Research ArticleCircuit Design of Surface Acoustic Wave Based MicroForce Sensor

Yuanyuan Li12 Wenke Lu1 Changchun Zhu3 Qinghong Liu4

Haoxin Zhang4 and Chenchao Tang2

1 College of Information Science and Technology Donghua University Shanghai 201620 China2 College of Electronic and Electrical Engineering Shanghai University of Engineering Science Shanghai 201620 China3 College of Electronics and Information Engineering Xirsquoan Jiaotong University Xirsquoan 710049 China4Xirsquoan Leitong Science amp Technology Co Ltd Xirsquoan 710049 China

Correspondence should be addressed to Wenke Lu luwenke3163com

Received 10 February 2014 Revised 7 April 2014 Accepted 7 April 2014 Published 29 April 2014

Academic Editor Weichao Sun

Copyright copy 2014 Yuanyuan Li et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Pressure sensors are commonly used in industrial production and mechanical system However resistance strain piezoresistivesensor and ceramic capacitive pressure sensors possess limitations especially inmicro force measurement A surface acoustic wave(SAW) based micro force sensor is designed in this paper which is based on the theories of wavelet transform SAW detection andpierce oscillator circuits Using lithium niobate as the basal material a mathematical model is established to analyze the frequencyand a peripheral circuit is designed to measure the micro forceThe SAW based micro force sensor is tested to show the reasonabledesign of detection circuit and the stability of frequency and amplitude

1 Introduction

Wavelet transform finds its application in many disciplinesand fields such as in image processing water-sound earth-quake detection biomedicine mechanical vibration pro-nunciation recognition communication chemical industryand torrent analysis [1] SAW devices are early examplesof microelectromechanical systems (MEMS) because of thecoupling needed between the electrical and mechanicalproperties as discussed by Ballantine et al [2]Themethod ofimplementing wavelet transform with SAW devices has beenfirst proposed by Peng et al [3ndash5] The wavelet transformdevice of SAWcan benefit from the excellent properties of theSAW devices namely passive small size low cost excellenttemperature stability high reliability and high reproducibil-ity which overcomes the complicated algorithms and highpower for VLSI [6 7] and big size and low reproducibilityfor optical devices [8] Wave propagation along the surfaceallows the sensitivity of the wavelet transform device of SAWto change in the external environment and the developmentof these sensors for applications such as gas detection

changes in fluid viscosity determination of stiffness constantsof mechanical vibration and detection of the onset of iceformation on aerospace structures [9ndash11]

Nowadays micromanipulation has performed to designeither mobile micro robots or a precise positioning deviceunder the control of mechanical systems Various tools formanipulating micro parts and assembling micro systemshave been developed and integrated Semiconductor straingauges are preferred when small forces have been measuredM Jungwirth has described the micromechanical precisionpressure sensor but in delay lines A silicon basedmicro forcesensor has been developed with larger electromechanicalcoupling coefficient 1198962 The three-axis micro force sensorhas been designed by Jungwirth et al with the problem ofmeasurement uncertainty The dual axis micro force sensorfor robotic manipulations needs to use strain gauges [12ndash15]

This paper proposes to use substrate materials of smallelectromechanical coupling coefficient 1198962 (128∘119884 shearLiNbO

3) in the manufacture to design the wavelet trans-

form device of SAW based micro force sensor which hashigh accuracy and sensitivity testing precision In addition

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 701723 9 pageshttpdxdoiorg1011552014701723

2 Mathematical Problems in Engineering

a mathematical model is established to analyze the frequencyof our sensor and a peripheral detection circuit is designedWithin the scope of effective measurement the SAW basedmicro force sensor possesses good linearity consistency andrepeatability in performance Besides it uses the piezoelectricproperties and the temperature stability of the crystal aswell as the frequency signal instead of the conventionalpressure sensor with voltage signal which makes the signalprocessing of this device more digital and possesses morestable performances

The succeeding sections are organized as follows Sec-tion 2 introduces the fundamental principles of designinginterdigital transducers (IDT) for wavelet transform deviceof SAW In Section 3 the peripheral detection circuit isexplained In addition the linear regression model is pro-vided in Section 4 Finally Section 5 delivers the testing andanalysis of SAW based micro force sensor which is used formeasuring various micro force

2 Design IDT for Wavelet TransformDevice of SAW

The wavelet function is

120595119904(119905) =

1

radic119904120595(

119905

119904) (1)

where 119904 denotes the scale of wavelet functionThe wavelet transform of signal 119891(119905) is

WT119904(120591) = 119891 (119905) lowast 120595

119904(119905)

= int119877

119891 (119905)1

radic119904120595(

120591 minus 119905

119904) 119889119905

=1

radic119904int119877

119891 (119905) 120595 (120591 minus 119905

119904) 119889119905

(2)

When 120595119904(119905) is a Morlet wavelet function formula (1) is

converted into [3ndash5]

120595119904(119905) =

1

radic119904119890minus(12)(119905119904)

2

1198901198952120587(119891

0119904)119905

= 119875119904(119905) 1198901198952120587(119891

0119904)119905

(3)

where 119875119904(119905) is the wavelet-envelope function 119875

119904(119905) =

(1radic119904)119890minus12(119905119904)

2

and 1198910119904 is the center frequency When

119904 = 2119896 119896 is a random number from minusinfin to +infin Thewavelet function shown in formula (3) is converted into theMorlet dyadic wavelet function [4 5] The microwave com-munication equipment of this paper design needs a single-scale wavelet transform processor of the center frequency 119891

0

which can be rewritten as

1198910=V119904

120582=

V119904

2 (119886 + 119887) (4)

where 120582 = 2(119886 + 119887) is the wavelength V119904is the speed of the

SAW and 119886 and 119887 are the width and the interval of IDTThe delay line in wavelet transform device of SAW

designed in this paper exhibits the basic structure in Figure 1and two acoustic electric transducers on the piezoelectric

characteristic substrate material polishing surface namedinput IDT and output IDT

As the Morlet wavelet transform of SAW devices isbased on formula (3) once all the parameters in (4) arerelatively fixed its center frequency of each scale should becorresponding with the only device The device has beendesigned and produced in this paper that is shown in Figure 2

3 Design of the Peripheral Detection Circuit

31 The Principle of Peripheral Detection Circuit After mak-ing the fabricated device the peripheral detection circuitneeds to be designed to get 119865

119898and 119891 which are the pressure

and the output frequency of the SAW based micro forcesensor Figure 3 shows the general structure of the SAWmicroforce sensor with IDTs

If the SAWresonator density of the piezoelectric substrateis119898 the unit is mg2 the dielectric constant is 120576 the electricalconductivity is 120590 the elastic parameter is 119888 the unit is nm2the environment temperature is 119905 and the pressure is 119901 [16]V119904based on the theory of surface disturbance is given as

V119904= V (119898 120576 120590 119888 119905 119901) (5)

After derivation (5) can be changed to

ΔV119904

V119904

=1

V119904

(120597V120597119898

Δ119898 +120597V120597120576Δ120576 +

120597V120597120590Δ120590

+120597V120597119888Δ119888 +

120597V120597119905Δ119905 +

120597V120597119901Δ119901)

(6)

Equation (6) has been used to calculate the relationshipbetween the propagation speed of available and the SAWoscillator frequency which is equal to the following equation

Δ119891

1198910

=ΔV119904

V119904

= minus1

VSAW(120597V120597119898

Δ119898 +120597V120597120576Δ120576 +

120597V120597120590Δ120590

+120597V120597119888Δ119888 minus

120597V120597119905Δ119905 +

120597V120597119901Δ119901)

(7)

The change in the oscillator frequency and the measure-ment of the parameters can be obtained by using (7) which isthe working principle of the SAWmicro force sensor circuit

32 The Actual Oscillator Circuit The mixing frequencycircuit is divided into two oscillator circuits one for thereference oscillator circuit with a fixed frequency and theother for the detector circuitThe frequency difference can bereceived from the mixing circuit Figure 4 shows the circuitframework

The oscillator circuit with fixed frequency in the dual-channel structure has an output signal which is used as thestable signal source during measurement The digital signalprocessing circuit is composed of a filter amixer an amplifierand a shaping circuit

Mathematical Problems in Engineering 3

Input IDT Output IDT

Input signal (electrical signal)

SAW signal Output

signal

a b Envelope of electrode-overlap

Figure 1 The transducer substrate of wavelet transform device of SAW

LiNbO3

Figure 2 The fabricated single-scale wavelet transform device of SAW

IDT 1

IDT 1

IDT 2

IDT 2

Si

Si

Piezoelectric

Pressure

Piezoelectric

Figure 3 General structure of the SAWmicro force sensor with two IDTs

The oscillator circuit

The digital signal processing circuit

BPF

BPF

Mixer LPF

Intermediate frequency amplifier

CircuitDetection

Output

120579

120579

L0

RF

Figure 4 The circuit framework of fixed frequency circuit

4 Mathematical Problems in Engineering

For a surface acoustic generator as the sensitive element ofthe SAW micro force sensor the frequency stability directlyaffects the resolution of the testing precision The oscillatorfrequency has depended on the conditions of the feedbackloop phaseTherefore the improvement of the SAWoscillatorfrequency stability also improves the performance of themicro force sensor

The Pierce oscillator circuit has a better stability com-paredwithColpitts andClapp circuits [17] Figure 5 shows theoscillator circuit of the SAW based micro force sensor basedon the principle of Pierce circuit and the combination withthe design requirements

The high-frequency triode 21198781198623357 affects the resonanceamplifier in the circuit by ensuring the normal startup of theoscillator circuit 119877

1is the DC bias resistance of this triode

and adjusting the value changes with DC working points 1198772

is the DC bias resistance of the triode 1199048050 that changesthe DC working points and transforms the bias current ofthe circuit This triode functions as the current source andstabilizes the circuit working stateThe SAW resonator affectsthe frequency selection in the feedback loop by inducingthe SAW oscillator frequency stability and improving theantijamming ability

To ensure that the feedback loop circuit phase is inbalance the inductance 119871 has been added to the Pierce circuitto eliminate the effect of the stability of the DC voltage sourcefrom the oscillator circuit The LC parallel resonant circuitalso affects the DC bypass circuit The feedback coefficient 119865is related to 119862

1and 119862

2and is given as

119865 =1198621

1198622

(8)

where 1198623 1198624 and 119871

2are the decoupling devices of the DC

source that can eliminate the effect of the oscillator circuitfrom the LC filter function

33 Determine the Parameters Thecircuit layout selection ofcomponents and calculated parameters are important Thework frequency of the micro force sensor is 50MHz thecenter frequency of the LC parallel resonant circuit shouldbe

1198910=

1

2120587radicLC (9)

To ensure that the amplitude of oscillator circuit hasbetter characteristics than the initial conditions 119862

2should

be smaller In addition the designed oscillator frequency isgiven the capacitance is selected as 51 pF From (10) 119871 canbe obtained as

119871 =1

(21205871198910)2

119862

(10)

Because parasitic parameters in practical circuits affecttheir performances 119871 must be adjustable By changing thenumber of turns of the air-core coil the coil inductance canbe fine-tuned and the frequency of the LC parallel resonantcircuit will be in accordance with the working frequency

SAW

1

2

s8050

2SC3357

OutL1

L = 298nH

R1

R = 27kOhm

C1

C2

C = 5pF

C = 5pF

R2

R = 27kOhm

L2

L = 298nH

C3

C4

+ minus3V

Figure 5 The Pierce circuit of the SAW based micro force sensor

of the SAW based micro force sensor The air-core coilinductance has been calculated by the following equation

119871 =001 times 119863 times 119873

2

(119871119873119863) + 044

(11)

where 119871 is the coil inductance (in 120583H) 119863 is the diameter ofthe coil (in cm)119873 is the number of coil turns and 119871119873 is thecoil length (in cm)

An oscillator frequency source should have good stabilityphase noise and high 119876 value [18] Figure 6 shows theequivalent circuit with 119862

2expressed in picofarads

The SAW resonator can work in series or parallel reso-nant frequencies upon operating in the feedback loop Thetransistor 21198781198623357 and 1199048050 provide the DC bias current inthe oscillator circuit design based on the requirements

4 The Linear Regression Model of the SAWBased Micro Force Sensor

41 Establishment of the Linear Regression Model Aftergetting the pressure of SAW sensor (119865

119898) and the output

frequency (119891) from the actual oscillator circuit the fittingfunction should be established The relationship between thepressure of this sensor (119865

119898) and the output frequency (119891) is

given as follows

119865119898= 1198960+ 1198961Δ119891 + 119896

2Δ1198912

+ 1198963Δ1198913

+ sdot sdot sdot + 119896119899Δ119891119899

sdot sdot sdot (12)

If 119865119894 119891119894 119894 = 1 2 119899 and 119899 = 5 the method of least

squares can be used to solve this function is given as

119865119898= 1198960+ 1198961Δ119891 + 119896

2Δ1198912

+ 1198963Δ1198913

+ 1198964Δ1198914

+ 1198965Δ1198915

+ 1198966Δ1198916

(13)

Mathematical Problems in Engineering 5

P1

C1

C2

L1

P2

Figure 6 The equivalent circuit of the SAW device

The regression coefficients 1198960 1198961 1198962 1198963 1198964 1198965 and 119896

6

can be calculated through formula (13)

