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Chapter 1 

Introduction to sensor-basedmeasurement systems

Võ Nhật Quang

HCMC University of Technology

DEPT. OF BIOMEDICAL ENGINEERING

Chapter 1 2

Objectives

To provide an overview of the course

To answer the question “What is a sensor?” 

To discuss the classification of sensors andsensor terminology

To introduce some typical sensors

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1.1 GENERAL CONCEPTS ANDTERMINOLOGY 

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1.1.1 Measurement system

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 A system is a combination of two or moreelements, subsystems, and partsnecessary to carry out one or morefunction.

One objective of a measurement can beprocess monitoring:

 Ambient temperature measurement

Gas and water volume measurement Clinical monitoring

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 Another objective could be to assistexperimental engineering:

Study temperature distribution inside anirregularly shaped object

Determine force distribution on adummy driver in a car crash

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1.1.2 Tranducers, Sensors, and Actuators

 A transducer is a device that converts asignal from one physical form to acorresponding signal having a differentphysical form.

It is an energy converter.

Six different kinds of signals: mechanical,thermal, magnetic, electric, chemical, andradiation

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Devices offering an electric output arecalled sensors.

Most measurement systems use electricsignals, and hence rely on sensors

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1.1.3 Signal conditioning and display

Signal conditioners are measuring systemelements that start with an electric sensoroutput signal and then yield a signal suitable fortransmission, display, or recording, or thatbetter meet the requirement of a subsequentstandard equipment or device.

Perform any: amplification, level shifting,filtering, impedance matching, modulation, anddemodulation.

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1.2 SENSOR CLASSIFICATION

In considering the need for a power supply: Modulating (active)

Self-generating (passive)

In considering output signal:  Analog

Digital

In considering the operating mode: Deflection

Null

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1.3 GENERAL INPUT – OUTPUTCONFIGURATION

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1.3.1 Interfering and modifying inputs:

In a measurement system the sensor is

chosen to gather information about themeasured quantity and to convert it to anelectric signal.

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Negative feedback is a common method toreduce the effect of modifying inputs, andit is the method used in null measurementsystems.

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G(s).H(s) >>1

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1.4 STATIC CHARACTERISTICS OFMEASUREMENT SYSTEMS Accuracy

Precision

Sensitivity

 Absolute error

Relative error

Linearity Resolution

Hysteresis

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 Accuracy is the quality that characterizesthe capacity of a measuring instrument forgiving results close to the true value of the

measured quantity.

1.4.1 Accuracy, Precision, and Sensitivity

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 Absolute error:

The difference between measurementresult and the true value

 Absolute error = Result – True value

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Relative error:

 A quotient between the absolute error and

the true value for the measured quantity

Relative error = Absolute error/ True value

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Precision is the quality that characterizesthe capability of a measuring instrumentof giving the same reading whenrepetitively measuring the same quantityunder the same prescribed conditions(environmental, operator, etc.), withoutregard for the coincidence or discrepancybetween the result and the true value

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The repeatability is the closeness ofagreement between successive resultsobtained with the same method under thesame conditions and in a short timeinterval

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The reproducibility is also related to thedegree of coincidence between successivereadings when the same quantity ismeasured with a given method, but in this

case with a long-term set ofmeasurements or with measurementscarried out by different people orperformed with different instruments or indifferent laboratories.

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The zero drift describes output variationswhen the input is zero.

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The sensitivity or scale factor is the slopeof the calibration, whether it is constant ornot along the measurement range.

For a sensor in which output y is relatedto the input x by the equation y = f(x),the sensitivity S(xa) at point xa, is

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1.4.2 Linearity and Resolution

The linearity describes the closenessbetween the calibration curve and aspecified straight line. Depending onwhich straight line is considered, severaldefinitions apply.

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Independent linearity: The straight line isdefined by the least squares criterion.With this sytem the maximal positive errorand the minimal negative error are equal.This is the method that usually gives the

 “best” quality.

Zero-Based Linearity: The straight line isalso defined by the least squares criterionbut with the additional restriction ofpassing through zero.

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Terminal-Based Linearity: The straight lineis defined by the output corresponding tothe lower input and the theoretical outputwhen the higher input is applied.

End-Points Linearity: The straight line isdefined by the real output when the input

is the minimum of the measurement rangeand the output when the input is themaximum.

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Theoretical Linearity: The straight line isdefined by the theoretical predictions

when designing the sensor.

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The main factors that influence linearityare resolution, threshold, and hysteresis.

The resolution (or discrimination) is the

minimal change of the input necessary toproduce a detectable change at theoutput.

When the input increment is from zero,then it is called the threshold.

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The hysteresis refers to the differencebetween two output values thatcorrespond to the same input, dependingon the direction (increasing or decreasing)of successive input values.

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1.4.3 Systematic errors

 An error is said to be systematic when inthe course of measuring the same value ofa given quantity under the sameconditions, it remains constant in absolutevalue and sign or varies according to a

definite law when measurement conditionschange

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Such errors are caused not only by theinstrument, but also by the method, theuser (in some cases), and a series offactors (climatic, mechanical, electrical,

etc.) that never are ideal – that is,constant and known.

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1.4.4 Random errors

Random errors are those that remain aftereliminating the causes of systematic

errors. They appear when the same valueof the same quantity is measuredrepeatedly, using the same instrumentand the same method.

Random errors are also called accidental(or fortuitous) errors

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1.5 DYNAMIC CHARACTERISTICS

The dynamic error is the differencebetween the indicated value and the truevalue for the measured quantity, when thestatic error is zero.

The speed of response indicates how fastthe measurement system reacts tochanges in the input variable.

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1.5.1 Zero-Order measurement systems

The output of a zero-order sensor isrelated to its input through an equation of

the type:y(t) = k.x(t)

k: static sensitivity

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1.5.2 First-Order Measurement Systems

In a first-order sensor there is an elementthat stores energy and another one thatdissipates it.

The relationship between the input x(t)and the output y(t) is described by adifferential equation with the form:

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The corresponding transfer function is

k = 1/a0: static sensitivity

τ= a1 /a0: time constantωc = 1/τ: corner (angular) frequency

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1.5.3 Second-Order Measurement Systems

 A second-order sensor contains twoenergy-storing elements and one energy-dissipating element. Its input x(t) and

output y(t) are related by a second-orderlinear differential equation of the form:

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The corresponding transfer function is

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Tài liệu tham khảo

Ramon Pallas Areny and John G. Webster,Sensors and signal conditioning, John

Wiley & Son Inc, 2001

Dr. Paul W Nutter, Sensors and sensing

 principles – Lecture 1, University ofManchester, 2008