 1WVoltage drop across shunt measured

Coil of wire wrapped around conductorMeasure induced voltage

ResistanceResistance measured several ways

Very accurately using bridge type circuitsApply known current to resistor

Measure voltage dropTemperature

Measuring temperature again reduces to Measuring voltage

Where does the voltage come from

Thermocouple ThermometryPhysics

Let's examine the physicsThermoelectricity discovered by Seebeck in 1821He found

When two wires made of dissimilar metals Connected to each other at two pointsTwo junctions held at different temperatures

Current will flowWill continue as long as there is a temperature difference

This is key point from two perspectives as we'll seePhenomenon called Seebeck EffectForce driving the current is Seebeck thermal emfThis electromotive force (voltage)

Parameter measured in thermocouple thermometry

Thermocouple is simply junction of two dissimilar metals

Implementation

BasicsConsider the following circuits

When circuit Containing two dissimilar metals completed

Will always be at lease one thermocouple in loop

Simple loop shown contains Two dissimilar metals A and B

Two junctionsTM - measurementTR - reference

Amount of current flowingRelated to temperature difference

DilemmaHow to measure current or emf

Without creating additional thermocouplesSince measurement devices usually use

Copper wire

Copper board materialMust be junctions between

Materials A and BCopper material

We now have the additional voltageseAC and eCB

We now take advantage of phenomenon we mentioned earlierIf we keep temperature of two C junctions the same - TR

No thermocouple emf generated

By keeping C junctions at same temperatureCan measure thermal emf as in following figureReferred to as isothermal context

Completing the MeasurementSince emf proportional to difference between TM and TRMust know TR to compute TMDone as follows

Again relying on physicsVoltage drop across PN junction

A

B

TRTM

TR

eAB

B

A

eAC

eCB

C

TR

eAB

B

A Cu

Cu

Proportional to temperatureKnowing voltage gives on the temperatureThus

Measurement and Stimulus SystemsMeasurement Systems Comprise

SensorsMeasurement CircuitryProcessingDisplay

Stimulus Systems CompriseConnectionStimulus Circuitry

Making Measurements Basics

ResolutionPrecision

AccuracyRepeatability

TR

eAB

B

A Cu

Cu

TM

DC

Read AZIntegrate

+-

+-

+VREF

-VREF

Unknown

Counter

-+

Control

Integrate

Read +

Read -

AZ

Compare

Measurement CircuitryA/D Conversion

Dual SlopeTraditional dual slope

Comprised of 3 intervalsIntegrate

Unknown input sampled for known timeUsually multiple of a line cycle

Voltage stored on integrate capacitorRead

Stored voltage deintegrated to 0 for unknown timeUses reference of opposite polarity

End of readOutput of integrator crosses zero

AutozeroInput connected to 0"0" voltage measuredStored and subtracted from each reading

Successive ApproximationSwitch state becomes a digital number

Process begins with LS resistor closedRepeat

Close ResistorCompare D/A output with unknown

If > ½ of unknownLeave resistor closed

Unknown

ResistorNetwork

VRef

8 4 2 1 +-

+-

Sampleand Hold

Denotes 1 in final digital wordElse

Open resistorDenotes 0 in final digital word

Until all resistors tested

Requires 1 clock period

For each bit in conversionInput to be present and stable for

Duration of conversionAccomplished by using sample and hold

Sample and HoldSchematically appears as:

Factors to consider

Acquisition TimeTime to reach full value of sampled signalTime for output of circuit to reach value of inputOutput follows input until circuit put into hold mode

Aperture TimeTime required to switch from sample to hold modeDuring this time

Output may change slightlyVariation in aperture time

Aperture uncertainty

Offset and Gain Errors

Droop Rate

+- +

-

V S

V O

Sample

V HC H

A 1 A 2

Rate of charge loss during hold time

Dielectric AbsorptionBe very careful with large capsBe very careful with high voltageCharge stored in dielectric of capacitorIf cap shorted for example

Short removedSmall voltage reappears on cap

Affects ability to respond to change

Differential MeasurementsConsider following differential circuit

Differential amplifier has Two input terminals

Labeled V1 and V2

Ground referenced outputLabeled Vo

Amplifier designed to Amplify

Difference between two signalsReject

Signals common to two inputsOutput can be expressed as following equation

LetVDM - Differential Mode Input Þ (V1 - V2)VCM - Common Mode Input Þ ½ (V1 + V2)AD - Differential Mode GainVOS- Offset VoltageCMRR - Common Mode Rejection Ratio