42 Calculate the Input and Output Variable RegressionThe sum of the variance (119876) between the dependent andindependent variables is given as [19]

119876 (1198960minus 1198966) =

119873

sum

119894=1

Δ2

119894

=

119873

sum

119894=1

[Δ119891119894minus 119865119894]2

(14)

where 119873 is the sampling point of the independent variablesTherefore the least squares estimation calculates the mini-mumvalue of119876 which implies that

and

1198960and

1198961and

1198962and

1198963and

1198964and

1198965 and

1198966must suit the following equation

119876(and

1198960and

1198961and

1198962and

1198963and

1198964and

1198965and

1198966)

=

119873

sum

119894=1

[Δ119891119894minus 119865119894]2

= minand

1198960minus

and

1198966

119873

sum

119894=1

[Δ119891119894minus 119865119894]2

(15)

whereand

1198960and

1198961and

1198962and

1198963and

1198964and

1198965 and 119896

6are the respective least

squares estimations of 1198960 1198961 1198962 1198963 1198964 1198965 and 119896

6

When

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198960

100381610038161003816100381610038161003816100381610038161198960=

and

1198960

= 0

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198961

100381610038161003816100381610038161003816100381610038161198960=

and

1198961

= 0

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198962

100381610038161003816100381610038161003816100381610038161198960=

and

1198962

= 0

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198963

100381610038161003816100381610038161003816100381610038161198960=

and

1198963

= 0

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198964

100381610038161003816100381610038161003816100381610038161198960=

and

1198964

= 0

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198965

100381610038161003816100381610038161003816100381610038161198960=

and

1198965

= 0

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198966

100381610038161003816100381610038161003816100381610038161198960=

and

1198966

= 0

(16)

The equation (17) can be derived by formula (15) and (16)119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894] = 0

119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894]Δ119891119894= 0

119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894]Δ1198912

119894

= 0

119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894]Δ1198913

119894

= 0

119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894]Δ1198914

119894

= 0

119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894]Δ1198915

119894

= 0

119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894]Δ1198916

119894

= 0

(17)

Equation (18) can be derived from formulas (14) and (17)Consider

119873and

1198960+and

1198961

119873

sum

119894=1

Δ119891 +and

1198962

119873

sum

119894=1

Δ1198912

+and

1198963

119873

sum

119894=1

Δ1198913

+and

1198964

119873

sum

119894=1

Δ1198914

+and

1198965

119873

sum

119894=1

Δ1198915

+and

1198966

119873

sum

119894=1

Δ1198916

=

119873

sum

119894=1

119865119894

and

1198960

119873

sum

119894=1

Δ119891 +and

1198961

119873

sum

119894=1

Δ1198912

+and

1198962

119873

sum

119894=1

Δ1198913

+and

1198963

119873

sum

119894=1

Δ1198914

+and

1198964

119873

sum

119894=1

Δ1198915

+and

1198965

119873

sum

119894=1

Δ1198916

+and

1198966

119873

sum

119894=1

Δ1198917

=

119873

sum

119894=1

119865119894Δ119891119894

6 Mathematical Problems in Engineering

and

1198960

119873

sum

119894=1

Δ1198912

+and

1198961

119873

sum

119894=1

Δ1198913

+and

1198962

119873

sum

119894=1

Δ1198914

+and

1198963

119873

sum

119894=1

Δ1198915

+and

1198964

119873

sum

119894=1

Δ1198916

+and

1198965

119873

sum

119894=1

Δ1198917

+and

1198966

119873

sum

119894=1

Δ1198918

=

119873

sum

119894=1

119865119894Δ1198912

119894

and

1198960

119873

sum

119894=1

Δ1198913

+and

1198961

119873

sum

119894=1

Δ1198914

+and

1198962

119873

sum

119894=1

Δ1198915

+and

1198963

119873

sum

119894=1

Δ1198916

+and

1198964

119873

sum

119894=1

Δ1198917

+and

1198965

119873

sum

119894=1

Δ1198918

+and

1198966

119873

sum

119894=1

Δ1198919

=

119873

sum

119894=1

119865119894Δ1198913

119894

and

1198960

119873

sum

119894=1

Δ1198914

+and

1198961

119873

sum

119894=1

Δ1198915

+and

1198962

119873

sum

119894=1

Δ1198916

+and

1198963

119873

sum

119894=1

Δ1198917

+and

1198964

119873

sum

119894=1

Δ1198918

+and

1198965

119873

sum

119894=1

Δ1198919

+and

1198966

119873

sum

119894=1

Δ11989110

=

119873

sum

119894=1

119865119894Δ1198914

119894

and

1198960

119873

sum

119894=1

Δ1198915

+and

1198961

119873

sum

119894=1

Δ1198916

+and

1198962

119873

sum

119894=1

Δ1198917

+and

1198963

119873

sum

119894=1

Δ1198918

+and

1198964

119873

sum

119894=1

Δ1198919

+and

1198965

119873

sum

119894=1

Δ11989110

+and

1198966

119873

sum

119894=1

Δ11989111

=

119873

sum

119894=1

119865119894Δ1198915

119894

and

1198960

119873

sum

119894=1

Δ1198916

+and

1198961

119873

sum

119894=1

Δ1198917

+and

1198962

119873

sum

119894=1

Δ1198918

+and

1198963

119873

sum

119894=1

Δ1198919

+and

1198964

119873

sum

119894=1

Δ11989110

+and

1198965

119873

sum

119894=1

Δ11989111

+and

1198966

119873

sum

119894=1

Δ11989112

=

119873

sum

119894=1

119865119894Δ1198916

119894

(18)

Equation (18) can be written as

119873and

1198960+ 119860and

1198961+ 119861and

1198962+ 119862and

1198963+ 119863and

1198964+ 119864and

1198965+ 119865and

1198966= 119872

119860and

1198960+ 119861and

1198961+ 119862and

1198962+ 119863and

1198963+ 119864and

1198964+ 119865and

1198965+ 119866and

1198966= 119875

119861and

1198960+ 119862and

1198961+ 119863and

1198962+ 119864and

1198963+ 119865and

1198964+ 119866and

1198965+ 119867and

1198966= 119876

119862and

1198960+ 119863and

1198961+ 119864and

1198962+ 119865and

1198963+ 119866and

1198964+ 119867and

1198965+ 119868and

1198966= 119877

119863and

1198960+ 119864and

1198961+ 119865and

1198962+ 119866and

1198963+ 119867and

1198964+ 119868and

1198965+ 119869and

1198966= 119878

119864and

1198960+ 119865and

1198961+ 119866and

1198962+ 119867and

1198963+ 119868and

1198964+ 119869and

1198965+ 119870and

1198966= 119879

119865and

1198960+ 119866and

1198961+ 119867and

1198962+ 119868and

1198963+ 119869and

1198964+ 119870and

1198965+ 119871and

1198966= 119880

(19)

where

119860 =

119873

sum

119894=1

Δ119891119894 119861 =

119873

sum

119894=1

Δ1198912

119894

119862 =

119873

sum

119894=1

Δ1198913

119894

119863 =

119873

sum

119894=1

Δ1198914

119894

119864 =

119873

sum

119894=1

Δ1198915

119894

119865 =

119873

sum

119894=1

Δ1198916

119894

119866 =

119873

sum

119894=1

Δ1198917

119894

119867 =

119873

sum

119894=1

Δ1198918

119894

119868 =

119873

sum

119894=1

Δ1198919

119894

119869 =

119873

sum

119894=1

Δ11989110

119894

119870 =

119873

sum

119894=1

Δ11989111

119894

119871 =

119873

sum

119894=1

Δ11989112

119894

119872 =

119873

sum

119894=1

119865119894 119875 =

119873

sum

119894=1

119865119894Δ1198911

119894

119876 =

119873

sum

119894=1

119865119894Δ1198912

119894

119877 =

119873

sum

119894=1

119865119894Δ1198913

119894

119878 =

119873

sum

119894=1

119865119894Δ1198914

119894

119879 =

119873

sum

119894=1

119865119894Δ1198915

119894

119880 =

119873

sum

119894=1

119865119894Δ1198916

119894

(20)

Coefficients 1198960to 1198966in (13) can be obtained and the input

and output variable regression of the SAW based micro forcesensor can be calculated by solving (18)

5 Testing and Analysis of the SAW BasedMicro Force Sensor

51 Actual Circuit Detection Results The output frequencyof the SAW based micro force sensor is conducted by usingthe network analyzer equipment E5061A (Figure 7) Force-measuring elements employ a cantilever beam loaded with0ndash20 kPa pressure and add 2 kPa to this beam at each time[20]

Figure 8 shows the test schematic The SAW based microforce sensor has been designed with a single channel For theinductive components the electromagnetic field interferenceis more sensitive two inductors have been placed at 90∘to reduce interference between these components Figure 9shows the actual circuit In the process of real production thedevice location and the connection between our devices aremore important

Mathematical Problems in Engineering 7

Table 1 Difference in frequency data for various pressures

(kPa)119865119898

0 2 4 6 8 10 12 14 16 18 20119891 (MHz) 49255389 49255391 49255378 49255393 49255434 49255459 49255474 49255481 49255447 49255486 49255497119891 (MHz) 49255321 49255312 49255298 49255296 49255338 49255343 49255357 49255359 49255319 49255361 49255363Δ119891 (Hz) 68 79 80 97 96 116 117 122 128 125 134

Network analyzerE5061A

Input IDT Output IDT

Piezoelectric substrate

Fn

Figure 7 Schematic of the SAW based micro force sensor

DC power Output ScopeThe micro

force sensor of SAW device

Figure 8 Test schematic diagram

52 The Fitting Curve for the Measured Frequency Figure 10shows the actual test waveform diagram [21]

To eliminate the system instability the experimental datahas been averaged in Table 1

Frequency experiment data samples have been gener-ated from (18) according to the different micro pressurereading and the estimated regression coefficients

and

1198960and

1198961and

1198962

and

1198963and

1198964and

1198965andand

1198966can be calculated The method of least

squares can reduce the error due to measurement inaccu-racies caused by the SAW device based micro force sensorThrough the minimization of squared errors of our actualdata the least squares method has the ability to find the bestmatching function data Additionally the fitting curve of theexperimental data shows that the circuit design is reasonableand the device exhibits good linearity (Figure 11) The pres-sure 119865

119898is proportional to the output frequency119891 which has

proved that the SAW detection and pierce oscillator circuithave correct logic function

Based on (13) the available in differentmicro force sensoroutput difference frequency transfer function is

119865119898(Δ119891) = 31441 times 10

minus1

+ 59057 times 10minus2

Δ119891119894

minus 23012 times 10minus4

Δ1198912

119894

+ 54127 times 10minus7

Δ1198913

119894

Table 2 Oscilloscope measurement results

Measurement parameter Averagevalue

Minimumvalue

Maximumvalue

Voltage output (mV) 320 314 326Frequency output(MHz) 492553965 49255296 49255497

minus 60364 times 10minus10

Δ1198914

119894

+ 30200 times 10minus13

Δ1198915

119894

minus 50540 times 10minus17

Δ1198916

119894

(21)

Because of the load impedance having affected the ampli-tude output of the micro force sensor the impedance of theoscilloscope probe during testing is set at 1mΩ to stabilize theoscillator amplitude The working circuit voltage and currentare 3V and 10mA Using the difference in frequency data forvarious pressures in Table 1 the Oscilloscope measurementresult has been calculated in Table 2

6 Conclusion

This paper has addressed three problems in designing theSAW based micro force sensor namely the envelope of IDTthe variable regression and the fitting curve analysis forthe measured frequency which are according to the wavelettransform method SAW detection and pierce oscillatorcircuits

The paper has also proposed themixing frequency circuitfor the reference oscillator and the detector circuit Thechanges between the oscillator frequency and the mea-surement of the parameters can be obtained through thepierce oscillator circuits and the difference in frequency datafor various pressures also can be established by the linearregression model By affecting the production of amplitudeof impedance and parasitic capacitance the output frequencyof 50MHz still has stabilized features and performance Theparameters of frequency amplitude frequency stability andamplitude stability have been measured during the deviceresponse and the sensor simulation

According to the Morlet wavelet transform SAW detec-tion and pierce oscillator circuits the experimental resultshave confirmed that the SAW based micro force sensor canimplement high reproducibility When the input transducerof our device has been designed with the envelope of theconducting strips our device performs well linearity Inaddition the device uses the piezoelectric properties and thetemperature stability of the crystal as well as the frequency

8 Mathematical Problems in Engineering

Figure 9 The actual circuit testing diagram

Figure 10 The actual test waveform diagram

Figure 11 The experimental data fitting curve

signal instead of the conventional pressure sensor withvoltage signal which has made the signal processing of thisdevice more digital and possessed more stable performancesThe SAW based micro force type can be fabricated and has

high performance in either mobile micro robots or a precisepositioning device under the control of mechanical system

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the National Natural ScienceFoundation of China (Grant no 61274078) the ResearchInnovation and Project of the Shanghai Municipal EducationCommission (Grant no 13ZZ049) the Doctoral ScientificFundProject of theMinistry of Education ofChina (Grant no20120075110006) and the Foundation of Shanghai Universityof Engineering Science (Grant no nhky-2013-10)

