Fundamentals and Practices of Sensing Technologies

by Dr. Keiji Taniguchi, Hon. Professor of Engineering

University of Fukui, Fukui, Japan

Xi’ an University of Technology, Xi’ an, China

Dr. Masahiro Ueda, Honorary Professor, Faculty of Education and Regional Studies

 University of Fukui, Fukui, Japan

Dr. Ningfeng Zeng, an Engineer of Sysmex Corporation

(A Global Medical Instrument Corporation), Kobe, Japan

Dr. Kazuhiko Ishikawa, Assistant Professor

Faculty of Education and Regional Studies, University of Fukui, Fukui, Japan


[Editor’s Note: This paper is presented as Part V of a series from the new book “Fundamentals and Practices of Sensing Technologies”; subsequent chapters will be featured in upcoming issues of this Journal.]



Chapter 2 (Section II): Overviews of Classical Transducers


2.6 Optical Sensors Using Photo Devices

Photo-devices such as photodiodes are used as sensors for converting optical flux into circuit current.

2.6.1 Optical Sensing Devices Using Photodiodes (10)

We deal with typical photodiodes, since many types of photodiodes exists.

A. General P -N Junction Photodiodes

The p-n junction photodiodes are classified into two categories: one is the depletion layer type and another is the avalanche type.

Figure 2.26(a) shows the p-n junction of a photodiode. The light is illuminated at the vicinity of the junction in the photodiode, and the following diode current  is caused:










Text Box: Fig.2.26 Photodiode Circuits




, where  is a dark current due to the thermal carriers, in other words, electrons and holes (See comment 2.1),   is a constant,   is a luminous flux on the surface, and  is the wavelength of the light.

The output voltage  of this circuit is, then, expressed as follows (See Fig.2.26 (b)):


The dark current is the most important factor for determining the sensitivity of the sensor, i.e., minimum detectable current.

B.  P-I-N Junction Photodiodes

The p-i-n junction photodiode has higher electric field layer made of an intrinsic semiconductor i between p and n regions shown in Fig. 2.26(a).

The carriers generated in junction regions are rapidly separated by the intrinsic layer which make possible faster frequency response, because such a constitution can minimize the generation of slow carriers.

 C . Avalanche Photodiodes

An avalanche photodiode operates at higher reverse biased voltage that is little smaller than a break down voltage. In this case, carriers in the depletion layer are accelerated, and then create more and more carriers by repeated collisions. There are, then, a lot of carriers in this layer by the avalanche multiplication effect which can give rise to a current gain of approximately


2.6.2 Photo Multiplier Tubes (9)

Figure 2.27 shows a structural model of photo multipliers. These are the most sensitive light sensing devices. The operation of these devices is as follows:














Fig.2.27 Structural Model of Photo Multipliers



(1) Photoelectrons  flow through the photo cathode toward dynode  due to the light irradiation on this photo cathode.

(2) These photoelectrons, dynodeemit secondary electrons ,  toward dynode .  Such operations are repeated between dynodes  and ,


(3) The multiplied photoelectrons on the dynode  are, finally, collected on an anode. The anode current  caused by these electrons is expressed as follows:

 ,     (2.24)

Thus, this device can be used for photons counting.


Example 2.12(7), (8) Figure 2.28(a) shows the configuration of a sensor for automated hematology analyzer using a photo-diode and two photo-multipliers. In this figure, the mechanism of the generation of sheath flow is shown in Fig. 1.28.

. Figure 2.28(b) shows the relationship between side scattered intensity and side fluorescence intensity. Figure 2.28(c) shows the relationship between side scattered intensity and forward scattered intensity. Figure 2.28(d) shows the relationship between side fluorescence intensity and forward scattered intensity. Figure 2.28(e) shows the relationship between side fluorescence intensity and forward scattered intensity. As is evident from these figures, the sensing system of this automated hematology analyzer can differentiate blood cells into many categories.
























