Fundamentals and Practices of Sensing Technologies
Keiji Taniguchi, Hon. Professor of
Dr. Masahiro Ueda, Honorary Professor, Faculty of Education and Regional Studies
Dr. Ningfeng Zeng, an Engineer of Sysmex Corporation
(A Global Medical
Dr. Kazuhiko Ishikawa, Assistant Professor
Faculty of Education and
[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:
, 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
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:
【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.
2.6.3 Image Sensors Constituted by Means of Photodiode Array (12)
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
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.
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) 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:
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.
【Example 2.14】Figure 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.
【Solution】In this figure, we can get the following relations:
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.
2.8 Application Examples for Measurements
2.8.1. Transducers or Sensors for Solid Mechanical Measurements（1 ）
A. Position or Displacement
As a symbol of this value, we use here “”.
This is the “scalar value” representing a special location of a point with respect to a reference point.
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 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.
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.
（2）Steady State Component in Displacement： (4)
（3）Transient 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:
From Eq. (8), the acceleration can be expressed as follows:
【Example 2.15】Find 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:
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: .
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,
(5) L. K. Baxter: Capacitive Sensors (Design and Applications), pp 40-81,
IEEE Press (1997)
(6) Mitsubishi Electric Corp. Ltd, Triple A: Acceleration sensor（2005-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.
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, .
(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.
In the figure, the following equations are obtained.
, , ,
, , ,
From these equations, the output voltage is expressed as follows:
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 ① and ② 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
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.
Twisted Cable for 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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