References

[1] I Daubechies ldquoThe wavelet transform time-frequency local-ization and signal analysisrdquo IEEE Transactions on InformationTheory vol 36 no 5 pp 961ndash1005 1990

[2] D S Ballantine R M White S J Martin et al Acoustic WaveSensor Theory Design and Physico-Chemical ApplicationsAcademic Press New York NY USA 1997

[3] Y H Peng Wavelet Transform and Its Engineering ApplicationScience Press Beijing China 1999 (Chinese)

[4] W K Lu C C Zhu J H Liu and Q Liu ldquoImplementingwavelet transform with SAW elementsrdquo Science in China ETechnological Sciences vol 46 no 6 pp 627ndash638 2003

[5] W-K Lu C-C Zhu J-H Liu and P-Y Wei ldquoStudy onimplementation of surface-acoustic-wave type of the wavelet-transformation and reconstruction elementrdquo Acta ElectronicaSinica vol 30 no 8 pp 1156ndash1159 2002 (Chinese)

[6] K Andra C Chakrabarti and T Acharya ldquoA VLSI architecturefor lifting-based forward and inverse wavelet transformrdquo IEEETransactions on Signal Processing vol 50 no 4 pp 966ndash9772002

[7] K K Parhi and T Nishitani ldquoVLSI architecture for discretewavelet transformsrdquo IEEE Transactions on Very Large ScaleIntegration (VLSI) Systems vol 1 no 2 pp 191ndash202 1993

[8] X Chen X Zhang K Chen and Q Li ldquoOptical wavelet-matched filtering with bacteriorhodopsin filmsrdquoApplied Opticsvol 36 no 32 pp 8413ndash8416 1997

Mathematical Problems in Engineering 9

[9] M von Schickfus R Stanzel T Kammereck D Weiskat WDittrich and H Fuchs ldquoImproving the SAW gas sensor deviceelectronics and sensor layerrdquo Sensors andActuators B Chemicalvol 19 no 1ndash3 pp 443ndash447 1994

[10] M K Tan L Y Yeo and J R Friend ldquoRapid fluid flow andmixing induced inmicrochannels using surface acousticwavesrdquoEurophysics Letters vol 87 no 4 pp 537ndash563 2009

[11] W CWilson D CMalocha N Y Kozlovski et al ldquoOrthogonalfrequency coded SAWsensors for aerospace SHMapplicationsrdquoSensors Journal vol 9 no 11 pp 1546ndash1556 2009

[12] M Jungwirth H Scherr and R Weigel ldquoMicromechanicalprecision pressure sensor incorporating SAW delay linesrdquo ActaMechanica vol 158 no 3-4 pp 227ndash252 2002

[13] S Muntwyler F Beyeler and B J Nelson ldquoThree-axis micro-force sensor with sub-micro-Newtonmeasurement uncertaintyand tunable force rangerdquo Journal of Micromechanics and Micro-engineering vol 20 no 2 pp 3165ndash3170 2010

[14] Y C Kim Y S Ihn H Moon et al ldquoLow cost dual axismicro force sensor for robotic manipulationsrdquo MicrosystemTechnologies vol 17 no 5ndash7 pp 1197ndash1205 2011

[15] K J Singh O Elmazria F Sarry et al ldquoEnhanced sensitivityof SAW-based Pirani vacuum pressure sensorrdquo IEEE SensorsJournal vol 11 no 6 pp 1458ndash1464 2011

[16] C B Wen and C C Zhu ldquoTime synchronous dyadic waveletprocessor array using surface acoustic wave devicesrdquo SmartMaterials and Structures vol 15 no 4 pp 939ndash945 2006

[17] W K Lu C C Zhu J F Zhang C Shi and X Z Lu ldquoStudyof small size wavelet transform processor and wavelet inverse-transform processor using SAWdevicesrdquoMeasurement Journalof the International Measurement Confederation vol 44 no 5pp 994ndash999 2011

[18] Y Kang Design of Surface Acoustic Wave Devices and ItsApplication Oscillator Circuit Changrsquoan University 2011

[19] X Z Lu Interfacial Stress Sensor for Artificial Skin ApplicationDonghua University 2012

[20] Y Y Li W K Lu C C Zhu et al ldquoAcoustic electric generationfor morlet wavelet transform of surface acoustic wave devicerdquoResearch Journal of Applied Sciences Engineering and Technol-ogy vol 5 no 4 pp 1203ndash1207 2013

[21] Y Y Li W K Lu and C C Zhu ldquoPspice equivalent circuitmodel for implementation of surface acoustic wave filterrdquoJournal of Donghua University vol 29 no 2 pp 148ndash152 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Mathematical Problems in Engineering

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Differential EquationsInternational Journal of

Volume 2014

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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Decision SciencesAdvances in

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Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

2 Mathematical Problems in Engineering

a mathematical model is established to analyze the frequencyof our sensor and a peripheral detection circuit is designedWithin the scope of effective measurement the SAW basedmicro force sensor possesses good linearity consistency andrepeatability in performance Besides it uses the piezoelectricproperties and the temperature stability of the crystal aswell as the frequency signal instead of the conventionalpressure sensor with voltage signal which makes the signalprocessing of this device more digital and possesses morestable performances

The succeeding sections are organized as follows Sec-tion 2 introduces the fundamental principles of designinginterdigital transducers (IDT) for wavelet transform deviceof SAW In Section 3 the peripheral detection circuit isexplained In addition the linear regression model is pro-vided in Section 4 Finally Section 5 delivers the testing andanalysis of SAW based micro force sensor which is used formeasuring various micro force

2 Design IDT for Wavelet TransformDevice of SAW

The wavelet function is

120595119904(119905) =

1

radic119904120595(

119905

119904) (1)

where 119904 denotes the scale of wavelet functionThe wavelet transform of signal 119891(119905) is

WT119904(120591) = 119891 (119905) lowast 120595

119904(119905)

= int119877

119891 (119905)1

radic119904120595(

120591 minus 119905

119904) 119889119905

=1

radic119904int119877

119891 (119905) 120595 (120591 minus 119905

119904) 119889119905

(2)

When 120595119904(119905) is a Morlet wavelet function formula (1) is

converted into [3ndash5]

120595119904(119905) =

1

radic119904119890minus(12)(119905119904)

2

1198901198952120587(119891

0119904)119905

= 119875119904(119905) 1198901198952120587(119891

0119904)119905

(3)

where 119875119904(119905) is the wavelet-envelope function 119875

119904(119905) =

(1radic119904)119890minus12(119905119904)

2

and 1198910119904 is the center frequency When

119904 = 2119896 119896 is a random number from minusinfin to +infin Thewavelet function shown in formula (3) is converted into theMorlet dyadic wavelet function [4 5] The microwave com-munication equipment of this paper design needs a single-scale wavelet transform processor of the center frequency 119891

0

which can be rewritten as

1198910=V119904

120582=

V119904

2 (119886 + 119887) (4)

where 120582 = 2(119886 + 119887) is the wavelength V119904is the speed of the

SAW and 119886 and 119887 are the width and the interval of IDTThe delay line in wavelet transform device of SAW

designed in this paper exhibits the basic structure in Figure 1and two acoustic electric transducers on the piezoelectric

characteristic substrate material polishing surface namedinput IDT and output IDT

As the Morlet wavelet transform of SAW devices isbased on formula (3) once all the parameters in (4) arerelatively fixed its center frequency of each scale should becorresponding with the only device The device has beendesigned and produced in this paper that is shown in Figure 2

3 Design of the Peripheral Detection Circuit

31 The Principle of Peripheral Detection Circuit After mak-ing the fabricated device the peripheral detection circuitneeds to be designed to get 119865

119898and 119891 which are the pressure

and the output frequency of the SAW based micro forcesensor Figure 3 shows the general structure of the SAWmicroforce sensor with IDTs

If the SAWresonator density of the piezoelectric substrateis119898 the unit is mg2 the dielectric constant is 120576 the electricalconductivity is 120590 the elastic parameter is 119888 the unit is nm2the environment temperature is 119905 and the pressure is 119901 [16]V119904based on the theory of surface disturbance is given as

V119904= V (119898 120576 120590 119888 119905 119901) (5)

After derivation (5) can be changed to

ΔV119904

V119904

=1

V119904

(120597V120597119898

Δ119898 +120597V120597120576Δ120576 +

120597V120597120590Δ120590

+120597V120597119888Δ119888 +

120597V120597119905Δ119905 +

120597V120597119901Δ119901)

(6)

Equation (6) has been used to calculate the relationshipbetween the propagation speed of available and the SAWoscillator frequency which is equal to the following equation

Δ119891

1198910

=ΔV119904

V119904

= minus1

VSAW(120597V120597119898

Δ119898 +120597V120597120576Δ120576 +

120597V120597120590Δ120590

+120597V120597119888Δ119888 minus

120597V120597119905Δ119905 +

120597V120597119901Δ119901)

(7)

The change in the oscillator frequency and the measure-ment of the parameters can be obtained by using (7) which isthe working principle of the SAWmicro force sensor circuit

32 The Actual Oscillator Circuit The mixing frequencycircuit is divided into two oscillator circuits one for thereference oscillator circuit with a fixed frequency and theother for the detector circuitThe frequency difference can bereceived from the mixing circuit Figure 4 shows the circuitframework

The oscillator circuit with fixed frequency in the dual-channel structure has an output signal which is used as thestable signal source during measurement The digital signalprocessing circuit is composed of a filter amixer an amplifierand a shaping circuit

Mathematical Problems in Engineering 3

Input IDT Output IDT

Input signal (electrical signal)

SAW signal Output

signal

a b Envelope of electrode-overlap

Figure 1 The transducer substrate of wavelet transform device of SAW

LiNbO3

Figure 2 The fabricated single-scale wavelet transform device of SAW

IDT 1

IDT 1

IDT 2

IDT 2

Si

Si

Piezoelectric

Pressure

Piezoelectric

Figure 3 General structure of the SAWmicro force sensor with two IDTs

The oscillator circuit

The digital signal processing circuit

BPF

BPF

Mixer LPF

Intermediate frequency amplifier

CircuitDetection

Output

120579

120579

L0

RF

Figure 4 The circuit framework of fixed frequency circuit

4 Mathematical Problems in Engineering

For a surface acoustic generator as the sensitive element ofthe SAW micro force sensor the frequency stability directlyaffects the resolution of the testing precision The oscillatorfrequency has depended on the conditions of the feedbackloop phaseTherefore the improvement of the SAWoscillatorfrequency stability also improves the performance of themicro force sensor

The Pierce oscillator circuit has a better stability com-paredwithColpitts andClapp circuits [17] Figure 5 shows theoscillator circuit of the SAW based micro force sensor basedon the principle of Pierce circuit and the combination withthe design requirements

The high-frequency triode 21198781198623357 affects the resonanceamplifier in the circuit by ensuring the normal startup of theoscillator circuit 119877

1is the DC bias resistance of this triode

and adjusting the value changes with DC working points 1198772

is the DC bias resistance of the triode 1199048050 that changesthe DC working points and transforms the bias current ofthe circuit This triode functions as the current source andstabilizes the circuit working stateThe SAW resonator affectsthe frequency selection in the feedback loop by inducingthe SAW oscillator frequency stability and improving theantijamming ability

To ensure that the feedback loop circuit phase is inbalance the inductance 119871 has been added to the Pierce circuitto eliminate the effect of the stability of the DC voltage sourcefrom the oscillator circuit The LC parallel resonant circuitalso affects the DC bypass circuit The feedback coefficient 119865is related to 119862

1and 119862

2and is given as

119865 =1198621

1198622

(8)

where 1198623 1198624 and 119871

2are the decoupling devices of the DC

source that can eliminate the effect of the oscillator circuitfrom the LC filter function

33 Determine the Parameters Thecircuit layout selection ofcomponents and calculated parameters are important Thework frequency of the micro force sensor is 50MHz thecenter frequency of the LC parallel resonant circuit shouldbe

1198910=

1

2120587radicLC (9)

To ensure that the amplitude of oscillator circuit hasbetter characteristics than the initial conditions 119862

2should

be smaller In addition the designed oscillator frequency isgiven the capacitance is selected as 51 pF From (10) 119871 canbe obtained as

119871 =1

(21205871198910)2

119862

(10)

Because parasitic parameters in practical circuits affecttheir performances 119871 must be adjustable By changing thenumber of turns of the air-core coil the coil inductance canbe fine-tuned and the frequency of the LC parallel resonantcircuit will be in accordance with the working frequency

SAW

1

2

s8050

2SC3357

OutL1

L = 298nH

R1

R = 27kOhm

C1

C2

C = 5pF

C = 5pF

R2

R = 27kOhm

L2

L = 298nH

C3

C4

+ minus3V

Figure 5 The Pierce circuit of the SAW based micro force sensor

of the SAW based micro force sensor The air-core coilinductance has been calculated by the following equation

119871 =001 times 119863 times 119873

2

(119871119873119863) + 044

(11)

where 119871 is the coil inductance (in 120583H) 119863 is the diameter ofthe coil (in cm)119873 is the number of coil turns and 119871119873 is thecoil length (in cm)

An oscillator frequency source should have good stabilityphase noise and high 119876 value [18] Figure 6 shows theequivalent circuit with 119862

2expressed in picofarads

The SAW resonator can work in series or parallel reso-nant frequencies upon operating in the feedback loop Thetransistor 21198781198623357 and 1199048050 provide the DC bias current inthe oscillator circuit design based on the requirements

