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 VII 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 3 (Section II):

Some Practical Examples of Recent Ceramic Sensors


3.5   Acoustic Transducers

3.5.1   Structure of Acoustic Transducer (1)-(4)

Fig. 3.16 shows the structure of an acoustic transducer using piezoelectric ceramic element. This transducer can radiate acoustic wave in a medium of space by means of the electrical signal. Therefore, the piezoelectric ceramic transducer is used as a radiator of the acoustic wave. This transducer can, also convert some of acoustic wave propagated in a medium of space into the electrical signal. Therefore, the piezoelectric ceramic transducer is used as the acoustic sensor.

The backside of this element is filled with an acoustic absorbing material to absorb acoustic energy propagated to the backside.




















A capacitive deviation of the piezoelectric ceramic element due to temperature changes can be compensated by means of the capacitor implemented in a metal case shown in this figure.


3.5.2   Equivalent Circuit for Acoustic Transducer (5)

Figure 3.17 shows the equivalent circuits for the piezoelectric ceramic element and a parallel resonant circuit for a receiver using this transducer.
























Figures 3.17 (a) and (b) are the piezoelectric ceramic element and its equivalent circuit, respectively.

Figure 3.17 (c) is a simplified equivalent circuit in the frequency range of  for the circuit shown in Fig. (b), where .

 Figure 3.17 (d) is a parallel equivalent circuit of Fig. (c),

where  ,  .

Figure 3.17  (e) is a parallel resonant circuit of a receiver used for suppressing reverberations.

The resonance angular frequency of the parallel resonant circuit is, then expressed as follows:


where  is an inductance of the receiving circuit.

The overall characteristic for two parallel capacitors,

(: Temperature) in the parallel resonant circuit is almost independent for the change of temperature.

3.5.3.  Principle of Distance Measurement (1)-(4)

Figure 3.18 shows a block diagram for transmitting and receiving circuits using the transducer. This system consists of two sets of these circuits.

Firstly a timing generator is triggered by a start signal from the CPU, and

 a rectangular pulse is generated. This pulse is amplified by a transmitting signal amplifier and is then sent to an acoustic transducer which transforms from the electric power to the acoustic power.

Secondary, this acoustic signal is radiated into a medium of space, and reflected and scattered waves from the medium are propagated toward the transducer of the original position as echo signals.

Finally, the received signal on the transducer is amplified and reformed into the pulse waveform.




















Figure 3.19 shows a transmitted signal and a received (echo) signal. The round-trip time of the transmitting signal is measured as a number of clock pulses, and the distance between an object and the transducer, is calculated by the following formula:




where  is the propagation velocity of the transmitted signal, is  the clock pulse repetition period,  is a number of clock pulses included in .

These details are described in section1.3 in chapter 1.



















3.5.4 Important Characteristics for Automobile Sensing Systems (1)-(4)

Important characteristics as a back acoustic sensor used for automobile sensing systems are as follows:

(1) The acoustic signal from the back wall must be detected, and that from the stopper must not detected as shown in Fig. 3.20(a).

(2) The horizontal directivity must have a wide radiation pattern, and the vertical directivity must have a sharp radiation pattern

as shown in Figs.3.20 (a) and (b).

Text Box:















Fig.3. 20 Radiation patterns of an acoustic sensing system

(Courtesy of Murata Manufacturing Co., Ltd.)





3.5.5   Application Examples of  Transducers  (1)-(4)

Figure3.21 shows an example of four back acoustic sensors used for an automobile.

A large number of sensing systems can precisely measure the position of objects.








Fig.3. 21 Implementations of the acoustic sensors

(Courtesy of Murata Manufacturing Co., Ltd.)


















3.6   Piezoelectric Vibrating Gyro Sensor(1)-(4)

3.6.1   Outlines of Sensor

A gyro sensor is used for measuring an angular velocity of an object. This sensor converts the angular velocity into an electrical signal.

3.6.2   Vibrating Gyro Sensor Elements

As shown in Fig. 3.21(a), a square bar vibrates caused by a vibrating PZT along the direction of  axis, and its vibrating pattern, i.e., vibration mode, is shown in Fig. 3.21(b)-. In a sense mode shown in Fig.3.21(b)-, when the vibrating gyro sensor rotates to the clockwise direction as shown in Fig.321(c), a sensing PZT fixed to perpendicular for axis of the square bar shown in Fig. 3.21(a) has an output voltage.