Text Box: Side Fluorescence Intensity

















Text Box: Forward Scattered Intensity



















Text Box: Forward Scattered Intensity 





















Text Box: Forward Scattered Intensity

Fig.2.28 Sensing System of Automated Hematology Analyzer and Measurement Results
















2.6.3 Image Sensors Constituted by Means of Photodiode Array (12)

Figure 2.29 shows the image sensors constituted by means of a photodiode array.

There are two types of techniques just as the methods for obtaining the output voltage: one uses charge-coupled devices (CCD), and another uses complementary metal- oxide semiconductor (CMOS) devices.



Text Box: ・・・・・・・・・Text Box: Vertical Shift Register















Text Box: Fig.2.29 Basic Construction of Area Image Sensor(12)


A. CCD Imaging Devices

Figure 2.30 shows a charge coupled device (CCD) image sensor. The charges generated

in photodiodes by photo energy projected from an image, are integrated in the image

section, and they are rapidly moved through the vertical analog shift registers in the

frame storage section as image information.

These image data are serially read out from the output  of an amplifier

through a horizontal analog shift register.

In this case, the numbers of pixels are . An optical low-pass filter fabricated

between an optical lens and the image sensor is used for rejecting an aliasing

phenomenon caused by a sampling operation for digitization.


Text Box: ・・・・Text Box: Vertical Analog Shift RegisterText Box: ・・・・Text Box: Vertical Analog Shift RegisterText Box: Vertical analog shift registerText Box: ・・・・Text Box: Vertical Analog Shift Register














Text Box: Fig.2.30 Constitution of CCD Area Image Sensor



B. CMOS Imaging Devices

Figure 2.31 shows the configuration of a pixel in photodiodes array in a CMOS imaging

device. The charges generated in photodiodes by the image information, are read out

from the output of an amplifier through the CMOS switches.


Text Box: Vertical Shift Register













Text Box: Fig.2.31  Constitution of a CMOS Area Image Sensor


Example 2.13

Show a block diagram of an image sensing system constituted by an image sensor, an A-D converter, a digital signal processor (DSP), and timing generators.


The block diagram of this system is shown in Fig.2.32.

The timing signals for synchronizing an image sensor, an A-D converter, and digital signal processor (DSP), are generated by a signal generator.














Fig.2.32 Constitution of Image Sensing System










2.7 Analog Signal Processing Circuits

2.7.1 Unbalanced Input Amplifiers

Figure 2.33 shows the typical circuits for unbalanced amplifiers, where one of signal source lines is grounded.























Text Box: Fig.2.33 Typical Circuits for Unbalanced Amplifiers




The output voltages of these amplifiers are expressed as follows:

(1)Inverting amplifier                         (2.25)

(2) Non-inverting amplifier         (2.26)      

(3) Voltage follower                                          (2.27)   


2.5.2 Typical Balanced Input Amplifier (11)

Figure.2.34 shows a typical balanced input amplifier circuit. This circuit consists of two stages: an amplification circuit and a subtraction circuit.

 (1) The output voltages of the differential amplifier are expressed as follows:

  ,           (2.28)

(2) In the subtracting circuit of 2nd stage, the output voltage  is expressed as follows:


where , and  are input voltages of the differential amplifier.

(3) From Eqs.(2.28 ) and (2.29), the output voltageof this circuit is expressed as follows:


whereand  are the input voltages of this amplifier.

This circuit has the large common- mode rejection ratio(CMRR

Differential gain/Common mode gain), and is useful for reducing the common- mode noise induced in the input signal.

The details of Fig.2.34 are described in the solution of Problem 2.2.


















Text Box: Fig.2.34 Circuit Configuration of Balanced Input Amplifier


Example 2.14Figure 2.35 shows a basic model of a differential  amplifier.

In this figure, the equivalent circuit of an input signal is described in Fig.2.35.

Find an output voltage , a differential mode gain, a common mode gain , and   a common mode rejection ratio (CMRR) which is defined as a ratio of the differential gain to the common mode gain:  in this amplifier.