4 The Linear Regression Model of the SAWBased Micro Force Sensor

41 Establishment of the Linear Regression Model Aftergetting the pressure of SAW sensor (119865

119898) and the output

frequency (119891) from the actual oscillator circuit the fittingfunction should be established The relationship between thepressure of this sensor (119865

119898) and the output frequency (119891) is

given as follows

119865119898= 1198960+ 1198961Δ119891 + 119896

2Δ1198912

+ 1198963Δ1198913

+ sdot sdot sdot + 119896119899Δ119891119899

sdot sdot sdot (12)

If 119865119894 119891119894 119894 = 1 2 119899 and 119899 = 5 the method of least

squares can be used to solve this function is given as

119865119898= 1198960+ 1198961Δ119891 + 119896

2Δ1198912

+ 1198963Δ1198913

+ 1198964Δ1198914

+ 1198965Δ1198915

+ 1198966Δ1198916

(13)

Mathematical Problems in Engineering 5

P1

C1

C2

L1

P2

Figure 6 The equivalent circuit of the SAW device

The regression coefficients 1198960 1198961 1198962 1198963 1198964 1198965 and 119896

6

can be calculated through formula (13)

42 Calculate the Input and Output Variable RegressionThe sum of the variance (119876) between the dependent andindependent variables is given as [19]

119876 (1198960minus 1198966) =

119873

sum

119894=1

Δ2

119894

=

119873

sum

119894=1

[Δ119891119894minus 119865119894]2

(14)

where 119873 is the sampling point of the independent variablesTherefore the least squares estimation calculates the mini-mumvalue of119876 which implies that

and

1198960and

1198961and

1198962and

1198963and

1198964and

1198965 and

1198966must suit the following equation

119876(and

1198960and

1198961and

1198962and

1198963and

1198964and

1198965and

1198966)

=

119873

sum

119894=1

[Δ119891119894minus 119865119894]2

= minand

1198960minus

and

1198966

119873

sum

119894=1

[Δ119891119894minus 119865119894]2

(15)

whereand

1198960and

1198961and

1198962and

1198963and

1198964and

1198965 and 119896

6are the respective least

squares estimations of 1198960 1198961 1198962 1198963 1198964 1198965 and 119896

6

When

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198960

100381610038161003816100381610038161003816100381610038161198960=

and

1198960

= 0

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198961

100381610038161003816100381610038161003816100381610038161198960=

and

1198961

= 0

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198962

100381610038161003816100381610038161003816100381610038161198960=

and

1198962

= 0

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198963

100381610038161003816100381610038161003816100381610038161198960=

and

1198963

= 0

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198964

100381610038161003816100381610038161003816100381610038161198960=

and

1198964

= 0

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198965

100381610038161003816100381610038161003816100381610038161198960=

and

1198965

= 0

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198966

100381610038161003816100381610038161003816100381610038161198960=

and

1198966

= 0

(16)

The equation (17) can be derived by formula (15) and (16)119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894] = 0

119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894]Δ119891119894= 0

119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894]Δ1198912

119894

= 0

119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894]Δ1198913

119894

= 0

119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894]Δ1198914

119894

= 0

119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894]Δ1198915

119894

= 0

119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894]Δ1198916

119894

= 0

(17)

Equation (18) can be derived from formulas (14) and (17)Consider

119873and

1198960+and

1198961

119873

sum

119894=1

Δ119891 +and

1198962

119873

sum

119894=1

Δ1198912

+and

1198963

119873

sum

119894=1

Δ1198913

+and

1198964

119873

sum

119894=1

Δ1198914

+and

1198965

119873

sum

119894=1

Δ1198915

+and

1198966

119873

sum

119894=1

Δ1198916

=

119873

sum

119894=1

119865119894

and

1198960

119873

sum

119894=1

Δ119891 +and

1198961

119873

sum

119894=1

Δ1198912

+and

1198962

119873

sum

119894=1

Δ1198913

+and

1198963

119873

sum

119894=1

Δ1198914

+and

1198964

119873

sum

119894=1

Δ1198915

+and

1198965

119873

sum

119894=1

Δ1198916

+and

1198966

119873

sum

119894=1

Δ1198917

=

119873

sum

119894=1

119865119894Δ119891119894

6 Mathematical Problems in Engineering

and

1198960

119873

sum

119894=1

Δ1198912

+and

1198961

119873

sum

119894=1

Δ1198913

+and

1198962

119873

sum

119894=1

Δ1198914

+and

1198963

119873

sum

119894=1

Δ1198915

+and

1198964

119873

sum

119894=1

Δ1198916

+and

1198965

119873

sum

119894=1

Δ1198917

+and

1198966

119873

sum

119894=1

Δ1198918

=

119873

sum

119894=1

119865119894Δ1198912

119894

and

1198960

119873

sum

119894=1

Δ1198913

+and

1198961

119873

sum

119894=1

Δ1198914

+and

1198962

119873

sum

119894=1

Δ1198915

+and

1198963

119873

sum

119894=1

Δ1198916

+and

1198964

119873

sum

119894=1

Δ1198917

+and

1198965

119873

sum

119894=1

Δ1198918

+and

1198966

119873

sum

119894=1

Δ1198919

=

119873

sum

119894=1

119865119894Δ1198913

119894

and

1198960

119873

sum

119894=1

Δ1198914

+and

1198961

119873

sum

119894=1

Δ1198915

+and

1198962

119873

sum

119894=1

Δ1198916

+and

1198963

119873

sum

119894=1

Δ1198917

+and

1198964

119873

sum

119894=1

Δ1198918

+and

1198965

119873

sum

119894=1

Δ1198919

+and

1198966

119873

sum

119894=1

Δ11989110

=

119873

sum

119894=1

119865119894Δ1198914

119894

and

1198960

119873

sum

119894=1

Δ1198915

+and

1198961

119873

sum

119894=1

Δ1198916

+and

1198962

119873

sum

119894=1

Δ1198917

+and

1198963

119873

sum

119894=1

Δ1198918

+and

1198964

119873

sum

119894=1

Δ1198919

+and

1198965

119873

sum

119894=1

Δ11989110

+and

1198966

119873

sum

119894=1

Δ11989111

=

119873

sum

119894=1

119865119894Δ1198915

119894

and

1198960

119873

sum

119894=1

Δ1198916

+and

1198961

119873

sum

119894=1

Δ1198917

+and

1198962

119873

sum

119894=1

Δ1198918

+and

1198963

119873

sum

119894=1

Δ1198919

+and

1198964

119873

sum

119894=1

Δ11989110

+and

1198965

119873

sum

119894=1

Δ11989111

+and

1198966

119873

sum

119894=1

Δ11989112

=

119873

sum

119894=1

119865119894Δ1198916

119894

(18)

Equation (18) can be written as

119873and

1198960+ 119860and

1198961+ 119861and

1198962+ 119862and

1198963+ 119863and

1198964+ 119864and

1198965+ 119865and

1198966= 119872

119860and

1198960+ 119861and

1198961+ 119862and

1198962+ 119863and

1198963+ 119864and

1198964+ 119865and

1198965+ 119866and

1198966= 119875

119861and

1198960+ 119862and

1198961+ 119863and

1198962+ 119864and

1198963+ 119865and

1198964+ 119866and

1198965+ 119867and

1198966= 119876

119862and

1198960+ 119863and

1198961+ 119864and

1198962+ 119865and

1198963+ 119866and

1198964+ 119867and

1198965+ 119868and

1198966= 119877

119863and

1198960+ 119864and

1198961+ 119865and

1198962+ 119866and

1198963+ 119867and

1198964+ 119868and

1198965+ 119869and

1198966= 119878

119864and

1198960+ 119865and

1198961+ 119866and

1198962+ 119867and

1198963+ 119868and

1198964+ 119869and

1198965+ 119870and

1198966= 119879

119865and

1198960+ 119866and

1198961+ 119867and

1198962+ 119868and

1198963+ 119869and

1198964+ 119870and

1198965+ 119871and

1198966= 119880

(19)

where

119860 =

119873

sum

119894=1

Δ119891119894 119861 =

119873

sum

119894=1

Δ1198912

119894

119862 =

119873

sum

119894=1

Δ1198913

119894

119863 =

119873

sum

119894=1

Δ1198914

119894

119864 =

119873

sum

119894=1

Δ1198915

119894

119865 =

119873

sum

119894=1

Δ1198916

119894

119866 =

119873

sum

119894=1

Δ1198917

119894

119867 =

119873

sum

119894=1

Δ1198918

119894

119868 =

119873

sum

119894=1

Δ1198919

119894

119869 =

119873

sum

119894=1

Δ11989110

119894

119870 =

119873

sum

119894=1

Δ11989111

119894

119871 =

119873

sum

119894=1

Δ11989112

119894

119872 =

119873

sum

119894=1

119865119894 119875 =

119873

sum

119894=1

119865119894Δ1198911

119894

119876 =

119873

sum

119894=1

119865119894Δ1198912

119894

119877 =

119873

sum

119894=1

119865119894Δ1198913

119894

119878 =

119873

sum

119894=1

119865119894Δ1198914

119894

119879 =

119873

sum

119894=1

119865119894Δ1198915

119894

119880 =

119873

sum

119894=1

119865119894Δ1198916

119894

(20)

Coefficients 1198960to 1198966in (13) can be obtained and the input

and output variable regression of the SAW based micro forcesensor can be calculated by solving (18)

5 Testing and Analysis of the SAW BasedMicro Force Sensor

51 Actual Circuit Detection Results The output frequencyof the SAW based micro force sensor is conducted by usingthe network analyzer equipment E5061A (Figure 7) Force-measuring elements employ a cantilever beam loaded with0ndash20 kPa pressure and add 2 kPa to this beam at each time[20]

Figure 8 shows the test schematic The SAW based microforce sensor has been designed with a single channel For theinductive components the electromagnetic field interferenceis more sensitive two inductors have been placed at 90∘to reduce interference between these components Figure 9shows the actual circuit In the process of real production thedevice location and the connection between our devices aremore important

Mathematical Problems in Engineering 7

Table 1 Difference in frequency data for various pressures

(kPa)119865119898

0 2 4 6 8 10 12 14 16 18 20119891 (MHz) 49255389 49255391 49255378 49255393 49255434 49255459 49255474 49255481 49255447 49255486 49255497119891 (MHz) 49255321 49255312 49255298 49255296 49255338 49255343 49255357 49255359 49255319 49255361 49255363Δ119891 (Hz) 68 79 80 97 96 116 117 122 128 125 134

Network analyzerE5061A

Input IDT Output IDT

Piezoelectric substrate

Fn

Figure 7 Schematic of the SAW based micro force sensor

DC power Output ScopeThe micro

force sensor of SAW device

Figure 8 Test schematic diagram

52 The Fitting Curve for the Measured Frequency Figure 10shows the actual test waveform diagram [21]

To eliminate the system instability the experimental datahas been averaged in Table 1

Frequency experiment data samples have been gener-ated from (18) according to the different micro pressurereading and the estimated regression coefficients

and

1198960and

1198961and

1198962

and

1198963and

1198964and

1198965andand

1198966can be calculated The method of least

squares can reduce the error due to measurement inaccu-racies caused by the SAW device based micro force sensorThrough the minimization of squared errors of our actualdata the least squares method has the ability to find the bestmatching function data Additionally the fitting curve of theexperimental data shows that the circuit design is reasonableand the device exhibits good linearity (Figure 11) The pres-sure 119865

119898is proportional to the output frequency119891 which has

proved that the SAW detection and pierce oscillator circuithave correct logic function

Based on (13) the available in differentmicro force sensoroutput difference frequency transfer function is

119865119898(Δ119891) = 31441 times 10

minus1

+ 59057 times 10minus2

Δ119891119894

minus 23012 times 10minus4

Δ1198912

119894

+ 54127 times 10minus7

Δ1198913

119894

Table 2 Oscilloscope measurement results

Measurement parameter Averagevalue

Minimumvalue

Maximumvalue

Voltage output (mV) 320 314 326Frequency output(MHz) 492553965 49255296 49255497

minus 60364 times 10minus10

Δ1198914

119894

+ 30200 times 10minus13

Δ1198915

119894

minus 50540 times 10minus17

Δ1198916

119894

(21)

Because of the load impedance having affected the ampli-tude output of the micro force sensor the impedance of theoscilloscope probe during testing is set at 1mΩ to stabilize theoscillator amplitude The working circuit voltage and currentare 3V and 10mA Using the difference in frequency data forvarious pressures in Table 1 the Oscilloscope measurementresult has been calculated in Table 2

6 Conclusion

This paper has addressed three problems in designing theSAW based micro force sensor namely the envelope of IDTthe variable regression and the fitting curve analysis forthe measured frequency which are according to the wavelettransform method SAW detection and pierce oscillatorcircuits

The paper has also proposed themixing frequency circuitfor the reference oscillator and the detector circuit Thechanges between the oscillator frequency and the mea-surement of the parameters can be obtained through thepierce oscillator circuits and the difference in frequency datafor various pressures also can be established by the linearregression model By affecting the production of amplitudeof impedance and parasitic capacitance the output frequencyof 50MHz still has stabilized features and performance Theparameters of frequency amplitude frequency stability andamplitude stability have been measured during the deviceresponse and the sensor simulation

