Download Testing, Measurement, and Troubleshooting

Testing, Measurement, and Troubleshooting
Terminology
Accuracy
Measure of an instrument's capability
To approach a true or absolute value
Bias
Measure of how closely the mean value
In series of repeated measurements
Approaches true value
Golden Unit
Unit whose behaviour is completely known
Used as a standard
Mean
Measure of the central value of set of measurements
1 N i
mean   mi
N i0
Residual
Measured value minus the mean
Resolution
Measure of ability to discern value of a measurement
Root Mean Square
Square Root of average of the average of the squares of the values
yi 2
rms value  
N N
Statistical Tolerance Interval
Estimate of amount of measurement variability
Due to test system
Excluding UUT variability
Test limits must be outside the STI limits
Test Limits
Upper and Lower physical limits of the measurement
True Value
Actual value of variable
UUT / DUT
Unit or device Under Test
Variance
Also know as precision
Has no unit of measure
Indication of relative degree of repeatability
How closely values within series of repeated measurements
Agree with each other
Basic Numbers
Typically represented in binary
Subject to word size
Consider 4 bit word
Can view bits in several ways
Resolution
Decide resolution desired
4 bits
Represent only integers
0-15
3bits + 1 bit
Represent numbers
0-7.5
2bits + 2 bits
Represent numbers
0-2.75
To represent 2.3
Best is 2.5 or 2.25
Error
0.2 or 0.5
All that can be resolved is
 0.25
When working with numbers
Faced with
Truncation
Rounding
Which is more / less accurate
Consider
x = original number
N.n
Value of LSB
2-n
Let's plot error vs original number
Truncated and Rounded numbers
XE
XE
X
Truncation
-2-n < ET  0
Rounding
-½ 2-n < ER  ½ 2-n
-n
2
-n
2 /2
Rounded
Truncated
X
Truncation
Rounding
Error
ER = XE - X
ET = XE - X
X
-n
2
0
2-n
0
½ 2-n ½ 2-n +
XE
Error
0
0
0
0
2-n
0
-2-n
0
-½ 2-n
½ 2-n
Observe:
Full range of the error is the same
Rounding
More evenly distributed
Maximum error less
Propagation of Error
Let's see how errors propagate under processing
Assume two perfect numbers
N1 and N2
Truncation
Implies ET < 1 LSB
Addition
We have
N1E + E1
N2E + E2
(N1E + E1) + (N2E + E2) =
N1E + N2E + E1+ E2
Thus
2 *2-n < ET  0  21-n < ET  0
Multiplication
We have
N1E + E1
N2E + E2
(N1E + E1) * (N2E + E2) =
(N1E * N2E) + (N2E * E1 + N1E * E2 ) + (E1 * E2 )
Neglect E1 * E2
Thus
Error now depends upon the size of the numbers
Example:
Let n = 3
Addition
Maximum error
21-n = 21-3 = 2-2 = 0.25
Multiplication
Let E1 = E2 = 2-n = 2-3
Let N1E = N2E = 25
Thus
25 * 25 = 1024
25 * 2-3 + 25 * 2-3 = 8
Almost 10% error
Maximum error
21-n = 21-3 = 2-2 = 0.25
Common Measurements
Voltage
Voltage measurement
Fundamental Electrical Engineering measurement
Method generally involves comparing
Unknown value against
Known reference
Done very accurately using bridge circuits
Early analog meters used unknown voltage
Deflect meter movement
Against calibrated dial
Calibration done by noting movement
By known reference
Contemporary digital meters
Accomplish same thing
Using digital methods
Will discuss several
Current
Current measured several ways
Current shunt
Precise resistor inserted in current path
Typical values 0.1 to 1
Voltage drop across shunt measured
Coil of wire wrapped around conductor
Measure induced voltage
Resistance
Resistance measured several ways
Very accurately using bridge type circuits
Apply known current to resistor
Measure voltage drop
Temperature
Measuring temperature again reduces to
Measuring voltage
Where does the voltage come from
Thermocouple Thermometry
Physics
Let's examine the physics
Thermoelectricity discovered by Seebeck in 1821
He found
When two wires made of dissimilar metals
Connected to each other at two points
Two junctions held at different temperatures
Current will flow
Will continue as long as there is a temperature difference
This is key point from two perspectives as we'll see
Phenomenon called Seebeck Effect
Force driving the current is Seebeck thermal emf
