measurement characteristics

Measurement CharacteristicsMeelis Sildoja

Measurement Characteristics - Meelis Sildoja, MRI

IntroductionMeasurement is the experimental process of acquiring any quantitative information. When doing a measurement, we compare the measurable quantity measurand - with another same type of quantity. This other quantity is called measurement unit

Measurand a physical quantity, property, or condition which is measured


MeasurementsCan be divided into direct or indirect measurementsDirect measurement measured quantity is registered directly from the instruments display.Measuring voltage vith voltmeter Measuring length with rulerIndirect measurement result is calculated (using formula) from the values obtained from direct measurementsFinding work done by current: U voltmeterI ammetert clockA=U*I*t


Classification of physical quantitesCan be divided for quantities which valueis determined uniquely and does not depend on the zero level masscan only be determined as a reference to some fixed zero levelpotential energy (zero level can be ground floor or 3d floor and result depends on that)Timebut time interval and change in potential energy belong to the upper class


Measurements main equationThe value of the measured quantity can be expressed as

where [Y] is the measurement unit and y is the number, which shows how many times the measurable quantity differs from the unit


What is instrumentInstrument is a device that transforms a physical variable of interest (the measurand ) into a form that is suitable for recording (the measurement)An example is ruler the measurand is the length of some objectthe measurement is the number of units (meters, inches, etc.) that represent the lengthIn order for the measurement to have consistent meaning, it is necessary to employ a standard system of units


Simple Instrument Model The key functional element of the instrument model is the sensor, which has the function of converting the physical variable input into a signal variable output Due to the property that signal variables can be manipulated in a transmission system, such as an electrical or mechanical circuit, they can be transmitted to a remote output or recording deviceIn electrical circuits, voltage is a common signal variable


Simple Instrument Model


Simple Instrument ModelIf the signal from Sensor output is small, it is needed to be amplified. In many cases it is also necessary for the instrument to provide a digital signal output for connection with a computer-based data acquisition systems.


SensorsSensor - the part of a measurement system that responds directly to the physical variable being measuredSensors can be categorized into two broad classes Passive sensorsActive sensors


Passive SensorsPassive sensors do not add energy as part of the measurement process, but may remove energy in their operation, ie energy is converted to measurable quantity One example of a passive sensor is a thermocouple, which converts a physical temperature into a voltage signal


Active SensorsActive sensors add energy to the measurement environment as part of the measurement processAn example of an active sensor is a radar or sonar, where actively out-sended radio (radar) or acoustic (sonar) waves reflect off of some object and thus measures its range from the sensorArecibo Observatory in Puerto RicoBesides being most powerful radio telescopes and the largest single unit telescope in the world, it is also a radar probably the world biggest active sensor though


Sensor Fusion (uniting of sensors)Sensor fusion - in this case, two or more sensors are used to observe the environment and their output signals are combined in some manner (typically in a processor) to provide a single enhanced measurement Examples:Sensor output relation to the ambient temp is taken account during the measurementsImage synthesis where radar, optical, and infrared images can be combined into a single enhanced image


Operational Modes of Instrumentation I(Null instrument)Null Instrument - A measuring device that balances the measurand against a known value, thus achieving a null condition. Two inputs are essential to the null instrument.Null measurement devices usually consist of 1. automatic or manual feedback system that allows the comparison of known standard value,2. an iterative balancing operation using some type of comparator3. and a null deflection at parity


Null instrumentAdvantages:Minimizes measurement loading errors (i.e. alter the value of the measured signal). Effective when the measurand is a very small value.minimizes interaction between the measuring system and the measurand, by balancing the unknown input against a known standard inputAchieving perfect parity (zero condition) is limited only by the state of the art of the circuit or scheme being employedDisatvantages:Slow - an iterative balancing operation requires more time to execute than simply measuring sensor input. Not suitable for fast measurements i.e. only for static measurements