According to the Morlet wavelet transform SAW detec-tion and pierce oscillator circuits the experimental resultshave confirmed that the SAW based micro force sensor canimplement high reproducibility When the input transducerof our device has been designed with the envelope of theconducting strips our device performs well linearity Inaddition the device uses the piezoelectric properties and thetemperature stability of the crystal as well as the frequency

8 Mathematical Problems in Engineering

Figure 9 The actual circuit testing diagram

Figure 10 The actual test waveform diagram

Figure 11 The experimental data fitting curve

signal instead of the conventional pressure sensor withvoltage signal which has made the signal processing of thisdevice more digital and possessed more stable performancesThe SAW based micro force type can be fabricated and has

high performance in either mobile micro robots or a precisepositioning device under the control of mechanical system

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the National Natural ScienceFoundation of China (Grant no 61274078) the ResearchInnovation and Project of the Shanghai Municipal EducationCommission (Grant no 13ZZ049) the Doctoral ScientificFundProject of theMinistry of Education ofChina (Grant no20120075110006) and the Foundation of Shanghai Universityof Engineering Science (Grant no nhky-2013-10)

References

[1] I Daubechies ldquoThe wavelet transform time-frequency local-ization and signal analysisrdquo IEEE Transactions on InformationTheory vol 36 no 5 pp 961ndash1005 1990

[2] D S Ballantine R M White S J Martin et al Acoustic WaveSensor Theory Design and Physico-Chemical ApplicationsAcademic Press New York NY USA 1997

[3] Y H Peng Wavelet Transform and Its Engineering ApplicationScience Press Beijing China 1999 (Chinese)

[4] W K Lu C C Zhu J H Liu and Q Liu ldquoImplementingwavelet transform with SAW elementsrdquo Science in China ETechnological Sciences vol 46 no 6 pp 627ndash638 2003

[5] W-K Lu C-C Zhu J-H Liu and P-Y Wei ldquoStudy onimplementation of surface-acoustic-wave type of the wavelet-transformation and reconstruction elementrdquo Acta ElectronicaSinica vol 30 no 8 pp 1156ndash1159 2002 (Chinese)

[6] K Andra C Chakrabarti and T Acharya ldquoA VLSI architecturefor lifting-based forward and inverse wavelet transformrdquo IEEETransactions on Signal Processing vol 50 no 4 pp 966ndash9772002

[7] K K Parhi and T Nishitani ldquoVLSI architecture for discretewavelet transformsrdquo IEEE Transactions on Very Large ScaleIntegration (VLSI) Systems vol 1 no 2 pp 191ndash202 1993

[8] X Chen X Zhang K Chen and Q Li ldquoOptical wavelet-matched filtering with bacteriorhodopsin filmsrdquoApplied Opticsvol 36 no 32 pp 8413ndash8416 1997

Mathematical Problems in Engineering 9

[9] M von Schickfus R Stanzel T Kammereck D Weiskat WDittrich and H Fuchs ldquoImproving the SAW gas sensor deviceelectronics and sensor layerrdquo Sensors andActuators B Chemicalvol 19 no 1ndash3 pp 443ndash447 1994

[10] M K Tan L Y Yeo and J R Friend ldquoRapid fluid flow andmixing induced inmicrochannels using surface acousticwavesrdquoEurophysics Letters vol 87 no 4 pp 537ndash563 2009

[11] W CWilson D CMalocha N Y Kozlovski et al ldquoOrthogonalfrequency coded SAWsensors for aerospace SHMapplicationsrdquoSensors Journal vol 9 no 11 pp 1546ndash1556 2009

[12] M Jungwirth H Scherr and R Weigel ldquoMicromechanicalprecision pressure sensor incorporating SAW delay linesrdquo ActaMechanica vol 158 no 3-4 pp 227ndash252 2002

[13] S Muntwyler F Beyeler and B J Nelson ldquoThree-axis micro-force sensor with sub-micro-Newtonmeasurement uncertaintyand tunable force rangerdquo Journal of Micromechanics and Micro-engineering vol 20 no 2 pp 3165ndash3170 2010

[14] Y C Kim Y S Ihn H Moon et al ldquoLow cost dual axismicro force sensor for robotic manipulationsrdquo MicrosystemTechnologies vol 17 no 5ndash7 pp 1197ndash1205 2011

[15] K J Singh O Elmazria F Sarry et al ldquoEnhanced sensitivityof SAW-based Pirani vacuum pressure sensorrdquo IEEE SensorsJournal vol 11 no 6 pp 1458ndash1464 2011

[16] C B Wen and C C Zhu ldquoTime synchronous dyadic waveletprocessor array using surface acoustic wave devicesrdquo SmartMaterials and Structures vol 15 no 4 pp 939ndash945 2006

[17] W K Lu C C Zhu J F Zhang C Shi and X Z Lu ldquoStudyof small size wavelet transform processor and wavelet inverse-transform processor using SAWdevicesrdquoMeasurement Journalof the International Measurement Confederation vol 44 no 5pp 994ndash999 2011

[18] Y Kang Design of Surface Acoustic Wave Devices and ItsApplication Oscillator Circuit Changrsquoan University 2011

[19] X Z Lu Interfacial Stress Sensor for Artificial Skin ApplicationDonghua University 2012

[20] Y Y Li W K Lu C C Zhu et al ldquoAcoustic electric generationfor morlet wavelet transform of surface acoustic wave devicerdquoResearch Journal of Applied Sciences Engineering and Technol-ogy vol 5 no 4 pp 1203ndash1207 2013

[21] Y Y Li W K Lu and C C Zhu ldquoPspice equivalent circuitmodel for implementation of surface acoustic wave filterrdquoJournal of Donghua University vol 29 no 2 pp 148ndash152 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

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Mathematical PhysicsAdvances in

Complex AnalysisJournal of

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OptimizationJournal of

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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

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Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 3

Input IDT Output IDT

Input signal (electrical signal)

SAW signal Output

signal

a b Envelope of electrode-overlap

Figure 1 The transducer substrate of wavelet transform device of SAW

LiNbO3

Figure 2 The fabricated single-scale wavelet transform device of SAW

IDT 1

IDT 1

IDT 2

IDT 2

Si

Si

Piezoelectric

Pressure

Piezoelectric

Figure 3 General structure of the SAWmicro force sensor with two IDTs

The oscillator circuit

The digital signal processing circuit

BPF

BPF

Mixer LPF

Intermediate frequency amplifier

CircuitDetection

Output

120579

120579

L0

RF

Figure 4 The circuit framework of fixed frequency circuit

4 Mathematical Problems in Engineering

For a surface acoustic generator as the sensitive element ofthe SAW micro force sensor the frequency stability directlyaffects the resolution of the testing precision The oscillatorfrequency has depended on the conditions of the feedbackloop phaseTherefore the improvement of the SAWoscillatorfrequency stability also improves the performance of themicro force sensor

The Pierce oscillator circuit has a better stability com-paredwithColpitts andClapp circuits [17] Figure 5 shows theoscillator circuit of the SAW based micro force sensor basedon the principle of Pierce circuit and the combination withthe design requirements

The high-frequency triode 21198781198623357 affects the resonanceamplifier in the circuit by ensuring the normal startup of theoscillator circuit 119877

1is the DC bias resistance of this triode

and adjusting the value changes with DC working points 1198772

is the DC bias resistance of the triode 1199048050 that changesthe DC working points and transforms the bias current ofthe circuit This triode functions as the current source andstabilizes the circuit working stateThe SAW resonator affectsthe frequency selection in the feedback loop by inducingthe SAW oscillator frequency stability and improving theantijamming ability

To ensure that the feedback loop circuit phase is inbalance the inductance 119871 has been added to the Pierce circuitto eliminate the effect of the stability of the DC voltage sourcefrom the oscillator circuit The LC parallel resonant circuitalso affects the DC bypass circuit The feedback coefficient 119865is related to 119862

1and 119862

2and is given as

119865 =1198621

1198622

(8)

where 1198623 1198624 and 119871

2are the decoupling devices of the DC

source that can eliminate the effect of the oscillator circuitfrom the LC filter function

33 Determine the Parameters Thecircuit layout selection ofcomponents and calculated parameters are important Thework frequency of the micro force sensor is 50MHz thecenter frequency of the LC parallel resonant circuit shouldbe

1198910=

1

2120587radicLC (9)

To ensure that the amplitude of oscillator circuit hasbetter characteristics than the initial conditions 119862

2should

be smaller In addition the designed oscillator frequency isgiven the capacitance is selected as 51 pF From (10) 119871 canbe obtained as

119871 =1

(21205871198910)2

119862

(10)

Because parasitic parameters in practical circuits affecttheir performances 119871 must be adjustable By changing thenumber of turns of the air-core coil the coil inductance canbe fine-tuned and the frequency of the LC parallel resonantcircuit will be in accordance with the working frequency

SAW

1

2

s8050

2SC3357

OutL1

L = 298nH

R1

R = 27kOhm

C1

C2

C = 5pF

C = 5pF

R2

R = 27kOhm

L2

L = 298nH

C3

C4

+ minus3V

Figure 5 The Pierce circuit of the SAW based micro force sensor

of the SAW based micro force sensor The air-core coilinductance has been calculated by the following equation

119871 =001 times 119863 times 119873

2

(119871119873119863) + 044

(11)

where 119871 is the coil inductance (in 120583H) 119863 is the diameter ofthe coil (in cm)119873 is the number of coil turns and 119871119873 is thecoil length (in cm)

An oscillator frequency source should have good stabilityphase noise and high 119876 value [18] Figure 6 shows theequivalent circuit with 119862

2expressed in picofarads

The SAW resonator can work in series or parallel reso-nant frequencies upon operating in the feedback loop Thetransistor 21198781198623357 and 1199048050 provide the DC bias current inthe oscillator circuit design based on the requirements

4 The Linear Regression Model of the SAWBased Micro Force Sensor

41 Establishment of the Linear Regression Model Aftergetting the pressure of SAW sensor (119865

119898) and the output

frequency (119891) from the actual oscillator circuit the fittingfunction should be established The relationship between thepressure of this sensor (119865

119898) and the output frequency (119891) is

given as follows

119865119898= 1198960+ 1198961Δ119891 + 119896

2Δ1198912

+ 1198963Δ1198913

+ sdot sdot sdot + 119896119899Δ119891119899

sdot sdot sdot (12)

If 119865119894 119891119894 119894 = 1 2 119899 and 119899 = 5 the method of least

squares can be used to solve this function is given as

119865119898= 1198960+ 1198961Δ119891 + 119896

2Δ1198912

+ 1198963Δ1198913

+ 1198964Δ1198914

+ 1198965Δ1198915

+ 1198966Δ1198916

(13)

Mathematical Problems in Engineering 5

P1

C1

C2

L1

P2

Figure 6 The equivalent circuit of the SAW device

The regression coefficients 1198960 1198961 1198962 1198963 1198964 1198965 and 119896

6

can be calculated through formula (13)

42 Calculate the Input and Output Variable RegressionThe sum of the variance (119876) between the dependent andindependent variables is given as [19]

119876 (1198960minus 1198966) =

119873

sum

119894=1

Δ2

119894

=

119873

sum

119894=1

[Δ119891119894minus 119865119894]2

(14)

where 119873 is the sampling point of the independent variablesTherefore the least squares estimation calculates the mini-mumvalue of119876 which implies that

and

1198960and

1198961and

1198962and

1198963and

1198964and

1198965 and

1198966must suit the following equation

119876(and

1198960and

1198961and

1198962and

1198963and

1198964and

1198965and

1198966)

=

119873

sum

119894=1

[Δ119891119894minus 119865119894]2

= minand

1198960minus

and

1198966

119873

sum

119894=1

[Δ119891119894minus 119865119894]2

(15)

whereand

1198960and

1198961and

1198962and

1198963and

1198964and

1198965 and 119896

6are the respective least

squares estimations of 1198960 1198961 1198962 1198963 1198964 1198965 and 119896

6

When

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198960

100381610038161003816100381610038161003816100381610038161198960=

and

1198960

= 0

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198961

100381610038161003816100381610038161003816100381610038161198960=

and

1198961

= 0

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198962

100381610038161003816100381610038161003816100381610038161198960=

and

1198962

= 0

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198963

100381610038161003816100381610038161003816100381610038161198960=

and

1198963

= 0

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198964

100381610038161003816100381610038161003816100381610038161198960=

and

1198964

= 0

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198965

100381610038161003816100381610038161003816100381610038161198960=

and

1198965

= 0

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198966

100381610038161003816100381610038161003816100381610038161198960=

and

1198966

= 0

(16)

The equation (17) can be derived by formula (15) and (16)119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894] = 0

119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894]Δ119891119894= 0

119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894]Δ1198912

119894

= 0

119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894]Δ1198913

119894

= 0

119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894]Δ1198914

119894

= 0

119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894]Δ1198915

119894

= 0

119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894]Δ1198916

119894

= 0

(17)