SolutionIn this figure, we can get the following relations:


, ,













Text Box: Fig.2.35   Basic Model of Differential Amplifier



From the relationships described  above , the output voltage

 is expressed as follows:


Here, we define as:, ,   so the output voltage is expressed as follows:



2.7.3 Small Signal Linear Rectifier (11)

Figure.2.36 shows a small signal linear rectifier circuit.

The output voltage  of this circuit is expressed as follows:


where , .

The details of Fig.2.36 are described in the solution of Problem 2.3.

















Text Box: Fig.2.36 Small Signal Linear Rectifier Circuit







2.8 Application Examples for Measurements

2.8.1. Transducers or Sensors for Solid Mechanical Measurements1

A. Position or Displacement

As a symbol of this value, we use here “”.

(a) Position

This is the “scalar value” representing a special location of a point with respect to a reference point.

(b) Displacement

This is the “vector value” representing a change in position of a point with respect to a reference point.

( c ) Position or Displacement Transducers

(1)Strain-gage (See section 2.2 in this chapter), (2) Relactive transducer( See section 2.3 in this chapter) , (3) Capacitive transducer ( See section 2.4 in this chapter), (4) Piezoelectric transducer ( See section 2.5 in this chapter)

B. Speed or Velocity Definition

,  ( is a time).

(a) Speed: This is a scalar value.

(b) Velocity: This is a vector value.

C. Definitions for Acceleration, Vibration and Shock

(a) Linear acceleration, ( is a time).

(b) Angular acceleration , ( is an angular frequency).

(c) Mechanical vibration: Usually the vibratory acceleration is applied.

(d) Shock: This is defined as a sudden non-periodic or transient excitation.

D. Principles of Measurements for Acceleration, Vibration and Shock(1)

(A) Acceleration

A dynamical quantity like acceleration is converted into a mechanical one. That is, a force is firstly converted into a displacement and is secondary converted into a voltage signal by means of a sensor such a VLDT (variable linear differential transformer). See section 2.3 in this chapter.

Under a linear movement, a velocity and an acceleration are expressed by the following equations as the time rate of the change of displacement  and velocity, respectively.

(1) Velocity:  ,  (2) Acceleration: 

where is the time. Figure 2.37 shows the sensing device for acceleration measurement. The sensor consists of a seismic mass , a damper of damping factor , and a spring of spring-constant .

Acceleration sensor is also used for measuring the vibration and shock.















We consider here a motion of the mass when a force  is firstly applied horizontally to

 a sensor-case as shown in Fig. 2.37 (b), and then removed. The mass will be returned to

its steady state position by the spring as shown in Fig. 2.37 (a). A displacement of the

mass is converted into an electrical signal by means of a transduction element such as

a LVDT. The equation of motion of the mass is expressed as follows:


 where  ,is a unit step function( when , then , , then ). The acceleration is, then expressed as follows:


where ,,, and will be described by Eqs.(6) and (9) in comment 2.2.

(B) Vibration and Shock

(1) A vibration can generally be approximated by the sinusoidal function:


where  expresses the real part of .

(2) A shock can be approximated by a unit- step function as follows:


where is a pulse width of the shock wave.

Comment 2.2(13)

In Fig.2.33 (a), the displacement  is expressed as follows:


 where we put , and   , so this equation is rewritten as follows:



The displacement is expressed as follows:


where, and  express a transient state displacement and a steady state displacement, respectively.

2Steady State Component in Displacement     (4)

3Transient State Component in Displacement

    The transient displacement can be obtained from the following equation.


Putting ,   we obtain   ,  .

By inserting these results into Eq. (5), we can, then, get  as follows:




For the case , the transient response is obtained as follows


From Eqs.(3), (4), (6), and (7), finally, the displacement is expressed as follows:


Two constants A1 and A2 of integration in equation (8), can be determined by means of the initial conditions, such as , and  for ;

,    .