ThusVo = AD (VOS + CMRR * VCM + VDM)

VOS - Offset VoltageSet VDM = VCM = 0For 0 input

Practical amplifiers have non zero output voltage - Vo

VOS

Represents equivalent input voltage required to produce such an outputVOS defined as Vo / AD

+-

V 1

V 2

V O

Offset voltage of practical amplifiersTypically few millivoltsMay be trimmed to less than 25 microvolts

Used in high precision amplifiers

Common Mode Rejection Ratio - CMRRReal amplifies show change in input offset when common mode input appliedChange proportional to common mode voltageConstant of proportionality

Called CMRR

Vo = AD *CMRR * VCM

= (AD *CMRR) * VCM

= AC VCM

Denote AC

Common Mode GainWorking backwards then

CMRR = AC / AD

CMR computed as 20 log10 (CMRR) dB

Typical values80-100 dB

Calculation of Test LimitsWe test with two questions in mind

If test says UUT goodIs it really good

If test says UUT badIs it really bad

We try to set up Test limitsTest system

To ensurePassing good productFailing bad productNot vice versa

Must keep in mindAll measured values

Contain some amount of error Due to variability of test system

Test system may introduce bias which further increases

Measurement errorConsider the following situation

Test system with no bias

Consider test system with negative bias

Doing It2 wire measurements

Has R1 and R2 in series with Unknown resistance

Spec LowerSTI - Measurement Variability

True ValueSpec Upper

Out of Spec TrueValue Passed

Spec Lower

STI - Measurement Variability

True Value

Negative Bias

Spec Upper

Out of Spec TrueValue Passed

R1

R2

Rx

Current Source

MeasurementDevice

4 wire measurementsEliminates drop in R1 and R2Measurement device

Large input impedanceNo current through R3 and R4

Measure at unknownEliminate cable impedance

GuardingTechnique used when very accurate analog measurements

Must be madeNeed arises from fact

Unwanted signals capacitively couple into circuitsRF and digital signals are the worst

IdeaPhysically isolate sensitive analog circuitry

MeasurementDevice

R1

R2

Rx

Current SourceR3

R4

AnalogDigital

Physically and ElectricallySeparate

Fiber Opticsor

Magnetic Loops

Corrections

Generating SignalsStimulus Circuitry

D/A Conversion

InstrumentsUnderstanding Specifications

FloorZeroTurn Over ErrorAccuracy Specification +

Percent ofReading +Range +Offset

Usually given for24 hour90 day1 year

Warm Up6 ½ Digit

What does this meanSensors and Transducers

Sensors and transducersUsed to sample real world phenomenonSensors

Usually based upon some fundamental physical property

TransducersTransform one property into anotherUsually from fundamental property

Into voltage or currentThat can be more easily measured

TypesPassive

Current ShuntsMentioned already

Thermocouples probably most commonGenerally alloys of

Iron, copper, nickel, chromium, aluminum, platinum, tungsten, rheniumSeveral alloys have trade names that have come into common usage

ConstantanCopper - Nickel

Chrommel Chromium - Nickel

AlumelAluminum - Nickel

Common configurations have been given letter designationJ -

Iron Constantan -270 C - 1200 C0-50mV

K Chrommel - AlumelUsed in oxidizing or inert environments0-50mV

TCopper Constantan-184 C - 371 C

R and SR - Platinum 13% RhodiumS - Platinum 10% Rhodium0-18mV0 C - 1450 C

RTDAn RTD is a Resistance Temperature DetectorBased on principle

Conductivity of material changes in predictable mannerWhen subjected to different temperature

Device constructedCoil of fine gauge wireWrapped around ceramic core

MaterialPlatinum, copper, nickel, tungstenPlatinum most frequently used

High operating rangeLinear characteristicsLong term stability

Most accurate measurements made4 wire resistance measurement

ActiveUsually amplifying or transducing the signalMany instrumentation transducers

4-20 mA

AccuracySensors and transducers

Vary widely in accuracyThermocouples

Typically 1%-3%As we've seen

Measurement system comprised ofSensorsMeasurement CircuitryProcessingDisplay

Each contributes to error budgetCan compensate if necessary

Configure systemCalibrate entire system

Non-linearityMost real world devices non-linearNeed to consider this when using

As sensor Often common sensors

Carefully studiedBehaviour fully understoodCharacterized by complex equation

InvolvingExponentialsLogsPower terms

Solving such equations in instrumentTime consumingDifficult

ConsequentlyManufacturers will approximate actual equation

Provide linearized version linearizationMeans they've done a curve fit to original equation