Equation (18) can be derived from formulas (14) and (17)Consider

119873and

1198960+and

1198961

119873

sum

119894=1

Δ119891 +and

1198962

119873

sum

119894=1

Δ1198912

+and

1198963

119873

sum

119894=1

Δ1198913

+and

1198964

119873

sum

119894=1

Δ1198914

+and

1198965

119873

sum

119894=1

Δ1198915

+and

1198966

119873

sum

119894=1

Δ1198916

=

119873

sum

119894=1

119865119894

and

1198960

119873

sum

119894=1

Δ119891 +and

1198961

119873

sum

119894=1

Δ1198912

+and

1198962

119873

sum

119894=1

Δ1198913

+and

1198963

119873

sum

119894=1

Δ1198914

+and

1198964

119873

sum

119894=1

Δ1198915

+and

1198965

119873

sum

119894=1

Δ1198916

+and

1198966

119873

sum

119894=1

Δ1198917

=

119873

sum

119894=1

119865119894Δ119891119894

6 Mathematical Problems in Engineering

and

1198960

119873

sum

119894=1

Δ1198912

+and

1198961

119873

sum

119894=1

Δ1198913

+and

1198962

119873

sum

119894=1

Δ1198914

+and

1198963

119873

sum

119894=1

Δ1198915

+and

1198964

119873

sum

119894=1

Δ1198916

+and

1198965

119873

sum

119894=1

Δ1198917

+and

1198966

119873

sum

119894=1

Δ1198918

=

119873

sum

119894=1

119865119894Δ1198912

119894

and

1198960

119873

sum

119894=1

Δ1198913

+and

1198961

119873

sum

119894=1

Δ1198914

+and

1198962

119873

sum

119894=1

Δ1198915

+and

1198963

119873

sum

119894=1

Δ1198916

+and

1198964

119873

sum

119894=1

Δ1198917

+and

1198965

119873

sum

119894=1

Δ1198918

+and

1198966

119873

sum

119894=1

Δ1198919

=

119873

sum

119894=1

119865119894Δ1198913

119894

and

1198960

119873

sum

119894=1

Δ1198914

+and

1198961

119873

sum

119894=1

Δ1198915

+and

1198962

119873

sum

119894=1

Δ1198916

+and

1198963

119873

sum

119894=1

Δ1198917

+and

1198964

119873

sum

119894=1

Δ1198918

+and

1198965

119873

sum

119894=1

Δ1198919

+and

1198966

119873

sum

119894=1

Δ11989110

=

119873

sum

119894=1

119865119894Δ1198914

119894

and

1198960

119873

sum

119894=1

Δ1198915

+and

1198961

119873

sum

119894=1

Δ1198916

+and

1198962

119873

sum

119894=1

Δ1198917

+and

1198963

119873

sum

119894=1

Δ1198918

+and

1198964

119873

sum

119894=1

Δ1198919

+and

1198965

119873

sum

119894=1

Δ11989110

+and

1198966

119873

sum

119894=1

Δ11989111

=

119873

sum

119894=1

119865119894Δ1198915

119894

and

1198960

119873

sum

119894=1

Δ1198916

+and

1198961

119873

sum

119894=1

Δ1198917

+and

1198962

119873

sum

119894=1

Δ1198918

+and

1198963

119873

sum

119894=1

Δ1198919

+and

1198964

119873

sum

119894=1

Δ11989110

+and

1198965

119873

sum

119894=1

Δ11989111

+and

1198966

119873

sum

119894=1

Δ11989112

=

119873

sum

119894=1

119865119894Δ1198916

119894

(18)

Equation (18) can be written as

119873and

1198960+ 119860and

1198961+ 119861and

1198962+ 119862and

1198963+ 119863and

1198964+ 119864and

1198965+ 119865and

1198966= 119872

119860and

1198960+ 119861and

1198961+ 119862and

1198962+ 119863and

1198963+ 119864and

1198964+ 119865and

1198965+ 119866and

1198966= 119875

119861and

1198960+ 119862and

1198961+ 119863and

1198962+ 119864and

1198963+ 119865and

1198964+ 119866and

1198965+ 119867and

1198966= 119876

119862and

1198960+ 119863and

1198961+ 119864and

1198962+ 119865and

1198963+ 119866and

1198964+ 119867and

1198965+ 119868and

1198966= 119877

119863and

1198960+ 119864and

1198961+ 119865and

1198962+ 119866and

1198963+ 119867and

1198964+ 119868and

1198965+ 119869and

1198966= 119878

119864and

1198960+ 119865and

1198961+ 119866and

1198962+ 119867and

1198963+ 119868and

1198964+ 119869and

1198965+ 119870and

1198966= 119879

119865and

1198960+ 119866and

1198961+ 119867and

1198962+ 119868and

1198963+ 119869and

1198964+ 119870and

1198965+ 119871and

1198966= 119880

(19)

where

119860 =

119873

sum

119894=1

Δ119891119894 119861 =

119873

sum

119894=1

Δ1198912

119894

119862 =

119873

sum

119894=1

Δ1198913

119894

119863 =

119873

sum

119894=1

Δ1198914

119894

119864 =

119873

sum

119894=1

Δ1198915

119894

119865 =

119873

sum

119894=1

Δ1198916

119894

119866 =

119873

sum

119894=1

Δ1198917

119894

119867 =

119873

sum

119894=1

Δ1198918

119894

119868 =

119873

sum

119894=1

Δ1198919

119894

119869 =

119873

sum

119894=1

Δ11989110

119894

119870 =

119873

sum

119894=1

Δ11989111

119894

119871 =

119873

sum

119894=1

Δ11989112

119894

119872 =

119873

sum

119894=1

119865119894 119875 =

119873

sum

119894=1

119865119894Δ1198911

119894

119876 =

119873

sum

119894=1

119865119894Δ1198912

119894

119877 =

119873

sum

119894=1

119865119894Δ1198913

119894

119878 =

119873

sum

119894=1

119865119894Δ1198914

119894

119879 =

119873

sum

119894=1

119865119894Δ1198915

119894

119880 =

119873

sum

119894=1

119865119894Δ1198916

119894

(20)

Coefficients 1198960to 1198966in (13) can be obtained and the input

and output variable regression of the SAW based micro forcesensor can be calculated by solving (18)

5 Testing and Analysis of the SAW BasedMicro Force Sensor

51 Actual Circuit Detection Results The output frequencyof the SAW based micro force sensor is conducted by usingthe network analyzer equipment E5061A (Figure 7) Force-measuring elements employ a cantilever beam loaded with0ndash20 kPa pressure and add 2 kPa to this beam at each time[20]

Figure 8 shows the test schematic The SAW based microforce sensor has been designed with a single channel For theinductive components the electromagnetic field interferenceis more sensitive two inductors have been placed at 90∘to reduce interference between these components Figure 9shows the actual circuit In the process of real production thedevice location and the connection between our devices aremore important

Mathematical Problems in Engineering 7

Table 1 Difference in frequency data for various pressures

(kPa)119865119898

0 2 4 6 8 10 12 14 16 18 20119891 (MHz) 49255389 49255391 49255378 49255393 49255434 49255459 49255474 49255481 49255447 49255486 49255497119891 (MHz) 49255321 49255312 49255298 49255296 49255338 49255343 49255357 49255359 49255319 49255361 49255363Δ119891 (Hz) 68 79 80 97 96 116 117 122 128 125 134

Network analyzerE5061A

Input IDT Output IDT

Piezoelectric substrate

Fn

Figure 7 Schematic of the SAW based micro force sensor

DC power Output ScopeThe micro

force sensor of SAW device

Figure 8 Test schematic diagram

52 The Fitting Curve for the Measured Frequency Figure 10shows the actual test waveform diagram [21]

To eliminate the system instability the experimental datahas been averaged in Table 1

Frequency experiment data samples have been gener-ated from (18) according to the different micro pressurereading and the estimated regression coefficients

and

1198960and

1198961and

1198962

and

1198963and

1198964and

1198965andand

1198966can be calculated The method of least

squares can reduce the error due to measurement inaccu-racies caused by the SAW device based micro force sensorThrough the minimization of squared errors of our actualdata the least squares method has the ability to find the bestmatching function data Additionally the fitting curve of theexperimental data shows that the circuit design is reasonableand the device exhibits good linearity (Figure 11) The pres-sure 119865

119898is proportional to the output frequency119891 which has

proved that the SAW detection and pierce oscillator circuithave correct logic function

Based on (13) the available in differentmicro force sensoroutput difference frequency transfer function is

119865119898(Δ119891) = 31441 times 10

minus1

+ 59057 times 10minus2

Δ119891119894

minus 23012 times 10minus4

Δ1198912

119894

+ 54127 times 10minus7

Δ1198913

119894

Table 2 Oscilloscope measurement results

Measurement parameter Averagevalue

Minimumvalue

Maximumvalue

Voltage output (mV) 320 314 326Frequency output(MHz) 492553965 49255296 49255497

minus 60364 times 10minus10

Δ1198914

119894

+ 30200 times 10minus13

Δ1198915

119894

minus 50540 times 10minus17

Δ1198916

119894

(21)

Because of the load impedance having affected the ampli-tude output of the micro force sensor the impedance of theoscilloscope probe during testing is set at 1mΩ to stabilize theoscillator amplitude The working circuit voltage and currentare 3V and 10mA Using the difference in frequency data forvarious pressures in Table 1 the Oscilloscope measurementresult has been calculated in Table 2

6 Conclusion

This paper has addressed three problems in designing theSAW based micro force sensor namely the envelope of IDTthe variable regression and the fitting curve analysis forthe measured frequency which are according to the wavelettransform method SAW detection and pierce oscillatorcircuits

The paper has also proposed themixing frequency circuitfor the reference oscillator and the detector circuit Thechanges between the oscillator frequency and the mea-surement of the parameters can be obtained through thepierce oscillator circuits and the difference in frequency datafor various pressures also can be established by the linearregression model By affecting the production of amplitudeof impedance and parasitic capacitance the output frequencyof 50MHz still has stabilized features and performance Theparameters of frequency amplitude frequency stability andamplitude stability have been measured during the deviceresponse and the sensor simulation

According to the Morlet wavelet transform SAW detec-tion and pierce oscillator circuits the experimental resultshave confirmed that the SAW based micro force sensor canimplement high reproducibility When the input transducerof our device has been designed with the envelope of theconducting strips our device performs well linearity Inaddition the device uses the piezoelectric properties and thetemperature stability of the crystal as well as the frequency

8 Mathematical Problems in Engineering

Figure 9 The actual circuit testing diagram

Figure 10 The actual test waveform diagram

Figure 11 The experimental data fitting curve

signal instead of the conventional pressure sensor withvoltage signal which has made the signal processing of thisdevice more digital and possessed more stable performancesThe SAW based micro force type can be fabricated and has

high performance in either mobile micro robots or a precisepositioning device under the control of mechanical system

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the National Natural ScienceFoundation of China (Grant no 61274078) the ResearchInnovation and Project of the Shanghai Municipal EducationCommission (Grant no 13ZZ049) the Doctoral ScientificFundProject of theMinistry of Education ofChina (Grant no20120075110006) and the Foundation of Shanghai Universityof Engineering Science (Grant no nhky-2013-10)

References

[1] I Daubechies ldquoThe wavelet transform time-frequency local-ization and signal analysisrdquo IEEE Transactions on InformationTheory vol 36 no 5 pp 961ndash1005 1990

[2] D S Ballantine R M White S J Martin et al Acoustic WaveSensor Theory Design and Physico-Chemical ApplicationsAcademic Press New York NY USA 1997

[3] Y H Peng Wavelet Transform and Its Engineering ApplicationScience Press Beijing China 1999 (Chinese)

[4] W K Lu C C Zhu J H Liu and Q Liu ldquoImplementingwavelet transform with SAW elementsrdquo Science in China ETechnological Sciences vol 46 no 6 pp 627ndash638 2003

[5] W-K Lu C-C Zhu J-H Liu and P-Y Wei ldquoStudy onimplementation of surface-acoustic-wave type of the wavelet-transformation and reconstruction elementrdquo Acta ElectronicaSinica vol 30 no 8 pp 1156ndash1159 2002 (Chinese)

[6] K Andra C Chakrabarti and T Acharya ldquoA VLSI architecturefor lifting-based forward and inverse wavelet transformrdquo IEEETransactions on Signal Processing vol 50 no 4 pp 966ndash9772002

[7] K K Parhi and T Nishitani ldquoVLSI architecture for discretewavelet transformsrdquo IEEE Transactions on Very Large ScaleIntegration (VLSI) Systems vol 1 no 2 pp 191ndash202 1993

[8] X Chen X Zhang K Chen and Q Li ldquoOptical wavelet-matched filtering with bacteriorhodopsin filmsrdquoApplied Opticsvol 36 no 32 pp 8413ndash8416 1997

Mathematical Problems in Engineering 9

[9] M von Schickfus R Stanzel T Kammereck D Weiskat WDittrich and H Fuchs ldquoImproving the SAW gas sensor deviceelectronics and sensor layerrdquo Sensors andActuators B Chemicalvol 19 no 1ndash3 pp 443ndash447 1994

[10] M K Tan L Y Yeo and J R Friend ldquoRapid fluid flow andmixing induced inmicrochannels using surface acousticwavesrdquoEurophysics Letters vol 87 no 4 pp 537ndash563 2009

[11] W CWilson D CMalocha N Y Kozlovski et al ldquoOrthogonalfrequency coded SAWsensors for aerospace SHMapplicationsrdquoSensors Journal vol 9 no 11 pp 1546ndash1556 2009