Null instrument - exampleAn equal arm balance scale with manual balance feedbackPotetntiometerAB is the potentiometer wire with resistance R1. The EMF of a standard DC source is e volts. The rheostat resistance is R . If the null pointis obtained at point C, then the EMF of e and e1 are equal


Operational Modes of Instrumentation II(Deflection instrument)Deflection instrument - a measuring device whose output deflects (deviates) proportional to the magnitude of the measurandDeflection instruments are the most common measuring instrumentsAdvantages:high dynamic response i.e. can be used for fast measurementscan be designed for either static or dynamic measurements or bothDisadvantages:by deriving its energy from the measurand, the act of measurement will influence the measurand and change the value of the variable being measured. This change is called a loading error.


Deflection isnstrument - exampleSpring scale as a deflection instrument. Scale has to be calibrated.


Flow chart of a deflection instrument Examples of signal conditioning are to multiply the deflection signal by some scaler magnitude, such as in amplification or filtering, or to transform the signal by some arithmetic functionThe logic flow chart for a deflection instrument is straightforward (e.g.multiplication of deflection signal due to amplification )


Analog and Digital SensorsAnalog sensors - provide a signal that is continuous in both its magnitude and its temporal (time) or spatial (space) contentDigital sensors - provide a signal that is a direct digital representation of the measurand. Digital sensors are basically binary (on or off ) devices. Essentially, a digital signal exists at only discrete values of time (or space)


Analog sensorThe defining word for analog is continuous i.e. if a sensor provides a continuous output signal that is directly proportional to the input signal, then it is analog

Thermocouple as an analog sensor


Digital sensorA common representation of digital signal is the discrete sampled signal, which represents a sensor output in a form that is discrete both in time or space and in magnitude.A rotating shaft with a revolution counter. Each revolution generates a spike.In this example, the continuous rotation of the shaft is analog but the revolution count is digital. The amplitude of the voltage spike is set to activate the counter and isnot related to the shaft rotational speed. Data can be sent either in serial or parallel format


Analog Readout InstrumentsAn analog readout instrument provides an output indication that is continuous and directly analogous to the behavior of the measurandFor example deflection of a pointer or an ink trace on a graduated scalethe intensity of a light beam or a sound wave


Digital Readout InstrumentsA digital readout instrument provides an output indication that is discreteMany digital devices combine features of an analog sensor with a digital readout or, in general, convert an analog signal to a discrete signal. In such situations, an analog to digital converter (ADC) is required. HP3458A digital multimeter, most widely used device in MRI


Input ImpedanceIn the ideal case, the act of measurement should not alter the value of the measured signal. Any such alteration is a loading errorLoading errors can be minimized by impedance matching of the source with the measuring instrument reduce the power needed for measurementThe power loss through the measuring instrument where Z(W) is the input impedance of the measuring instrument, and E(V) is the source voltage potential being measured To minimize the power loss, the input impedance should be large


Input impedance - connecting instruments The potential actually sensed by device 2 will be

The difference between the actual potential E1 and the measured potential E2 is a loading error. High input impedance Z2 relative to Z1 minimizes this error. A general rule is for the input impedance to be at least 100 times the source impedance to reduce the loading error to 1%.An equivalent circuit is formed by applying a measuring instrument (device 2) to the output terminals of an instrument (device 1).


CalibrationCalibration is the relationship between the physical measurement variable (input) and the signal variable (output) for a specific sensorCalibration curve graph that characterizes sensor or instrument response to a physical inputSensitivity of the device is determined by the slope of the calibration curve.Dynamic range - the difference between the smallest and largest physical inputs that can reliably be measured by an instrument Saturation - increasing the physical input value to the level where there is no change in output signalCalibration curve example.


