ENTC 4350

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ENTC 4350

• Theories of Measurement

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Basics of Measurements

• Measurement assignment of numerals to represent
  physical properties
• Two Types of Measurements for Data
• Qualitative
• Quantitative

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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

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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

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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

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Definition Decibels

• A1 V2/V1 A2 V3/V2
• Total Gain A1A2 V2/V1 V3/V2

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Definition Decibels

• Now if everything was in dB
• Total Gain A1 (dB) A2 (dB)

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Calculation of Gain given dB

• dB 20 Log (output/ input)
• Output input 10dB/20

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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.

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Decibel example

• Solution
• Gain 5 dB 10 dB 6 dB -1 dB 20 dB
• or
• 20 dB 20 log (Gain)
• Gain 1020/20 10

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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

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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

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MEAN

• Mean ?
• 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

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Variance

• Variance ?
• Example Variance (2-3)2 ( 3-3) 2 (3-3)2
  (4 3)2 (3 3)2 /5 2 / 5 0.4

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Standard Deviation

• Standard Deviation ?
• Example Standard Deviation (0.4)1/2
• Note with small populations use N-1 instead of N

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Root Mean Square (RMS)

• RMS used in electrical circuits

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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

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Voltage Indicators
Vp
Vrms
Vpp
Vrms Vp .707 (Sine wave)
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Frequency and Period
Period, T
f1
(
)
t
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RMS Root-Mean-Square

• RMS is a measure of a signal's average power.
• Instantaneous power delivered to aresistor is
  P v(t)2/R.
• To get average power, integrate and divide by the
  period

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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.

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RMS Root-Mean-Square

• All the following voltage waveforms have the same
  RMS value, and should indicate 1.000 VAC on an
  rms meter

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Three Categories of Measurement

• Direct Measurement
• Indirect Measurement
• Null Measurement

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Direct Measurement

• Direct Measurement holding a measurand up to a
  calibrated standard and comparing them eg. meter
  stick

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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

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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

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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.

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Definitions of Factors that Affect Measurements

• Validity Statement of how well instrument
  actually measures what it is supposed to measure
• Eg. youre 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.

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Definitions of Factors that Affect Measurements

• Reliability and Repeatability
• Reliability ? statement of a measurements
  consistency of getting the same values of
  measurand on different trials
• Repeatibility ? getting the same value when
  exposed to the same stimulus

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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

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Definitions of Factors that Affect Measurements
continued
Good Precision (Sm. Std) Good Accuracy (Xi Xo)
Good Precision (Sm. Std) Bad Accuracy (Xi ltlt Xo
or Xi gtgt Xo)
Bad Precision (Large. Std) Good Accuracy (Xi
Xo)
Bad Precision (Large. Std) Bad Accuracy (Xi ltlt
Xo or Xi gtgt Xo)
Xi Where the measurement is supposed to be Xo
Mean of Data
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Example of Precision and Accuracy
Good Precision (Sm. Std) Bad Accuracy (Xi ltlt Xo
or Xi gtgt Xo)
Good Precision (Sm. Std) Good Accuracy (Xi Xo)
Bad Precision (Large. Std) Bad Accuracy (Xi ltlt
Xo or Xi gtgt Xo)
Bad Precision (Large. Std) Good Accuracy (Xi
Xo)
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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)

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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)

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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

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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

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Theoretical Error

• The difference between the theoretical equation
  and the simplified math equation.

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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

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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 .

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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.

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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.

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Quantization Error

• Error due to digitization of data and is the
  value between 2 levels.

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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

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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

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Error Contribution Analysis

• Error Budget Analysis to determine allowable
  error to each individual component to ensure
  overall error not too high.
• Error Calculation

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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

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Operation Definitions

• To keep procedure constant so that the results
  are repeatable.
• Example of Standards
• ANSIAmerican National Standard Institute
• ITUInternational Telecommunication Union
• AAMIAssociation for the Advancement of
  Medical Instrumentation
• IEEEInstitute for Electrical and Electronic
  Engineers

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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

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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