Download Electronic Instrumentation Errors in Measurements

Electronic Instrumentation
Errors in Measurements
* In this presentation definitions and examples
from Wikipedia, HowStaffWorks and some other sources
were used
Lecturer: Dr. Samuel Kosolapov
Items to be
defined/refreshed/discussed
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Systematic Error
Random Error
Example with OA zero offset
Normal Distribution
Mean and Deviation
Accuracy and Precision
Absolute and relative error
Significant Digits. Scientific notation
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Types of Errors in Measurements
Measurement Error (or Observational Error)
is the difference (delta)
between
measured value of quantity
and
the true value of quantity
Two types of Measurement Errors:
Systematic Errors
and
Random Errors
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Systematic Error versus Random Error
Systematic Error:
Value of the error is the same
IF
we use the instrument
in the same way
and in the same case
Systematic Error
in most cases
can be reduced by better design
and/or by using special procedure : calibration
Random Error:
Value of the error
vary from measurement to measurement
Origin of random error is due to factors that are out of our control.
In some cases significance of random error can be reduced by better design
and/of by using math operations like averaging and filtration
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Systematic Error : Calibration
Suppose we know that Y = A*X
Q. How one can evaluate Systematic Error
from the experimental graph
Suppose we know that Y = A*X
Q. What is the “Calibration Equation” ?
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Systematic Error in OA. Voltage offset
According to OA equation Vout = A(Vp – Vm)
Vout must be == 0
Practically, Vout != 0
 Output offset voltage
Output-offset voltage
represents the internal imbalance of an op-amp
(for example in the differential amplifier)
The output-offset voltage is defined as the
measured output voltage when the input
terminals are shorted together
The output-offset voltage may be modeled
by placing a voltage source AoVIO
in series with the output voltage source –Ao(v+ - v-)
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Systematic Error in OA. Voltage offset
Vout = – Ao(v+ - v-) + AoVIO
Systematic Error
 All OA circuits from TAE must be re-analyzed now
by taking into account this systematic error
Some high quality OA uses laser trimming of the
resistors during production
 Time of production and price ???
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Internal Offset Null adjust.
(Recommended by producer)
https://www.youtube.com/watch?v=uYryH28yFAc
Problem: this adjustment must be done MANUALLY for every circuit
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External Offset Null adjust. Inverting Amplifier
http://www.eeweb.com/company-blog/ms_kennedy/m.s.-kennedy-operational-amplifiers
This adjustments can be used when more DC control is needed
Problem: this adjustment must be done MANUALLY for every circuit
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External Offset Null adjust. Non-Inverting Amplifier
http://www.eeweb.com/company-blog/ms_kennedy/m.s.-kennedy-operational-amplifiers
Problem: this adjustment must be done MANUALLY for every circuit
+ problems with gain
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External Offset Null adjust. Differential Amplifier
http://www.eeweb.com/company-blog/ms_kennedy/m.s.-kennedy-operational-amplifiers
Problem: this adjustment must be done MANUALLY for every circuit
+ many additional problems with gain and CMRR
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Example. TLC4502 Self-calibrating precision dual OA
http://www.datasheetarchive.com/files/texas-instruments/data/sc/docs/msp/showcase/vol20/showpg07.htm
Modern solution: combination of Analog and Digital elements
TLC4502 achieves precision by automatically nulling its
input offset voltage during power up.
During the calibration procedure (on power up),
the operational amplifier is removed from the signal path
and both inputs are tied to GND.
Then output voltage is measured by ADC. Measured value
is stored at SAR (successive-approximation register) and
used to generate compensation voltage (by using DAC).
This self-calibrating procedure typically requires 300 ms to
complete.
After calibration , the calibration circuitry drops out of the
signal path, becoming transparent to the user.
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Random Error
Random Error:
Value of the error
vary from measurement to measurement
 A number of measurements is a must
Xmeasured = Xreal + RANDOM_ERROR
Averaging:
Xmeasured = Xreal + RANDOM_ERROR
For Normal Distribution RANDOM_ERROR = 0
Q.Non-trivial question:
Does averaging always “eliminates random error ?
A. Not always.
 Other filters like “median filter” can be used
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Example of Normal (Gaussian) Distribution
http://www.astro.umass.edu/~schloerb/ph281/Lectures/NormalDistribution/NormalDistribution.pdf
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Mean and Variance for Normal (Gaussian) Distribution
Mean
Variance : Mean Square Deviation from Mean
s Standard Deviation: Root Mean Square
Deviation from Mean (RMS)
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Mean practical calculation
for Normal (Gaussian) Distribution
Mean
Most likely value of mean is the sample mean
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Some statistics results
for Normal (Gaussian) Distribution
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C-code for calculating
Mean, Variance and Standard Deviation
Real-time calculations:
(for N measurements already available)
Sum = 0
SumSq = 0
for (int i=0; i<N; i++)
{
Sum += X[i];
SumSq += X[i]*X[i] ; // better then POW !!!!
}
Mean = Sum / N
Variance = s*s = (N*SumSq – Sum*Sum) / N
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Accuracy and Precision
Accuracy refers to the closeness of a measured value to a standard or known value.
For example, if in lab you obtain a weight measurement of 3.2 kg for a given substance,
but the actual or known weight is 10 kg,
then your measurement is not accurate.
In this case, your measurement is not close to the known value.
Precision refers to the closeness of two or more measurements to each other.
Using the example above,
if you weigh a given substance five times,
and get 3.2 kg each time,
then your measurement is very precise.
Precision is independent of accuracy.
You can be very precise but inaccurate, as described above.
You can also be accurate but imprecise.
If on average, your measurements for a given substance are close to the known value,
but the measurements are far from each other,
then you have accuracy without precision.
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Accuracy and Precision
A good analogy for understanding accuracy and precision
is to imagine
a basketball player shooting baskets.
If the player shoots with accuracy,
his aim will always take the ball close to or into the basket.
If the player shoots with precision,
his aim will always take the ball to the same location
which may or may not be close to the basket.
A good player will be both accurate and precise
by shooting the ball the same way each time
and each time making it in the basket.
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Accuracy and Precision. Example
http://gpsworld.com/gnss-systemalgorithms-methodsinnovation-accuracy-versus-precision-9889/
Accuracy is the difference between the true value and our best estimate of it.
While the definition may be clear, the practice is not. How much samples we need to collect ?
 Serious statistics
methods must be
used
 Most real-life
distributions are not
normal
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Absolute and Relative Error
For measured x
absolute error = Δx
Example : absolute error = ±1mm
relative error = absolute error / value of thing measured
relative error = Δx / x
Scientific notation
must be used
(next slide)
Example:
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Accuracy and Precision Significant Digits
Length of the bar is 3.23 cm. All digits are significant here
0
1
2
3
4
cm
What is the length of the bar in mkm ?
32300 mkm. Are all digits here significant ?
NO !!!
Correct record is: 3.23 E4 mkm (Scientific notation)
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Control Questions
• What have I learned ?
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Literature to read
1. TBD
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