Error types and sourcesSystematic errors (bias) measured values have similar deviation from correct valueRandom errors (noise) measured values deviate randomly around mean value. Noise describes the precison of measurements


Correct termsMeasurement is described by its discrimination , its precision , and its accuracyThese are too often used interchangeably, but they cover different concepts:Discrimination - the smallest increment that can be discerned. Term resolution is used as a synonym, but according to the book", it is now officially decleared as incorrect!Precision - the spread of values obtained during the measurements. Two terms that should be used here are:repeatability - variation for a set of measurements made in a very short periodreproducibility same concept, but for measurements made over a long periodAccuracy - is the closeness of a measurement to the value defined to be the true value


Discrimination, precision and accuracyTwo sets of arrow shots fired into a target to understand the measurement concepts of discrimination, precision, and accuracy


Systematic error sources If measurements are made at temperature other than the sensor was calibrated it introduces systematic error. If systematic error source is known, it can be corrected for by the use of compensation methodsAging of the components will change the sensor response and hence the calibrationDamage or abuse of the sensor can also change the calibration

Invasiveness - the measurement process itself changes the intended measurand. This is key concern in many measurement problems. Reading measurements by human observer common error source is parallax i.e. reading dial from non-normal angleNB! Interaction between measurand and measurement device is always present


Invasivness - exampleReducing invasivness to use high impedance electronic devices to measure voltage Extreme invasivenesslarge warm thermometer to measure the temperature of a small volume of cold fluid


Periodical calibrationIn order to prevent systematic errors, sensors should be periodically recalibrated


Random error sourcesAn example for N1 would be background noise received by a microphoneAn example of N2 would be thermal noise within a sensitive transducer, such as an infrared sensorA common example of N3 is 50 Hz interference from the electric power gridThe noise will be amplified along with the signal as it passes through the amplifierNoise is presented as signal to noise ratio (SNR). SNR(dB)=10*log(Psignal/Pnoise)


Random noiseWhat if Psignal < Pnoise ?If some identifying characteristics of that signal are known and sufficient signal processing power is available, then the signal can be interpreted.Example of such signal processing is the human ability to hear a voice in a loud noise environment


Estimating the measurement accuracyError is defined as the difference between the measured value and the true value of the measurand E =(measured) - (true)whereE = the measurement error(measured) = the value obtained by a measurement(true) = the true value of the measurandError can almost not be ever known, becuse we dont know the (true) value, error can only be estimated.


What is uncertainty?

Uncertainty of measurement is a parameter that describes the distribution of the (thinkable) measured valuesThe word uncertainty expresses the boubt to the exactness of the result of the measurement Measurement result is the measurement value with its uncertainty


Classification of uncertaintiesStandard uncertainty uncertainty of a measurement expressed as a standard deviation Standard uncertainty consists of many components which are divided into two categoriestype A uncertainty which is estimated using statistical methodsuA(x), where x denotes the measured value for which the uncertainty is giventype B uncertainty which is estimated using means other than statistical analysisuB(x)Combined standard uncertainty - Expanded uncertainty Where k is the coverage factor, typically in range 2-3


How to estimate uncertainties?Type A when taking multiple values the distribution of these values corresponds to normal or Gaussian distribution

Where the sx describes the broadness of the curve and its square is called variances = standard deviations2 = variance


How to estimate uncertainties II?Standard deviation

Where xt is the true valueSince we dont know the true value, we use

Where is the mean value and sx experimental standard deviationand


How to estimate uncertainties III?If you take e.g. 100 measurements and divide them to 10 series each consisting 10 values and then calculate the mean to each series, you can show that the Stdev of the mean of the series is related to the Stdev of one series as follows

Number n under the square-root, is the number of measurements in one series


In order for the measurement to have consistent meaning, it is necessary to employ a standard system of units by which the measurementfrom one instrument can be compared with the measurement of another.Signal variables have the property that they can be manipulated in a transmission system, such as an electrical or mechanical circuit. Due to this property, the signal variable can be transmitted to a remote output or recording device.In electrical circuits, voltage is a common signal variable.Dispalcement -> movement of some mechanical part, e.g. spring in NewtonmeterLight the change of intensity of lightPressure - ??If the signal from Sensor output is small, it is needed to be amplified. In many cases it is also necessary for the instrument to provide a digital signal output for connection with a computer-based data acquisition systems.Sensors can be categorized into two broad classes depending on how they interact with the environment they are measuring.Active sensors - add energy to the measurement environment as part of the measurement process. An example of an active sensor is a radar or sonar system, where the distance to some object is measured by actively sending out a radio (radar) or acoustic (sonar) wave to reflect off of some object and measureits range from the sensor.

