Download Direct Measurement

ENTC 4350
Theories of
Measurement
Basics of Measurements

Measurement = assignment of
numerals to represent physical
properties
• Two Types of Measurements for Data
• Qualitative
• Quantitative
Qualitative Measurements

Qualitative = Non-numerical or verbally
descriptive also have 2 types
• Nominal = no order or rank eg. list
• Ordinal = allows for ranking but differences
between data is meaningless eg.
alphabetical list
Quantitative Measurements

Quantitative = Numerical Ranking also
have 2 types
• Interval = meaningless comparison eg.
calendar
• Ratio = based on fixed or natural zero
point eg. weight, pressure, Kelvin
Definition Decibels

dB = 20 log (Gain) where Gain = Voutput/
Vinput can also be in current or power
• Why bother?
• Easier math because you can add and subtract db
instead of multiplying and dividing
V1
A1
V2
A2
V3
Definition Decibels


A1 = V2/V1 A2 = V3/V2
Total Gain = A1*A2 = V2/V1 * V3/V2
Definition Decibels

Now if everything was in dB
• Total Gain = A1 (dB) + A2 (dB)
Calculation of Gain given dB

dB = 20 Log (output/ input)
• Output = input 10dB/20
Decibel example
Question
 An amplifier has 3 amplifier states and a
1 db attenuator in cascade. Assuming
all impedances are matched, what is the
overall gain if the amplifiers are 5, 10, 6
dB? Express your answer in dB and
nondB form.
Decibel example

Solution:
• Gain = 5 dB + 10 dB + 6 dB -1 dB = 20 dB
or
• 20 dB = 20 log (Gain)
• Gain = 1020/20 =10
Variation and Error



Variation  caused by small errors in
measurement process
Error  caused by limitation of machine
Data will exhibit variation where you will
see a distribution in data. You can
quantify distribution by calculating mean,
variance, and standard deviation
Variation and Error


Data will exhibit variation where you will
see a distribution in data.
You can quantify distribution by
calculating the
• mean,
• variance, and
• standard deviation
MEAN
N

Mean  X  
i 1
Xi
N
• where Xi = data point and N = Total number of points

Example data points = 2,3,3,4,3 Mean
• Xbar = (2 + 3 + 3 + 4 + 3 ) / 5 = 3
Variance
 Xi  X 
N

Variance   2

2
i 1
N
• Example Variance =[(2-3)2 + ( 3-3) 2 + (3-3)2
+ (4 – 3)2 + (3 – 3)2] /5 = 2 / 5 = 0.4
Standard Deviation
 Xi  X 
N

Standard
Deviation   
2
i 1
N
• Example Standard Deviation = (0.4)1/2
• Note with small populations use N-1 instead of N
Root Mean Square (RMS)
VRMS

1

T

V t   dt

t2
2
t1
RMS used in electrical circuits
Root Mean Square (RMS)




VRMS= RMS value in voltage
T = time interval from t1 to t2
V(t) = time varying voltage signal
With a sine wave
VRMS
VP

 0.707V p
2
Voltage Indicators
Vp
Vrms
Vpp
Vrms = Vp · .707 (Sine wave)
Frequency and Period
Period, T
f1( t )
f = 1/T
w = 2pf
RMS: Root-Mean-Square

RMS is a measure of a signal's
average power.
• Instantaneous power delivered to a
resistor is: P= [v(t)]2/R.
• To get average power, integrate and divide
by the period:
Pavg 
11

R T

to T
to

V 
v 2 (t ) dt   rm s
R

2
2
Solving
for Vrms:
1
Vrm s  
T

to T
to

v (t ) dt 

2
2
RMS: Root-Mean-Square

An AC voltage with a given RMS value
has the same heating (power) effect
as a DC voltage with that same value.
RMS: Root-Mean-Square

All the following voltage waveforms
have the same RMS value, and should
indicate 1.000 VAC on an rms meter:
1.733 v
1.414 v
Waveform
Vpeak
Vrms
1
1v
1v
Sine
1.414
1
Triangle
1.733
1
Square
1
1
DC
1
1
All = 1 WATT
Three Categories of Measurement



Direct Measurement:
Indirect Measurement:
Null Measurement:
Direct Measurement

Direct Measurement: holding a measurand
up to a calibrated standard and comparing
them eg. meter stick
Indirect Measurement

Indirect Measurement: Measuring
something other than an actual
measurement
• This is typically done when direct measurement is
difficult to obtain or is dangerous.
• Example blood pressure can be obtained using a
catheter with pressure transducer or can be
obtained using Korotkoff Sounds
• Neural activity of brain, direct measurement would
be implanting of electrodes or use of indirect
measurement of MRI
Null Measurement

Null Measurement: Compared calibrated
source to an unknown measurand and
adjust till one or other until difference is zero
• Electrical Potentiometer used in Wheatstone
Bridge
Definitions of Factors that Affect
Measurements
• Error  normal random variation not a
mistake,
• If you have a nonchanging parameter and
you measure this repeatedly, the
measurement will not always be precisely
the same but will cluster around a mean
Xo.
• The deviation around Xo = error term where
you can assume your measurement is Xo as
long is deviation is small.
Definitions of Factors that Affect
Measurements