The constants  and  are, then, determined as follows:

 ,     (9)

From Eq. (8), the acceleration can be expressed as follows:


Example 2.15Find the acceleration and the displacement in the case of  shown in Eq.(6) in comment (2.2).


From Eqs. (3), (4),and, the displacement and the velocity  dx/dt are expressed as follows:



Using initial conditions of  and , for t=0 in Eqs.(11) and( 12), the constants,  and  can be obtained as follows:

,  and

   ,and     (13

The acceleration can, then be expressed as follows:


E. Force and Pressure (Force/Unit Area) Sensors

Strain gage force transducers are most widely used. The PZT force transducers are used for dynamic compression force measurements. They are described in sections 2.2 and 2.5 of this chapter.

2.8.2. Transducers or Sensors for Fluid Mechanical Measurements

A. Liquid Level Transducers or Sensors

For example, the capacitive transducers and photo sensors described in sections 2.4 and 2.6 of this chapter are used for these measurements.

B. Pressure Transducers or Sensors

For example, these devices are described in 2.8.1 E in this chapter.

C. Flow Sensors ( 4)

Figure 2.38 shows a differential pressure sensing method for fluid flow measurement. A flow rate  determined by the time rate of fluid motion and a volume-metric flow  for a circular pipe shown in this figure, are expressed as follows:



where , , andis the height (head) of fluid: .








Text Box: Fig.2.38  Example of Differential Pressure Sensing Methods.



2.8.3 Transducers for Thermal Measurements(1)

Temperature transducers or sensors are classified to two categories: one is surface transducers, and another is immersion- probe transducers. These are described in sections 2.1 and 2.2 of this chapter.

2.8.4 Transducers or Sensors for Acoustic Measurements

For example, these devices are described in chapter 3 in this book.

2.8.5 Transducers or Sensors for Optical Measurements

Photo conductive junction transducers and photo multiplier tubes are described in section 2.6 of this chapter.

2.8.6 Transducers or Sensors for Nuclear Radiation Measurements(1)

Nuclear radiations are divided broadly into two categories: one is the radiation with the emission of charged and uncharged particles such as (protons) and (electrons) particles and neutrons, and another is electromagnetic wave radiations such as x and gamma rays from the atomic nuclei.

These radiations can be measured by means of the ionized transduction elements shown in Fig. 2.39. In this figure, (a) shows a gas tube transduction element connected to an electrical conversion circuit, (b) also shows a solid crystal transduction element, and finally, ( c ) shows a semiconductor transduction element. In these transduction elements, the ionizations are occurred due to the nuclear radiation. As the results in this circuit, the current  shown in figure (a) flows, and the output voltage  is obtained as: .






























(1) D. Christiansen: Electronics Engineers’ Handbook, 4th Edition, pp.13.1-13.50   

 IEEE Press (1997)

(2) R. C. Dorf: Electrical Engineering Hand Book, p.14,p.1156, pp.1088-1091, CRC Press (1993)

(3) P. Kantrowtts, G.Kousourou, L. Zucker: Electronic Measurements, pp.294-298,

Prentice Hall (1979)

(4) P.H. Garrett: Analog system for Microprocessors and Minicomputers, pp.1-40,

Reston (1978)

(5) L. K. Baxter: Capacitive Sensors (Design and Applications), pp 40-81,

IEEE Press (1997)

(6) Mitsubishi Electric Corp. Ltd, Triple A: Acceleration sensor2005-October

(7) K.Turuda, T.Tyji, T.Usui, S.Kitajima, A.Kihara, M.Murai, Y.Kasada, Q.Li,

Y.Yamada and S.Kamihira: Evaluation and Clinical Usefulness of the Automated Hematology Analizer, Sysmex XE-2100TM, Sysmex Journal International, Vol.19, No2 (Winter1999)

(8) Overview of Automated Hematology analyzer XE-2100TM, Product Development

Division, Sysmex Corporation, pp.76-84, Sysmex Journal, Vol.22, No1 (Spring 1999)