Null measurement devices usually consist of automatic or manual feedback system that allows the comparison of known standard value, (tagasiside)an iterative balancing operation using some type of comparator (iteratiivne tasakaalustamine)and a null deflection at parity (null-hlve vrdsuse juures.)AB is the potentiometer with resistance R. The EMF of a standard DC source is e volts. The rheostat resistance is R . If the null point (Galvanometer is showing zero) is obtained at point J, then the EMF of e and e1 are equal.The name is derived from a common form of instrument where there is a physical deflection of a prime element that is linked to an output scale, such as a pointer or other type of readout, which deflects to indicate the measured value.

Advantages:high dynamic response that can be achieved for dynamic measurements i.e. can be used for fast measurementscan be designed for either static or dynamic measurements or both

The measured value is estimated on how much the spring is pressed togetherStress the signal conditioningThe deflection signal is transmitted to signal conditioners that act to condition the signal into a desired form. Examples of signal conditioning are to multiply the deflection signal by some scaler magnitude, such as in amplification or filtering, or to transform the signal by some arithmetic function.

If a sensor provides a continuous output signal that is directly proportional to the input signal, then it is analog.2 Loading errors can occur at any junction along the signal chain but can be minimized by impedance matching of the source with the measuring instrumentTypically, a sensor (or an entire instrument system) is calibrated by providing a known physical input to the system and recording the output. Figure. In this example, the sensor has a linear response for values of the physical input less than X0.

In some cases, the sensor will not respond to very small values of the physical input variable. Neither can it not be used in high values (saturation). The more spreaded are the measurement results the less precise is the meausrementThe word precision is not a word describing a quality of the measurement and is incorrectly used as such.Systematic error sources For example, if temperature is modifying an input, using the sensor at a temperature other than the calibrated temperature will result in a systematic error. In many cases, if the systematic error source is known, it can be corrected for by the use of compensation methods.There are other factors that can also cause a change in sensor calibration resulting in systematic errors. In some sensors, aging of the components will change the sensor response and hence the calibration. Damage or abuse of the sensor can also change the calibration. In order to prevent these systematic errors, sensors should be periodically recalibrated.Systematic errors can also be introduced if the measurement process itself changes the intended measurand. This issue, defined as invasiveness, is a key concern in many measurement problems.

There are other factors that can also cause a change in sensor calibration resulting in systematic errors. In some sensors, aging of the components will change the sensor response and hence the calibration. Damage or abuse of the sensor can also change the calibration. In order to prevent these systematic errors, sensors should be periodically recalibrated.

Finally, systematic errors or bias can be introduced by human observers when reading the measurement. A common example of observer bias error isparallax error. This is the error that results when an observer reads a dial from a non-normal angle.

Systematic errors can also be introduced if the measurement process itself changes the intended measurand. This issue, defined as invasiveness, is a key concern in many measurement problems.An extreme example of invasiveness would be to use a large warm thermometer to measure the temperature of a small volume of cold fluid An example for N1 would be background noise received by a microphone.An example of N2 would be thermal noise within a sensitive transducer, such as an infrared sensor (cooling is used to minimize thermal noise).A common example of N3 is 50 Hz interference from the electric power grid that is introduced if the transmission path is not well grounded, or if an inadvertent (careless) electric grand loop causes the wiring to act as an antenna.

The noise will be amplified along with the signal as it passes through the amplifier in Figure 1.8. Though noise is not the in level of the combined noise sources, but it is presented as signal to noise ratio (SNR). It is defined as the ratio of the signal power to the power in the combined noise sources. Usually expressed in dB units.

measurement characteristics

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