The document discusses various topics related to measurement accuracy including definitions of accuracy and precision. It describes sources of error such as systematic errors, random errors, and quantization errors. It also discusses ways to improve accuracy such as filtering, averaging, and guardbanding. Finally, it covers calibration techniques, data analysis methods like histograms and distributions, and the relationship between noise, test time, and yield.

1. Measurement

2. • Measurement Accuracy
• Definitions of Accuracy
– Closeness with which an instrument reading approaches
the true value of the variable being measured.
– The maximum error in the measurement of a physical
quantity in terms of the output of an instrument when
referred to the individual instrument calibrations.
– The degree of conformance of a test instrument to
absolute standards.
– The ability to produce an average measured value which
agrees with the true value or standard being used.

3. • Measurement Accuracy
• Precision
– A measure of the reproducibility of the measurements.
» Given a fixed value of a variable, precision is a
measure of the degree to which successive
measurements differ from one another.
– The degree to which repeated measurements of a given
quantity agree when obtained by the same method and
under the same conditions.
– Also called repeatability or reproducibility.
– The ability to repeatedly measure the same product or
service and obtain the same results.

4. • Measurement Accuracy
– Book Terminology
• Accuracy - to refers to the overall closeness of an
averaged measurement to the true value.
• Repeatability - the consistency with which that
measurement can be made.
– The word precision will be avoided.
• Accuracy takes all error sources into account
– Systematic Errors
– Random Errors
– Resolution (Quantization Errors)

5. • Measurement Accuracy
• Systematic Errors
– Errors that appear consistently from measurement to
measurement
» Ideal Value = 100mV
» Measurements : 101mV, 103mV, 102mV, 101mV,
102mV, 103mV, 103mV, 101mV, 102mV
» Average Error : 2mV
» Caused by DC offsets, gain errors, non-linearities in
the DVM
» Systematic errors can often be reduced through
calibrations.

6. • Measurement Accuracy
• Random Errors
– Notice that the list of numbers in the last slide vary from
101mV to 103mV.
– All measurement tools have random errors even $2
Million Automated test instruments
– Random Errors are perfectly normal in analog and mixed-signal
measurements.
– Big challenge is in determining whether the random error
is caused by a bad DIB design, bad DUT design or by the
tester itself.

7. • Measurement Accuracy
• Resolution (Quantization Errors)
– Notice that in the previous list of numbers, the
measurement was always rounded off to the nearest
milivolt.
– Limited resolution results from the fact that continuous
analog signals must be converted to digital format (using
ADC’s) before a computer can evaluate the test results.
– The inherent error in ADCs and measurement
instrumentation is called Quantization Error.
– Quantization error is a result of the conversion from an
infinitely variable input voltage to a finite set of possible
outputs from the ADC.

8. • Measurement Accuracy
• Repeatability
– Non-repeatable answers are a fact of life for mixed-signal
test engineer
– Could be caused by random noise or other external
influences
– If a test engineer gets the same value multiple times in a
row, it should raise the question of ranging of the
measurement tool.
– Repeatability is desirable, but it does not in itself
guarantee accuracy.

9. • Measurement Accuracy
• Stability
– The degree to which a series of supposedly identical
measurements remains constant over time, temperature,
humidity, and all other time varying factors is referred to
as stability.
– Testers are equipped with temperature sensors to allow
recalibration if a certain change in temperature occurs.
– Caution must be exercised in the power-up of the tester,
since temperature of tester electronics must stabilize
before calibrations are accurate
– Also, if the test cabinet or test head are opened, the
temperature must stabilize before any calibrations can be
performed.

10. • Measurement Accuracy
• Correlation
– The ability to get the same answer using different pieces
of hardware or software.
» Tester - to - Bench Correlation
» Tester - to - Tester Correlation
» Program - to - Program Correlation
» DIB - to - DIB Correlation
» Day - to - Day Correlation

11. • Measurement Accuracy
– Terminology
• Reproducibility
» Reproducibility is often incorrectly used interchangeably
with repeatability
» Reproducibility is defined as the statistical deviations
between a particular measurement taken by any
operator on any group of testers on any given day using
any DIB board.
» Repeatability is used to describe the ability of a single
tester and DIB board to get the same answer multiple
times as the test program is repeatedly executed.
» If a measurement is highly repeatable, but not
reproducible, then the test program may consistently
pass a particular DUT one day but then may consistently
fail the same DUT on another day or on another tester.