This electromotive force (voltage)
Parameter measured in thermocouple thermometry
Thermocouple is simply junction of two dissimilar metals
Implementation
Basics
Consider 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 junctions
TM - measurement
TR - reference
Amount of current flowing
Related to temperature difference
Dilemma
How to measure current or emf
Without creating additional thermocouples
Since measurement devices usually use
Copper wire
Copper board material
Must be junctions between
Materials A and B
Copper material
We now have the additional voltages
eAC and eCB
A
TR
TM
B
TR
A
eAC
C
eAB
eCB
B
We now take advantage of phenomenon we mentioned earlier
If we keep temperature of two C junctions the same - TR
No thermocouple emf generated
By keeping C junctions at same temperature
Can measure thermal emf as in following figure
Referred to as isothermal context
TR
A
Cu
eAB
Completing the Measurement
Since emf proportional to difference between TM and TR
Must know TR to compute TM
Done as follows
Again relying on physics
Voltage drop across PN junction
Proportional to temperature
Knowing voltage gives on the temperature
Thus
A
Cu
B
TR
Cu
TM
eAB
DC
Cu
B
Measurement and Stimulus Systems
Measurement Systems Comprise
Sensors
Measurement Circuitry
Processing
Display
Stimulus Systems Comprise
Connection
Stimulus Circuitry
Making Measurements
Basics
Resolution
Precision
Accuracy
Repeatability
Measurement Circuitry
Integrate
+VREF
Unknown
+
-
-
+
+
-VREF
Read Read +
A/D Conversion
Integrate
Dual Slope
Traditional dual slope
Comprised of 3 intervals
Integrate
AZ
Read
AZ
Compare
Counter
Control
Unknown input sampled for known time
Usually multiple of a line cycle
Voltage stored on integrate capacitor
Read
Stored voltage deintegrated to 0 for unknown time
Uses reference of opposite polarity
End of read
Output of integrator crosses zero
Autozero
Input connected to 0
"0" voltage measured
Stored and subtracted from each reading
Successive Approximation
Switch state becomes a digital number
Resistor
Network
8
4
2
1
+
+
VRef
Unknown
Sample
and Hold
Process begins with LS resistor closed
Repeat
Close Resistor
Compare D/A output with unknown
If > ½ of unknown
Leave resistor closed
Denotes 1 in final digital word
Else
Open resistor
Denotes 0 in final digital word
Until all resistors tested
Requires
1 clock period
For each bit in conversion
Input to be present and stable for
Duration of conversion
Accomplished by using sample and hold
Sample and Hold
Schematically appears as:
A1
VS
Sample
+
CH
VH
A2
+
-
Factors to consider
Acquisition Time
Time to reach full value of sampled signal
Time for output of circuit to reach value of input
Output follows input until circuit put into hold mode
Aperture Time
Time required to switch from sample to hold mode
During this time
Output may change slightly
Variation in aperture time
Aperture uncertainty
Offset and Gain Errors
Droop Rate
Rate of charge loss during hold time
VO
Dielectric Absorption
Be very careful with large caps
Be very careful with high voltage
Charge stored in dielectric of capacitor
If cap shorted for example
Short removed
Small voltage reappears on cap
Affects ability to respond to change
Differential Measurements
Consider following differential circuit
V1
V2
+
-
VO
Differential amplifier has
Two input terminals
Labeled V1 and V2
Ground referenced output
Labeled Vo
Amplifier designed to
Amplify
Difference between two signals
Reject
Signals common to two inputs
Output can be expressed as following equation
Let
VDM - Differential Mode Input  (V1 - V2)
VCM - Common Mode Input  ½ (V1 + V2)
AD
- Differential Mode Gain
VOS - Offset Voltage
CMRR - Common Mode Rejection Ratio
Thus
Vo = AD (VOS + CMRR * VCM + VDM)
VOS - Offset Voltage
Set VDM = VCM = 0
For 0 input
Practical amplifiers have non zero output voltage - Vo
VOS
Represents equivalent input voltage required to produce such an output
VOS defined as Vo / AD
Offset voltage of practical amplifiers
