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 V1V2 V3 A1 A2

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 10 dB/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.

Solution: Gain = 5 dB + 10 dB + 6 dB -1 dB = 20 dB or 20 dB = 20 log (Gain) Gain = 10 20/20 =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 Mean  where X i = data point and N = Total number of points Example data points = 2,3,3,4,3 Mean Xbar = ( ) / 5 = 3

Variance Variance  Example Variance =[(2-3) 2 + ( 3-3) 2 + (3-3) 2 + (4 – 3) 2 + (3 – 3) 2 ] /5 = 2 / 5 = 0.4

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

Root Mean Square (RMS) RMS used in electrical circuits

Root Mean Square (RMS) V RMS = RMS value in voltage T = time interval from t 1 to t 2 V(t) = time varying voltage signal With a sine wave

Voltage Indicators Vrms = Vp ·.707 (Sine wave) Vpp Vrms Vp

f = 1/T  = 2  f Frequency and Period Period, T f1()t

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: Solving for Vrms:

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 V AC on an rms meter: v Waveform Vpeak Vrms Sine v Triangle v DC 1 1 v Square 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 Xo Xi Xi = Where the measurement is supposed to be Xo = Mean of Data Xi Good Precision (Sm. Std) Good Accuracy (Xi ~ Xo) Good Precision (Sm. Std) Bad Accuracy (Xi << Xo or Xi >> Xo) Bad Precision (Large. Std) Good Accuracy (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) Good Precision (Sm. Std) Bad Accuracy (Xi > Xo) Bad Precision (Large. Std) Good Accuracy (Xi ~ Xo) Bad Precision (Large. Std) Bad Accuracy (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 = 255 segments

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. Error Calculation =

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