12. • Calibration and Checkers
– Traceability to Standards
• National Institute of Standards and Technology
(NIST)
• Thermally stabilized standardized instrument
– periodically replaced by a freshly calibrated source
– Hardware Calibration
• Any mechanical process which brings a piece of
equipment back into agreement with calibration
standards
– usually not a convenient process
– Robotic manipulations can be used to automate the
process, but it is still not optimal

13. • Calibration and Checkers
– Software Calibration
• The basic idea behind software calibration is the
separation of the instrument’s ideal operation from
its non-idealities so that a model of the instruments
non-ideal operation can be constructed, followed
by a correction of the non-ideal behavior using a
mathematical routine written in software.
• Most testers have extensive calibration processes
for each measurement range in the tester
instrumentation

14. • Calibration and Checkers
– System Calibrations & Checkers
• Checkers verify the functionality of the hardware instruments
in the tester.
• Calibration and checkers are often found in the same
program.
– Several levels of checkers and calibrations are used
» Calibration reference source replacement and re-calibration
is performed approximately every six months
» Extensive performance evaluation (PV) process is used to
verify the tester is in compliance with its published
specifications
» Automated calibrations on test floor as conditions warrant
them

15. • Calibration and Checkers
– Focussed Instrument Calibrations
• Accuracy of faster instruments can be improved by
periodically referencing them back to slower more
accurate instruments.
• Test specific calibration to focus on the exact
parameters of the test
• Tester Focussed calibration may not be necessary
on all tests any longer, yet DIB focussed calibrations
will remain a major task of the test engineer

16. • Calibration and Checkers
– Focussed DIB Circuit Calibrations
• Often, circuits are added to the DIB board to
improve the accuracy of the particular test, or to
buffer a weak output of a device before it is tested.
• Since DIB circuits are added in series between the
DUT and the tester, the contribution of calibration
factors must be treated accordingly.
• It is critical that the test engineer have a clear
understanding which characteristics of each DIB
circuit affects the test being performed.
• Review of example 4-3 found on p 4-17.

17. • Calibration and Checkers
– DIB Checkers
• Verifies the basic functionality of the DIB circuits.
• Performed in the first run of the test program along
with the calibration
• Every possible relay and circuit path should be
checked to produce a go-nogo response verifying
the functionality of as much of the DIB board as
possible.

18. • Calibration and Checkers
– Tester Specifications
• Test engineers must determine if the tester
instrument is capable of making the measurements
they require.
• Due to the lack of information about specification
values from the manufacturer, the test engineer
needs to understand the spec conditions and the
variations from that spec which will affect the
performance of the instrument.
– A good example is a specification of the “noise floor” of a
tester. In a professional shielded room with no digital
circuits operating, the noise floor will be totally different
from when the same tester is operating at a university.

19. • Calibration and Checkers
– Tester Specifications
• Example of a DC meter
– five output ranges (set by a PGA internally and calibrated)
– accuracy is specified as a percentage of the measured
value - with a limit of 1 mV or 2.5 mV.
» Assumes the measurement is made 100 times and
averaged
» single measurement may have greater measurement
error along with repeatability error.
– Meter may also pass the signal through a low pass filter
with the input either enabled or disabled.
» Indicates extra settling time
» if filter is disabled, is the spec still true????

20. • Dealing with Measurement Error
– Filtering
• Acts as a hardware averaging circuit and allows only
the desired frequencies to pass.
– The closer the cutoff frequency to the measurement
frequency, the more noise is removed.
• Unfortunately, the lower the frequency, the longer
the test time required for settling
– Settling time is inversely proportional to the cutoff
frequency.

21. • Dealing with Measurement Error
– Averaging
• A form of discrete time filtering that can be used to
improve the repeatability of a measurement.
• To reduce the effect of noise on a voltage
measurement by a factor of two, one has to take
four times as any readings and average them.
• This quickly results in a point of diminishing returns
with respect to test times.
– Note: Do not average values in dB - always convert to
linear form and average - then return them to dB form.

22. • Dealing with Measurement Error
– Guardbanding
• If a particular measurement is known to be accurate and
repeatable with a worst cast uncertainty of ± e, then the
final test limits should be tightened by e to insure that no
bad devices are shipped to the customer.
– Guardbanding Positive Test Limit = Positive Test Limit - e
– Guardbanding Negative Test Limit = Negative Test Limit + e
• The only way to reduce guardbanding is to increase
accuracy and repeatability - this increases test time and
may not be a viable option.