Typically few millivolts
May be trimmed to less than 25 microvolts
Used in high precision amplifiers
Common Mode Rejection Ratio - CMRR
Real amplifies show change in input offset when common mode input applied
Change proportional to common mode voltage
Constant of proportionality
Called CMRR
Vo
= AD *CMRR * VCM
= (AD *CMRR) * VCM
= AC VCM
Denote AC
Common Mode Gain
Working backwards then
CMRR = AC / AD
CMR computed as
20 log10 (CMRR) dB
Typical values
80-100 dB
Calculation of Test Limits
We test with two questions in mind
If test says UUT good
Is it really good
If test says UUT bad
Is it really bad
We try to set up
Test limits
Test system
To ensure
Passing good product
Failing bad product
Not vice versa
Must keep in mind
All measured values
Contain some amount of error
Due to variability of test system
Test system may introduce bias which further increases
Measurement error
Consider the following situation
Test system with no bias
STI - Measurement Variability
Spec Lower
True Value
Spec Upper
Out of Spec True
Value Passed
Consider test system with negative bias
STI - Measurement Variability
Spec Upper
Spec Lower
True Value
Negative Bias
Out of Spec True
Value Passed
Doing It
2 wire measurements
Has R1 and R2 in series with
Unknown resistance
Current Source
R1
Measurement
Device
Rx
R2
4 wire measurements
Eliminates drop in R1 and R2
Measurement device
Large input impedance
No current through R3 and R4
Measure at unknown
Eliminate cable impedance
R3
Current Source
R1
Measurement
Device
Rx
R2
R4
Guarding
Technique used when very accurate analog measurements
Must be made
Need arises from fact
Unwanted signals capacitively couple into circuits
RF and digital signals are the worst
Idea
Physically isolate sensitive analog circuitry
Fiber Optics
or
Magnetic Loops
Digital
Physically and Electrically
Separate
Corrections
Generating Signals
Stimulus Circuitry
D/A Conversion
Analog
Instruments
Understanding Specifications
Floor
Zero
Turn Over Error
Accuracy Specification +
Percent of
Reading +
Range +
Offset
Usually given for
24 hour
90 day
1 year
Warm Up
6 ½ Digit
What does this mean
Sensors and Transducers
Sensors and transducers
Used to sample real world phenomenon
Sensors
Usually based upon some fundamental physical property
Transducers
Transform one property into another
Usually from fundamental property
Into voltage or current
That can be more easily measured
Types
Passive
Current Shunts
Mentioned already
Thermocouples probably most common
Generally alloys of
Iron, copper, nickel, chromium, aluminum, platinum, tungsten, rhenium
Several alloys have trade names that have come into common usage
Constantan
Copper - Nickel
Chrommel
Chromium - Nickel
Alumel
Aluminum - Nickel
Common configurations have been given letter designation
JIron Constantan
-270 C - 1200 C
0-50mV
K
Chrommel - Alumel
Used in oxidizing or inert environments
0-50mV
T
Copper Constantan
-184 C - 371 C
R and S
R - Platinum 13% Rhodium
S - Platinum 10% Rhodium
0-18mV
0 C - 1450 C
RTD
An RTD is a Resistance Temperature Detector
Based on principle
Conductivity of material changes in predictable manner
When subjected to different temperature
Device constructed
Coil of fine gauge wire
Wrapped around ceramic core
Material
Platinum, copper, nickel, tungsten
Platinum most frequently used
High operating range
Linear characteristics
Long term stability
Most accurate measurements made
4 wire resistance measurement
Active
Usually amplifying or transducing the signal
Many instrumentation transducers
4-20 mA
Accuracy
Sensors and transducers
Vary widely in accuracy
Thermocouples
Typically 1%-3%
As we've seen
Measurement system comprised of
Sensors
Measurement Circuitry
Processing
Display
Each contributes to error budget
Can compensate if necessary
Configure system
Calibrate entire system
Non-linearity
Most real world devices non-linear
Need to consider this when using
As sensor
Often common sensors
Carefully studied
Behaviour fully understood
Characterized by complex equation
Involving