[12] M Jungwirth H Scherr and R Weigel ldquoMicromechanicalprecision pressure sensor incorporating SAW delay linesrdquo ActaMechanica vol 158 no 3-4 pp 227ndash252 2002

[13] S Muntwyler F Beyeler and B J Nelson ldquoThree-axis micro-force sensor with sub-micro-Newtonmeasurement uncertaintyand tunable force rangerdquo Journal of Micromechanics and Micro-engineering vol 20 no 2 pp 3165ndash3170 2010

[14] Y C Kim Y S Ihn H Moon et al ldquoLow cost dual axismicro force sensor for robotic manipulationsrdquo MicrosystemTechnologies vol 17 no 5ndash7 pp 1197ndash1205 2011

[15] K J Singh O Elmazria F Sarry et al ldquoEnhanced sensitivityof SAW-based Pirani vacuum pressure sensorrdquo IEEE SensorsJournal vol 11 no 6 pp 1458ndash1464 2011

[16] C B Wen and C C Zhu ldquoTime synchronous dyadic waveletprocessor array using surface acoustic wave devicesrdquo SmartMaterials and Structures vol 15 no 4 pp 939ndash945 2006

[17] W K Lu C C Zhu J F Zhang C Shi and X Z Lu ldquoStudyof small size wavelet transform processor and wavelet inverse-transform processor using SAWdevicesrdquoMeasurement Journalof the International Measurement Confederation vol 44 no 5pp 994ndash999 2011

[18] Y Kang Design of Surface Acoustic Wave Devices and ItsApplication Oscillator Circuit Changrsquoan University 2011

[19] X Z Lu Interfacial Stress Sensor for Artificial Skin ApplicationDonghua University 2012

[20] Y Y Li W K Lu C C Zhu et al ldquoAcoustic electric generationfor morlet wavelet transform of surface acoustic wave devicerdquoResearch Journal of Applied Sciences Engineering and Technol-ogy vol 5 no 4 pp 1203ndash1207 2013

[21] Y Y Li W K Lu and C C Zhu ldquoPspice equivalent circuitmodel for implementation of surface acoustic wave filterrdquoJournal of Donghua University vol 29 no 2 pp 148ndash152 2012

Submit your manuscripts athttpwwwhindawicom

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Mathematical Problems in Engineering

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Differential EquationsInternational Journal of

Volume 2014

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Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Mathematical PhysicsAdvances in

Complex AnalysisJournal of

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OptimizationJournal of

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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

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Operations ResearchAdvances in

Journal of

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Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

4 Mathematical Problems in Engineering

For a surface acoustic generator as the sensitive element ofthe SAW micro force sensor the frequency stability directlyaffects the resolution of the testing precision The oscillatorfrequency has depended on the conditions of the feedbackloop phaseTherefore the improvement of the SAWoscillatorfrequency stability also improves the performance of themicro force sensor

The Pierce oscillator circuit has a better stability com-paredwithColpitts andClapp circuits [17] Figure 5 shows theoscillator circuit of the SAW based micro force sensor basedon the principle of Pierce circuit and the combination withthe design requirements

The high-frequency triode 21198781198623357 affects the resonanceamplifier in the circuit by ensuring the normal startup of theoscillator circuit 119877

1is the DC bias resistance of this triode

and adjusting the value changes with DC working points 1198772

is the DC bias resistance of the triode 1199048050 that changesthe DC working points and transforms the bias current ofthe circuit This triode functions as the current source andstabilizes the circuit working stateThe SAW resonator affectsthe frequency selection in the feedback loop by inducingthe SAW oscillator frequency stability and improving theantijamming ability

To ensure that the feedback loop circuit phase is inbalance the inductance 119871 has been added to the Pierce circuitto eliminate the effect of the stability of the DC voltage sourcefrom the oscillator circuit The LC parallel resonant circuitalso affects the DC bypass circuit The feedback coefficient 119865is related to 119862

1and 119862

2and is given as

119865 =1198621

1198622

(8)

where 1198623 1198624 and 119871

2are the decoupling devices of the DC

source that can eliminate the effect of the oscillator circuitfrom the LC filter function

33 Determine the Parameters Thecircuit layout selection ofcomponents and calculated parameters are important Thework frequency of the micro force sensor is 50MHz thecenter frequency of the LC parallel resonant circuit shouldbe

1198910=

1

2120587radicLC (9)

To ensure that the amplitude of oscillator circuit hasbetter characteristics than the initial conditions 119862

2should

be smaller In addition the designed oscillator frequency isgiven the capacitance is selected as 51 pF From (10) 119871 canbe obtained as

119871 =1

(21205871198910)2

119862

(10)

Because parasitic parameters in practical circuits affecttheir performances 119871 must be adjustable By changing thenumber of turns of the air-core coil the coil inductance canbe fine-tuned and the frequency of the LC parallel resonantcircuit will be in accordance with the working frequency

SAW

1

2

s8050

2SC3357

OutL1

L = 298nH

R1

R = 27kOhm

C1

C2

C = 5pF

C = 5pF

R2

R = 27kOhm

L2

L = 298nH

C3

C4

+ minus3V

Figure 5 The Pierce circuit of the SAW based micro force sensor

of the SAW based micro force sensor The air-core coilinductance has been calculated by the following equation

119871 =001 times 119863 times 119873

2

(119871119873119863) + 044

(11)

where 119871 is the coil inductance (in 120583H) 119863 is the diameter ofthe coil (in cm)119873 is the number of coil turns and 119871119873 is thecoil length (in cm)

An oscillator frequency source should have good stabilityphase noise and high 119876 value [18] Figure 6 shows theequivalent circuit with 119862

2expressed in picofarads

The SAW resonator can work in series or parallel reso-nant frequencies upon operating in the feedback loop Thetransistor 21198781198623357 and 1199048050 provide the DC bias current inthe oscillator circuit design based on the requirements

4 The Linear Regression Model of the SAWBased Micro Force Sensor

41 Establishment of the Linear Regression Model Aftergetting the pressure of SAW sensor (119865

119898) and the output

frequency (119891) from the actual oscillator circuit the fittingfunction should be established The relationship between thepressure of this sensor (119865

119898) and the output frequency (119891) is

given as follows

119865119898= 1198960+ 1198961Δ119891 + 119896

2Δ1198912

+ 1198963Δ1198913

+ sdot sdot sdot + 119896119899Δ119891119899

sdot sdot sdot (12)

If 119865119894 119891119894 119894 = 1 2 119899 and 119899 = 5 the method of least

squares can be used to solve this function is given as

119865119898= 1198960+ 1198961Δ119891 + 119896

2Δ1198912

+ 1198963Δ1198913

+ 1198964Δ1198914

+ 1198965Δ1198915

+ 1198966Δ1198916

(13)

Mathematical Problems in Engineering 5

P1

C1

C2

L1

P2

Figure 6 The equivalent circuit of the SAW device

The regression coefficients 1198960 1198961 1198962 1198963 1198964 1198965 and 119896

6

can be calculated through formula (13)

42 Calculate the Input and Output Variable RegressionThe sum of the variance (119876) between the dependent andindependent variables is given as [19]

119876 (1198960minus 1198966) =

119873

sum

119894=1

Δ2

119894

=

119873

sum

119894=1

[Δ119891119894minus 119865119894]2

(14)

where 119873 is the sampling point of the independent variablesTherefore the least squares estimation calculates the mini-mumvalue of119876 which implies that

and

1198960and

1198961and

1198962and

1198963and

1198964and

1198965 and

1198966must suit the following equation

119876(and

1198960and

1198961and

1198962and

1198963and

1198964and

1198965and

1198966)

=

119873

sum

119894=1

[Δ119891119894minus 119865119894]2

= minand

1198960minus

and

1198966

119873

sum

119894=1

[Δ119891119894minus 119865119894]2

(15)

whereand

1198960and

1198961and

1198962and

1198963and

1198964and

1198965 and 119896

6are the respective least

squares estimations of 1198960 1198961 1198962 1198963 1198964 1198965 and 119896

6

When

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198960

100381610038161003816100381610038161003816100381610038161198960=

and

1198960

= 0

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198961

100381610038161003816100381610038161003816100381610038161198960=

and

1198961

= 0

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198962

100381610038161003816100381610038161003816100381610038161198960=

and

1198962

= 0

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198963

100381610038161003816100381610038161003816100381610038161198960=

and

1198963

= 0

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198964

100381610038161003816100381610038161003816100381610038161198960=

and

1198964

= 0

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198965

100381610038161003816100381610038161003816100381610038161198960=

and

1198965

= 0

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198966

100381610038161003816100381610038161003816100381610038161198960=

and

1198966

= 0

(16)

The equation (17) can be derived by formula (15) and (16)119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894] = 0

119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894]Δ119891119894= 0

119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894]Δ1198912

119894

= 0

119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894]Δ1198913

119894

= 0

119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894]Δ1198914

119894

= 0

119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894]Δ1198915

119894

= 0

119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894]Δ1198916

119894

= 0

(17)

Equation (18) can be derived from formulas (14) and (17)Consider

119873and

1198960+and

1198961

119873

sum

119894=1

Δ119891 +and

1198962

119873

sum

119894=1

Δ1198912

+and

1198963

119873

sum

119894=1

Δ1198913

+and

1198964

119873

sum

119894=1

Δ1198914

+and

1198965

119873

sum

119894=1

Δ1198915

+and

1198966

119873

sum

119894=1

Δ1198916

=

119873

sum

119894=1

119865119894

and

1198960

119873

sum

119894=1

Δ119891 +and

1198961

119873

sum

119894=1

Δ1198912

+and

1198962

119873

sum

119894=1

Δ1198913

+and

1198963

119873

sum

119894=1

Δ1198914

+and

1198964

119873

sum

119894=1

Δ1198915

+and

1198965

119873

sum

119894=1

Δ1198916

+and

1198966

119873

sum

119894=1

Δ1198917

=

119873

sum

119894=1

119865119894Δ119891119894

6 Mathematical Problems in Engineering

and

1198960

119873

sum

119894=1

Δ1198912

+and

1198961

119873

sum

119894=1

Δ1198913

+and

1198962

119873

sum

119894=1

Δ1198914

+and

1198963

119873

sum

119894=1

Δ1198915

+and

1198964

119873

sum

119894=1

Δ1198916

+and

1198965

119873

sum

119894=1

Δ1198917

+and

1198966

119873

sum

119894=1

Δ1198918

=

119873

sum

119894=1

119865119894Δ1198912

119894

and

1198960

119873

sum

119894=1

Δ1198913

+and

1198961

119873

sum

119894=1

Δ1198914

+and

1198962

119873

sum

119894=1

Δ1198915

+and

1198963

119873

sum

119894=1

Δ1198916

+and

1198964

119873

sum

119894=1

Δ1198917

+and

1198965

119873

sum

119894=1

Δ1198918

+and

1198966

119873

sum

119894=1

Δ1198919

=

119873

sum

119894=1

119865119894Δ1198913

119894

and

1198960

119873

sum

119894=1

Δ1198914

+and

1198961

119873

sum

119894=1

Δ1198915

+and

1198962

119873

sum

119894=1

Δ1198916

+and

1198963

119873

sum

119894=1

Δ1198917

+and

1198964

119873

sum

119894=1

Δ1198918

+and

1198965

119873

sum

119894=1

Δ1198919

+and

1198966

119873

sum

119894=1

Δ11989110

=

119873

sum

119894=1

119865119894Δ1198914

119894

and

1198960

119873

sum

119894=1

Δ1198915

+and

1198961

119873

sum

119894=1

Δ1198916

+and

1198962

119873

sum

119894=1

Δ1198917

+and

1198963

119873

sum

119894=1

Δ1198918

+and

1198964

119873

sum

119894=1

Δ1198919

+and

1198965

119873

sum

119894=1

Δ11989110

+and

1198966

119873

sum

119894=1

Δ11989111

=

119873

sum

119894=1

119865119894Δ1198915

119894

and

1198960

119873

sum

119894=1

Δ1198916

+and

1198961

119873

sum

119894=1

Δ1198917

+and

1198962

119873

sum

119894=1

Δ1198918

+and

1198963

119873

sum

119894=1

Δ1198919

+and

1198964

119873

sum

119894=1

Δ11989110

+and

1198965

119873

sum

119894=1

Δ11989111

+and

1198966

119873

sum

119894=1

Δ11989112

=

119873

sum

119894=1

119865119894Δ1198916

119894

(18)