Piecewise linearLeast squares

When such is the caseNeed to consider

Conformity to original equationSpecified as conformity error

ErrorsSources

Instruments / GeneratorsOffset and Common Mode

Usually refer to differential mode type inputsOffset

Offset error is built in or acquired bias in signalCommon to both polarities of signalCannot be eliminated by differential techniques

Common ModeError signal inherent in signalInverting signal

Inverts errorCan be substantially reduced by differential methods

Ability to eliminateCommon Mode Rejection - CMR

NumbersLet's consider the following circuit

E = 100 V ± 1%

I = 10 A ± 1%R = 10 W ± 1%

Now calculate the power dissipated in RPower

EI = (100 V ± 1%) * (10A ± 1%)= 1000 ± 10*1% ± 100*1% ± 1%*1%= 1000 ± 1.1 Þ 998.9 - 1001.1

I2R = (10A ± 1%)*(10A ± 1%)*(10 W ± 1%)= (100 ± 20*1% ± 1%*1%)= (100 ± 0.2)*(10 W ± 1%)= 1000 ± 2 ± 100*1% ± 0.2*1%= 1000 ± 3 Þ 997 - 1003

E2/R = (100 V ± 1%)*(100 V ± 1%) / (10 W ± 1%)= (10000 ± 2 ± 1%*1%) / (10 W ± 1%)= 908.9 Þ 1111.3

PhysicsTemperature -

As a source Seebeck Effect

As a side effectDrift

Fundamental physical propertiesAffected by

TemperaturePressureHumidity

Must be aware of such changes

I

R

E

Design aroundCompensate for

AgePhysical properties also change with ageCapacitors are notoriously bad

HandlingRMS

MeasuringRMS

We have power in resistor due to constant current asP = I2R

Ieff effective value of periodic currentConstant value of currentWhich will produce same power in resistor

As produced on average by periodic current

In sinusoidal steady stateAverage power in resistor given as Pave = [PR(t)]ave = ½RIpeak

2

If we let P = Pave and I = Ieff in above equationWe have

II

effpeak2

With some juggling

VV

effpeak2

For nonsinusoidal but periodic currentAverage power given as

PT

Ri t dtave t

t T

1 2

0

012

Again with some simple math we have

IT

i t dteff t

t T

1 2

0

012

and

VT

v t dteff t

t T

1 2

0

012

For sinusoidal signalsThese become

I II

rms effpeak 2

and

V VV

rms effpeak 2

Many voltmeters measure RMS voltageUsing sinusoidal model

True RMSMeasures power in signal into precise loadCompute Vrms from that

ACRMSTrue RMSAveragePeak to Peak

DC

Know What You’re ReadingCheck calibration

Limitations on EquipmentMost commonly usedPower Supplies

Check current limitCompliance voltage

Signal GeneratorsRise and Fall times limitationsOffset

OscilloscopesSample Rate

AliasingProbe capacitanceBandwidth Limitations Grounding of scope probes

Digital VoltmetersFloorBandwidth LimitationsLinearityGuardingImpedance mismatchInput impedance

ResistanceCapacitance

TroubleshootingBasics

With power onNever install parts Never wire circuitSolder

Most soldering irons have grounded tipNever handle chips by pins

Even TTLS parts can be damaged by staticFailure mechanism

Punch through on gate oxideOften won't fail immediately

Leads to DOAConnect all unused inputs

VCC through 10K Ground

Before components installedMeasure power - ground impedanceIf short

Can sometimes identify by 4 wire ohms measurement

Make certain all chips properly bypassed

Use power and ground planes if at all possibleBuild such planes using cross hatch pattern

Permits better heat flow during manufacture

VoltageMake sure on all proper pinsMake sure proper level

May have to adjust current limit on power supplyMany circuits will run with power

Parasitically supplied throughInput protection circuitry

GroundMake sure connected on all pins

Include Power On Reset circuitMake certain reset worksMake certain reset off when trying to run

TemperatureBe aware of temperature of componentsUnderstand what hot really is

Signal LevelKnow what signal levels to expect out of a componentKnow what bad signals look like