Exponentials
Logs
Power terms
Solving such equations in instrument
Time consuming
Difficult
Consequently
Manufacturers will approximate actual equation
Provide linearized version linearization
Means they've done a curve fit to original equation
Piecewise linear
Least squares
When such is the case
Need to consider
Conformity to original equation
Specified as conformity error
Errors
Sources
Instruments / Generators
Offset and Common Mode
Usually refer to differential mode type inputs
Offset
Offset error is built in or acquired bias in signal
Common to both polarities of signal
Cannot be eliminated by differential techniques
Common Mode
Error signal inherent in signal
Inverting signal
Inverts error
Can be substantially reduced by differential methods
Ability to eliminate
Common Mode Rejection - CMR
Numbers
Let's consider the following circuit
E = 100 V  1%
I = 10 A  1%
R = 10   1%
R
I
E
Now calculate the power dissipated in R
Power
EI
= (100 V  1%) * (10A  1%)
= 1000  10*1%  100*1%  1%*1%
= 1000  1.1  998.9 - 1001.1
I2R
= (10A  1%)*(10A  1%)*(10   1%)
= (100  20*1%  1%*1%)
= (100  0.2)*(10   1%)
= 1000  2  100*1%  0.2*1%
= 1000  3  997 - 1003
E2/R
= (100 V  1%)*(100 V  1%) / (10   1%)
= (10000  2  1%*1%) / (10   1%)
= 908.9  1111.3
Physics
Temperature As a source
Seebeck Effect
As a side effect
Drift
Fundamental physical properties
Affected by
Temperature
Pressure
Humidity
Must be aware of such changes
Design around
Compensate for
Age
Physical properties also change with age
Capacitors are notoriously bad
Handling
RMS
Measuring
RMS
We have power in resistor due to constant current as
P = I2R
Ieff effective value of periodic current
Constant value of current
Which will produce same power in resistor
As produced on average by periodic current
In sinusoidal steady state
Average power in resistor given as
Pave = [PR(t)]ave = ½RIpeak2
If we let P = Pave and I = Ieff in above equation
We have
I peak
I eff 
2
With some juggling
Veff 
V peak
2
For nonsinusoidal but periodic current
Average power given as
1
 1 t 0T
2
Pave    Ri 2 t dt 
T t0

Again with some simple math we have
1
I eff
 1 t 0 T
2
   i 2 t dt 
T t0

Veff
 1 t 0 T
2
   v 2 t dt 
T t0

and
1
For sinusoidal signals
These become
I rms  I eff 
I peak
2
and
Vrms  Veff 
Vpeak
2
Many voltmeters measure RMS voltage
Using sinusoidal model
True RMS
Measures power in signal into precise load
Compute Vrms from that
AC
RMS
True RMS
Average
Peak to Peak
DC
Know What You’re Reading
Check calibration
Limitations on Equipment
Most commonly used
Power Supplies
Check current limit
Compliance voltage
Signal Generators
Rise and Fall times limitations
Offset
Oscilloscopes
Sample Rate
Aliasing
Probe capacitance
Bandwidth Limitations
Grounding of scope probes
Digital Voltmeters
Floor
Bandwidth Limitations
Linearity
Guarding
Impedance mismatch
Input impedance
Resistance
Capacitance
Troubleshooting
Basics
With power on
Never install parts
Never wire circuit
Solder
Most soldering irons have grounded tip
Never handle chips by pins
Even TTLS parts can be damaged by static
Failure mechanism
Punch through on gate oxide
Often won't fail immediately
Leads to DOA
Connect all unused inputs
VCC through 10K
Ground
Before components installed
Measure power - ground impedance
If short
Can sometimes identify by 4 wire ohms measurement
Make certain all chips properly bypassed
Use power and ground planes if at all possible
Build such planes using cross hatch pattern
Permits better heat flow during manufacture
Voltage
Make sure on all proper pins
Make sure proper level
May have to adjust current limit on power supply
Many circuits will run with power
Parasitically supplied through
Input protection circuitry
Ground
Make sure connected on all pins
Include Power On Reset circuit
Make certain reset works
Make certain reset off when trying to run
Temperature
Be aware of temperature of components
Understand what hot really is
Signal Level
Know what signal levels to expect out of a component
Know what bad signals look like