The voltage which is caused by the Corioli’s force, is proportional to the angular velocity . The force acts on the cross section of the square bars as illustrated in Fig.3.21 ( c ) .  The gyro sensor converts the angular velocity into the output voltage.

Wires for supporting square bar are positioned to the nodes of vibration of square bars as shown in Fig. 3.21 (b). The relationships among the angular velocity , the vibrating velocity , and the Corioli’s forceis expressed as follows:


where is the mass of the square bar.









Text Box:





















(c)Relationships  among vibration, rotation, and  Corioli’s force



Fig. 3.22 Structure of a gyro sensor

(Courtesy of Murata Manufacturing Co., Ltd.)




3.6.3   Relationships between Input and Output Characteristics of Sensor

The output of PZT is linearly proportional to Corioli’s force, and is then given by the following equation from equation (3.2),

.     (3.3)

 where  is the proportional constant, and .

Figure 3.23 shows an experimental result between the angular velocity  applied, and the output voltage of the gyro-sensor. As shown in this figure, there is the offset voltage, and then the relationship between  and  is expressed as follows:



















3.6.4   Signal Processing Circuit for Sensor

Figure 3.24 shows a signal processing circuit for the gyro sensor. The output voltage from the gyro sensor is amplified to AVout by means of an AC- coupled operational amplifier with the amplification factor A (In this case A=10) which gives the final output = AVout, as shown in this figure.


















3.6.5   Application Examples of Gyro Sensor

We show here two application examples of the gyro sensor.

(1) Figure 3.25(a) shows the gyro sensor used for a correction of azimuth in a global positioning system (GPS) implemented for the automobile navigation.

(2) Figure 3.25(b) shows the two gyro sensors used for two- dimensional corrections of the center of an image obtained from a video camera supported by unstable human hands.


Text Box:








Fig. 3.25 Application examples of the gyro sensor

(Courtesy of Murata Manufacturing Co., Ltd.)








(1)Akira Murata : Wonderful stones, Nikkei Inc. (1994)

(2) Wonderful Ceramics (New materials and new technologies in 20th Century),

Supervised  by Yutaka Takagi, Teturo Tanaka,  Edited by Murata Manufacturing Co. Ltd,  MARUZEN Co. Ltd(1990)

(3) Satoru Fujishima: Piezo-ceramics, Shokabo Publishing Co. Ltd (1993)

(4) Technical data for sensing devices (2007), Presented by Murata Manufacturing Co. Ltd.

(5) Metamorphosis,pp.8-9,No112005.12, Edited by Murata Manufacturing

 Co. Ltd.



Problems and solutions


3.1 Find the output voltage  in the circuit shown in Fig.3.17.


SolutionLet’s show again the circuit in Fig. 3.17.














In Fig.3.26, ,  ,  ,  ,  

. >From these equations, we obtain the following result:


In this equation,

(1) If , then . 

(2) The frequency satisfying a condition of  is , and then the output voltage is .


3.2 Find the output voltage , and a cut off frequency in low frequency ranges in the circuit shown in Fig.3.27.





















The following equations can be obtained in the circuit shown in Fig.3.27.

,    ,

(1) An output voltage is then expressed as: .

(2) The frequency satisfying a condition of  is as follows:


3.3 Show a circuit diagram for measuring ranges (round- trip times).



We show a circuit configuration and a truth table of a R-S flip flop used in the circuit in Figs. 3.28 (a) and (b). We also show the operating waveforms of the R-S flip flop, an and- circuit, and a clock pulse generator in Fig.3.28(c).









































3.4 Find the output voltage  in the circuit with a FET shown in Fig.3.20.


This circuit is well known as a source follower or a common drain circuit.




































The following equations are obtained from the equivalent circuit in figure 3.20 (b).


The output voltage is approximated as follows from these equations:


where  expresses an amplification factor,  a drain resistance,  a drain current,  a voltage between the gate and the source, and   a load resistance.

3.5 In the circuit shown in Fig.3.21,

(1) Find an output voltage , when   is given as an input voltage. Where  is an off set voltage.

(2) Find  when the output voltage  is offset free.















(1) We obtain the following equations using Fig.3.21.


,  ,   


The output voltage is, then, obtained as follows:



(2) Inserting  into Eq. (1), the output voltage  is expressed

 as follows:




The required condition is as follows, for which the output voltage  is offset free:



,     (3)


[Chapter 4 will be presented in the upcoming May-June 2010 issue of this Journal.]


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