(9) H.Ozaki, K.Taniguchi: Sensors and Signal Processing (2nd Edition), pp.17-25,

Kyoritsu Pub.Co. Ltd. (1988), (In Japanese)

(10) H.Ozaki, Y.Kanata, K.Taniguchi, M.Yokoyama: Analog Electronic Circuits

(2nd Edition), pp.110-111, Kyoritu Pub.Co. Ltd. (1992), (In Japanese)

(11) K. Taniguchi (Edition): Fundamentals of Signal Processing, pp.72-76, Kyoritsu Pub.Co. Ltd. (2001), (In Japanese)

(12) Television Institute Edition: Television Image Information Engineering

Handbook, pp.156-163, Ohm Pub. Co. Ltd.(1990),(In Japanese)

(13) H. Ozaki : Transient Phenomena of Electrical Circuits(2nd Edition),pp.18-22,

Kyoritu Pub. Co. Ltd. (1982), (In Japanese)









Problems and solutions

2.1 In a capacitive transducer shown in Figure2.40, calculate the following two values:

(1) Small change in the capacitance

(2) Ratio  in a case of , and.


(1):From Eq.(2.15),

, ,













2.2 Derive Eqs.(2.28) and(2.29).


(1)In the differential amplification circuit shown inFig.2.34,  is the voltage between point A and the ground, and  is also the voltage between point B and the ground. So, the following equations are obtained.

 ,, ,

From these equations,and  are expressed as follows:


(2) In subtraction circuit shown inFig.2.34, the following equations are obtained.


From these equations, is expressed as follows:


(3) From the results obtained above,  is expressed as follows:


2.3 Derive Eq.(2.31), where, . 


In Fig2.36,

(1) if ,  then    , ,   ,

From these equations, the output voltage is expressed as .

(2) if  ,   then ,,   ,

where , .  From these equations, the output voltage is expressed as .

From the results described above, the output voltage  that is independent to the polarity of the input voltage, is expressed as follows:

2.4 Find the gain and the cut- off frequency of the circuit shown in Fig.2.41.











Fig.2.41 Low Pass Filter Circuit



(1) Gain:

In the figure, the following equations are obtained.

 , ,  ,

,  , , 

From these equations, the output voltage  is expressed as follows:


where .

 In the case of  ,,the gain of this circuit is expressed as follows:



(2) Cut- off frequency:

From the equation , the cut- off frequency is expressed as follows:




2.5 Explain the reason that a twisted-cable is used for the connection between a sensor and an amplifier.

(1) Model for Induced Noise

We think about the circuit model for the voltage induced on the twisted-cable from a noise source shown in Fig.2.6.

(a) Induced Voltage due to Magnetic Field from Noise Source

Figure 2.42(a) shows a model for calculating a voltage induced in a coil by the

propagation of the magnetic field.The induced voltage is expressed as follows:


where  is  the magnetic flux which is linkage with the coil ,is the inner surface area of the coil,   is the permeability in the coil.

From the above equation, it is necessary to have the small surface area of coils.

Figure 2.42(b) shows a model of the cancellation of voltages induced in two coils twisted.

The two coils and are cross-connected each other. So the induced voltages are almost cancelled.






















(b) Voltage due to Electric Field Induced from Noise Source

As shown in Fig. 2.43, the output voltagein the coil, which is induced by the electric field shown in Fig. 2.44 (a), is expressed as follows:



Fig.2.43 Cancellation of Output Voltage Induced in Coil









(2) Cancellation of the voltages induced from Noise Source

From the results mentioned above, the output of the line twisted each other

can greatly decrease the noise voltage induced in the line.

The two dimensional model is shown in Fig.2.44

In this figure, Fig.2.44 (a) is a model of the twisted pair cable, and Fig. 2.44(b) is the model of the line with a sensor.









Fig.2.44  Twisted Cable for Sensor 











[Chapter 3 will be presented in the upcoming January-February 2010 issue of this Journal.]



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