Validity = Statement of how well
instrument actually measures what it is
supposed to measure
• Eg. you’re developing a blood pressure
sensor with a diaphragm that has a strain
gauge.
• This instrument is only valid if the deflection of
the strain gauge is correlated to blood
pressure.
Definitions of Factors that Affect
Measurements
•
Reliability and Repeatability
• Reliability  statement of a
measurement’s consistency of getting the
same values of measurand on different
trials
• Repeatibility  getting the same value
when exposed to the same stimulus
Definitions of Factors that Affect
Measurements continued

Accuracy and Precision:
• Accuracy  Freedom from error, how
close is a measurement to a standard
• Precision  exactness of successive
measurements, has small standard
deviations and variance under
repeated trials
Definitions of Factors that Affect
Measurements continued
Xi
Xo
Xi
Xo
Xi
Xo
Good Precision (Sm. Std) Good Precision (Sm. Std) Bad Precision (Large. Std)
Good Accuracy (Xi ~ Xo) Bad Accuracy (Xi << Xo Good Accuracy (Xi ~ Xo)
or Xi >> Xo)
Xi = Where the measurement is supposed to be
Xo = Mean of Data
Xi
Xo
Bad Precision (Large. Std)
Bad Accuracy (Xi << Xo
or Xi >> Xo)
Example of Precision and Accuracy
Good Precision (Sm. Std)
Good Accuracy (Xi ~ Xo)
Bad Precision (Large. Std)
Good Accuracy (Xi ~ Xo)
Good Precision (Sm. Std)
Bad Accuracy (Xi << Xo or Xi >> Xo)
Bad Precision (Large. Std)
Bad Accuracy (Xi << Xo or Xi >> Xo)
Tactics to Decrease Error on Practical
Measurements:
1. Make Measurements several Times
2. Make Measurements on Several Instruments
3. Make successive Measurements on different
parts of instruments (different parts of ruler)
Definitions of Factors that Affect
Measurements cont.

Resolution – Degree to which a
measurand can be broken into
identifiable adjacent parts ex pictures dpi
(dots per square inch)
More Resolution
Less Resolution
Definitions of Factors that Affect
Measurements cont.

Binary Resolution
• If you have 8 Bits that will represent 10 V
what is the resolution of the system?
• Resolution = 10 – 0 / 255 = 39 mV per bit
• 8 bits gives you 28 = 256 values or 256 -1 =
255 segments
3
2.5
2
1.5
1
3
2
1
Error

Measurement Error Deviation
between actual value of measurand
and indicated value produced by
instrument
• Categories of Error
• Theoretical Error:
• Static Error:
• Dynamic
• Instrument Insertion Error
Theoretical Error:

The difference between the theoretical
equation and the simplified math
equation.
Static Error:

Errors that are always present even in
unchanging system and therefore are
not a function of time or frequency.
•
•
•
•
Reading Static Error:
Environmental Static Error:
Characteristic Static Errors:
Quantization Error:
Reading Static Error:

Misreading of Digital display output
• Parallax Reading Error error when not
•
•
measuring straight on (water in measuring
cup).
Interpolation Error  Error in estimating
correct value
Last Digit Bobble Error  Digital display
variations when the LSB varies between 2
values .
Environmental Static Error:

Temperature, pressure, electromagnetic
fields, and radiation can change output
• Eg. electrical components are rated as
industrial temperature, temp = -50 to 85C.
Characteristic Static Errors:

Residual error that is not reading or
environment
• Eg. zero offset, gain error, processing error,
linearity error, hysteresis, repeatibility or
resolution, or manufacturing deficiencies.
Quantization Error:

Error due to digitization of data and is
the value between 2 levels.
Dynamic Error:

When a measurand is changing or is in
motion during measurement process
• Eg. inertia of mechanical indicating
devices during measurement of rapidly
changing parameters
• Eg. analog meters or frequency, slew rate
limitation of instrumentation
Instrument Insertion Error:

Measurement process should not
significantly alter phenomenon being
measured
• Eg. If you are measuring body temp and
performing laser surgery the laser will heat
the surrounding area and not give an accurate
body temperature
Error Contribution Analysis

Error Budget = Analysis to determine
allowable error to each individual
component to ensure overall error not
too high.
N
• Error Calculation =  

i 1
2
i
Error Contribution Analysis

Why not take just summation of the
average?
• Because noise error can be positive and
negative thus canceling and showing less
error that what truly exists.
• Also need to depict standard deviation
because need to denote spread in your
data
Operation Definitions

To keep procedure constant so that the
results are repeatable.
• Example of Standards
• ANSI—American National Standard
Institute
• ITU—International Telecommunication
Union
• AAMI—Association for the Advancement of
Medical Instrumentation
• IEEE—Institute for Electrical and Electronic
Engineers
Summary





Define and understand how to depict
system gain in dB and non dB format
Define 2 Types of Measurement
Calculate Mean, Variance and Standard
Deviation
Define 3 categories of Measurement
Explain 5 factors that Affect
Measurement
Summary





Define Accuracy and Precision
Define 4 types of Error
Describe one way to avoid Error
What is an Error Budget and how do you
calculate Error
What are Standards and why are they
important