23. • Basic Data Analysis
– Datalogs
• A concise list of results generated by the test
program
– test number
– test category
– test description
– maximum and minimum test limits
– measured result
– Pass / fail indication

24. • Sequencer: S_continuity
• 1000 Neg PPMU Cont Failing Pins: 0
• Sequencer: S_VDAC_SNR
• 5000 DAC Gain Error T_VDAC_SNR -1.00 dB < -0.13 dB < 1.00 dB
• 5001 DAC S/2nd T_VDAC_SNR 60.0 dB <= 63.4 dB
• 5002 DAC S/3rd T_VDAC_SNR 60.0 dB <= 63.6 dB
• 5003 DAC S/THD T_VDAC_SNR 60.00 dB <= 60.48 dB
• 5004 DAC S/N T_VDAC_SNR 55.0 dB <= 70.8 dB
• 5005 DAC S/N+THD T_VDAC_SNR 55.0 dB <= 60.1 dB
• Sequencer: S_UDAC_SNR
• 6000 DAC Gain Error T_UDAC_SNR -1.00 dB < -0.10 dB < 1.00 dB
• 6001 DAC S/2nd T_UDAC_SNR 60.0 dB <= 86.2 dB
• 6002 DAC S/3rd T_UDAC_SNR 60.0 dB <= 63.5 dB
• 6003 DAC S/THD T_UDAC_SNR 60.00 dB <= 63.43 dB
• 6004 DAC S/N T_UDAC_SNR 55.0 dB <= 61.3 dB
• 6005 DAC S/N+THD T_UDAC_SNR 55.0 dB <= 59.2 dB
• Sequencer: S_UDAC_Linearity
• 7000 DAC POS ERR T_UDAC_Lin -100.0 mV < 7.2 mV < 100.0 mV
• 7001 DAC NEG ERR T_UDAC_Lin -100.0 mV < 3.4 mV < 100.0 mV
• 7002 DAC POS INL T_UDAC_Lin -0.90 lsb < 0.84 lsb < 0.90 lsb
• 7003 DAC NEG INL T_UDAC_Lin -0.90 lsb < -0.84 lsb < 0.90 lsb
• 7004 DAC POS DNL T_UDAC_Lin -0.90 lsb < 1.23 lsb (F) < 0.90 lsb
• 7005 DAC NEG DNL T_UDAC_Lin -0.90 lsb < -0.83 lsb < 0.90 lsb
• 7006 DAC LSB SIZE T_UDAC_Lin 0.00 mV < 1.95 mV < 100.00 mV
• 7007 DAC Offset V T_UDAC_Lin -100.0 mV < 0.0 mV < 100.0 mV
• 7008 Max Code Width T_UDAC_Lin 0.00 lsb < 1.23 lsb < 1.50 lsb
• 7009 Min Code Width T_UDAC_Lin 0.00 lsb < 0.17 lsb < 1.50 lsb
• Bin: 10

25. • Basic Data Analysis
– Histograms
• A graphical method used to view the repeatability
of numerical data
– Ideally the values of the acquired data should be closely
packed
– Statistical relevance of the data is determined by the
number of samples taken - in Test engineering, the
minimum for statistical relevance is 100.
– Histograms also give numerical values which indicate the
fit to the standard bell curve, including the mean and
standard deviation

27. • Basic Data Analysis
– Normal (Gaussian) Distributions
• Any summation of a large number of random
variables results in a Gaussian distribution.
• The variations in a typical mixed-signal measurement
comes from a summation of many different sources
of noise and crosstalk in both the device and the
tester instrument.
– The standard deviation of the Gaussian distribution is
roughly equal to one sixth of the total variation from the
minimum value to the maximum value
– In the example the standard deviation is 0.0029 dB, so we
would expect to see values ranging from -0.139 dB to
-0.121 dB. These values are labeled as “Mean -3 sigma”
and “Mean +3 sigma”

28. • Basic Data Analysis
– Non-Gaussian Distributions
• Bimodal
• Outliers

29. • Basic Data Analysis
– Noise, Test Time and Yield
• Yield = total good devices / total tested devices
• Definite trade off between test time and production
yield.
• Designer controls the design margins which reduce
the need for guardbanding
• Centering of design within the specifications
– May cost extra silicon or extra power
– May make the test unnecessary