Equation (18) can be written as

119873and

1198960+ 119860and

1198961+ 119861and

1198962+ 119862and

1198963+ 119863and

1198964+ 119864and

1198965+ 119865and

1198966= 119872

119860and

1198960+ 119861and

1198961+ 119862and

1198962+ 119863and

1198963+ 119864and

1198964+ 119865and

1198965+ 119866and

1198966= 119875

119861and

1198960+ 119862and

1198961+ 119863and

1198962+ 119864and

1198963+ 119865and

1198964+ 119866and

1198965+ 119867and

1198966= 119876

119862and

1198960+ 119863and

1198961+ 119864and

1198962+ 119865and

1198963+ 119866and

1198964+ 119867and

1198965+ 119868and

1198966= 119877

119863and

1198960+ 119864and

1198961+ 119865and

1198962+ 119866and

1198963+ 119867and

1198964+ 119868and

1198965+ 119869and

1198966= 119878

119864and

1198960+ 119865and

1198961+ 119866and

1198962+ 119867and

1198963+ 119868and

1198964+ 119869and

1198965+ 119870and

1198966= 119879

119865and

1198960+ 119866and

1198961+ 119867and

1198962+ 119868and

1198963+ 119869and

1198964+ 119870and

1198965+ 119871and

1198966= 119880

(19)

where

119860 =

119873

sum

119894=1

Δ119891119894 119861 =

119873

sum

119894=1

Δ1198912

119894

119862 =

119873

sum

119894=1

Δ1198913

119894

119863 =

119873

sum

119894=1

Δ1198914

119894

119864 =

119873

sum

119894=1

Δ1198915

119894

119865 =

119873

sum

119894=1

Δ1198916

119894

119866 =

119873

sum

119894=1

Δ1198917

119894

119867 =

119873

sum

119894=1

Δ1198918

119894

119868 =

119873

sum

119894=1

Δ1198919

119894

119869 =

119873

sum

119894=1

Δ11989110

119894

119870 =

119873

sum

119894=1

Δ11989111

119894

119871 =

119873

sum

119894=1

Δ11989112

119894

119872 =

119873

sum

119894=1

119865119894 119875 =

119873

sum

119894=1

119865119894Δ1198911

119894

119876 =

119873

sum

119894=1

119865119894Δ1198912

119894

119877 =

119873

sum

119894=1

119865119894Δ1198913

119894

119878 =

119873

sum

119894=1

119865119894Δ1198914

119894

119879 =

119873

sum

119894=1

119865119894Δ1198915

119894

119880 =

119873

sum

119894=1

119865119894Δ1198916

119894

(20)

Coefficients 1198960to 1198966in (13) can be obtained and the input

and output variable regression of the SAW based micro forcesensor can be calculated by solving (18)

5 Testing and Analysis of the SAW BasedMicro Force Sensor

51 Actual Circuit Detection Results The output frequencyof the SAW based micro force sensor is conducted by usingthe network analyzer equipment E5061A (Figure 7) Force-measuring elements employ a cantilever beam loaded with0ndash20 kPa pressure and add 2 kPa to this beam at each time[20]

Figure 8 shows the test schematic The SAW based microforce sensor has been designed with a single channel For theinductive components the electromagnetic field interferenceis more sensitive two inductors have been placed at 90∘to reduce interference between these components Figure 9shows the actual circuit In the process of real production thedevice location and the connection between our devices aremore important

Mathematical Problems in Engineering 7

Table 1 Difference in frequency data for various pressures

(kPa)119865119898

0 2 4 6 8 10 12 14 16 18 20119891 (MHz) 49255389 49255391 49255378 49255393 49255434 49255459 49255474 49255481 49255447 49255486 49255497119891 (MHz) 49255321 49255312 49255298 49255296 49255338 49255343 49255357 49255359 49255319 49255361 49255363Δ119891 (Hz) 68 79 80 97 96 116 117 122 128 125 134

Network analyzerE5061A

Input IDT Output IDT

Piezoelectric substrate

Fn

Figure 7 Schematic of the SAW based micro force sensor

DC power Output ScopeThe micro

force sensor of SAW device

Figure 8 Test schematic diagram

52 The Fitting Curve for the Measured Frequency Figure 10shows the actual test waveform diagram [21]

To eliminate the system instability the experimental datahas been averaged in Table 1

Frequency experiment data samples have been gener-ated from (18) according to the different micro pressurereading and the estimated regression coefficients

and

1198960and

1198961and

1198962

and

1198963and

1198964and

1198965andand

1198966can be calculated The method of least

squares can reduce the error due to measurement inaccu-racies caused by the SAW device based micro force sensorThrough the minimization of squared errors of our actualdata the least squares method has the ability to find the bestmatching function data Additionally the fitting curve of theexperimental data shows that the circuit design is reasonableand the device exhibits good linearity (Figure 11) The pres-sure 119865

119898is proportional to the output frequency119891 which has

proved that the SAW detection and pierce oscillator circuithave correct logic function

Based on (13) the available in differentmicro force sensoroutput difference frequency transfer function is

119865119898(Δ119891) = 31441 times 10

minus1

+ 59057 times 10minus2

Δ119891119894

minus 23012 times 10minus4

Δ1198912

119894

+ 54127 times 10minus7

Δ1198913

119894

Table 2 Oscilloscope measurement results

Measurement parameter Averagevalue

Minimumvalue

Maximumvalue

Voltage output (mV) 320 314 326Frequency output(MHz) 492553965 49255296 49255497

minus 60364 times 10minus10

Δ1198914

119894

+ 30200 times 10minus13

Δ1198915

119894

minus 50540 times 10minus17

Δ1198916

119894

(21)

Because of the load impedance having affected the ampli-tude output of the micro force sensor the impedance of theoscilloscope probe during testing is set at 1mΩ to stabilize theoscillator amplitude The working circuit voltage and currentare 3V and 10mA Using the difference in frequency data forvarious pressures in Table 1 the Oscilloscope measurementresult has been calculated in Table 2

6 Conclusion

This paper has addressed three problems in designing theSAW based micro force sensor namely the envelope of IDTthe variable regression and the fitting curve analysis forthe measured frequency which are according to the wavelettransform method SAW detection and pierce oscillatorcircuits

The paper has also proposed themixing frequency circuitfor the reference oscillator and the detector circuit Thechanges between the oscillator frequency and the mea-surement of the parameters can be obtained through thepierce oscillator circuits and the difference in frequency datafor various pressures also can be established by the linearregression model By affecting the production of amplitudeof impedance and parasitic capacitance the output frequencyof 50MHz still has stabilized features and performance Theparameters of frequency amplitude frequency stability andamplitude stability have been measured during the deviceresponse and the sensor simulation

According to the Morlet wavelet transform SAW detec-tion and pierce oscillator circuits the experimental resultshave confirmed that the SAW based micro force sensor canimplement high reproducibility When the input transducerof our device has been designed with the envelope of theconducting strips our device performs well linearity Inaddition the device uses the piezoelectric properties and thetemperature stability of the crystal as well as the frequency

8 Mathematical Problems in Engineering

Figure 9 The actual circuit testing diagram

Figure 10 The actual test waveform diagram

Figure 11 The experimental data fitting curve

signal instead of the conventional pressure sensor withvoltage signal which has made the signal processing of thisdevice more digital and possessed more stable performancesThe SAW based micro force type can be fabricated and has

high performance in either mobile micro robots or a precisepositioning device under the control of mechanical system

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the National Natural ScienceFoundation of China (Grant no 61274078) the ResearchInnovation and Project of the Shanghai Municipal EducationCommission (Grant no 13ZZ049) the Doctoral ScientificFundProject of theMinistry of Education ofChina (Grant no20120075110006) and the Foundation of Shanghai Universityof Engineering Science (Grant no nhky-2013-10)

References

[1] I Daubechies ldquoThe wavelet transform time-frequency local-ization and signal analysisrdquo IEEE Transactions on InformationTheory vol 36 no 5 pp 961ndash1005 1990

[2] D S Ballantine R M White S J Martin et al Acoustic WaveSensor Theory Design and Physico-Chemical ApplicationsAcademic Press New York NY USA 1997

[3] Y H Peng Wavelet Transform and Its Engineering ApplicationScience Press Beijing China 1999 (Chinese)

[4] W K Lu C C Zhu J H Liu and Q Liu ldquoImplementingwavelet transform with SAW elementsrdquo Science in China ETechnological Sciences vol 46 no 6 pp 627ndash638 2003

[5] W-K Lu C-C Zhu J-H Liu and P-Y Wei ldquoStudy onimplementation of surface-acoustic-wave type of the wavelet-transformation and reconstruction elementrdquo Acta ElectronicaSinica vol 30 no 8 pp 1156ndash1159 2002 (Chinese)

[6] K Andra C Chakrabarti and T Acharya ldquoA VLSI architecturefor lifting-based forward and inverse wavelet transformrdquo IEEETransactions on Signal Processing vol 50 no 4 pp 966ndash9772002

[7] K K Parhi and T Nishitani ldquoVLSI architecture for discretewavelet transformsrdquo IEEE Transactions on Very Large ScaleIntegration (VLSI) Systems vol 1 no 2 pp 191ndash202 1993

[8] X Chen X Zhang K Chen and Q Li ldquoOptical wavelet-matched filtering with bacteriorhodopsin filmsrdquoApplied Opticsvol 36 no 32 pp 8413ndash8416 1997

Mathematical Problems in Engineering 9

[9] M von Schickfus R Stanzel T Kammereck D Weiskat WDittrich and H Fuchs ldquoImproving the SAW gas sensor deviceelectronics and sensor layerrdquo Sensors andActuators B Chemicalvol 19 no 1ndash3 pp 443ndash447 1994

[10] M K Tan L Y Yeo and J R Friend ldquoRapid fluid flow andmixing induced inmicrochannels using surface acousticwavesrdquoEurophysics Letters vol 87 no 4 pp 537ndash563 2009

[11] W CWilson D CMalocha N Y Kozlovski et al ldquoOrthogonalfrequency coded SAWsensors for aerospace SHMapplicationsrdquoSensors Journal vol 9 no 11 pp 1546ndash1556 2009

[12] M Jungwirth H Scherr and R Weigel ldquoMicromechanicalprecision pressure sensor incorporating SAW delay linesrdquo ActaMechanica vol 158 no 3-4 pp 227ndash252 2002

[13] S Muntwyler F Beyeler and B J Nelson ldquoThree-axis micro-force sensor with sub-micro-Newtonmeasurement uncertaintyand tunable force rangerdquo Journal of Micromechanics and Micro-engineering vol 20 no 2 pp 3165ndash3170 2010

[14] Y C Kim Y S Ihn H Moon et al ldquoLow cost dual axismicro force sensor for robotic manipulationsrdquo MicrosystemTechnologies vol 17 no 5ndash7 pp 1197ndash1205 2011

[15] K J Singh O Elmazria F Sarry et al ldquoEnhanced sensitivityof SAW-based Pirani vacuum pressure sensorrdquo IEEE SensorsJournal vol 11 no 6 pp 1458ndash1464 2011

[16] C B Wen and C C Zhu ldquoTime synchronous dyadic waveletprocessor array using surface acoustic wave devicesrdquo SmartMaterials and Structures vol 15 no 4 pp 939ndash945 2006

[17] W K Lu C C Zhu J F Zhang C Shi and X Z Lu ldquoStudyof small size wavelet transform processor and wavelet inverse-transform processor using SAWdevicesrdquoMeasurement Journalof the International Measurement Confederation vol 44 no 5pp 994ndash999 2011

[18] Y Kang Design of Surface Acoustic Wave Devices and ItsApplication Oscillator Circuit Changrsquoan University 2011

[19] X Z Lu Interfacial Stress Sensor for Artificial Skin ApplicationDonghua University 2012

[20] Y Y Li W K Lu C C Zhu et al ldquoAcoustic electric generationfor morlet wavelet transform of surface acoustic wave devicerdquoResearch Journal of Applied Sciences Engineering and Technol-ogy vol 5 no 4 pp 1203ndash1207 2013

[21] Y Y Li W K Lu and C C Zhu ldquoPspice equivalent circuitmodel for implementation of surface acoustic wave filterrdquoJournal of Donghua University vol 29 no 2 pp 148ndash152 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

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OptimizationJournal of

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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

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Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 5

P1

C1

C2

L1

P2

Figure 6 The equivalent circuit of the SAW device

The regression coefficients 1198960 1198961 1198962 1198963 1198964 1198965 and 119896

6

can be calculated through formula (13)

42 Calculate the Input and Output Variable RegressionThe sum of the variance (119876) between the dependent andindependent variables is given as [19]

119876 (1198960minus 1198966) =

119873

sum

119894=1

Δ2

119894

=

119873

sum

119894=1

[Δ119891119894minus 119865119894]2

(14)

where 119873 is the sampling point of the independent variablesTherefore the least squares estimation calculates the mini-mumvalue of119876 which implies that

and

1198960and

1198961and

1198962and

1198963and

1198964and

1198965 and

1198966must suit the following equation

119876(and

1198960and

1198961and

1198962and

1198963and

1198964and

1198965and

1198966)

=

119873

sum

119894=1

[Δ119891119894minus 119865119894]2

= minand

1198960minus

and

1198966

119873

sum

119894=1

[Δ119891119894minus 119865119894]2

(15)

whereand

1198960and

1198961and

1198962and

1198963and

1198964and

1198965 and 119896

6are the respective least

squares estimations of 1198960 1198961 1198962 1198963 1198964 1198965 and 119896

6

When

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198960

100381610038161003816100381610038161003816100381610038161198960=

and

1198960

= 0

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198961

100381610038161003816100381610038161003816100381610038161198960=

and

1198961

= 0

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198962

100381610038161003816100381610038161003816100381610038161198960=

and

1198962

= 0

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198963

100381610038161003816100381610038161003816100381610038161198960=

and

1198963

= 0

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198964

100381610038161003816100381610038161003816100381610038161198960=

and

1198964

= 0

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198965

100381610038161003816100381610038161003816100381610038161198960=

and

1198965

= 0

120597119876(1198960 1198961 1198962 1198963 1198964 1198965)

1205971198966

100381610038161003816100381610038161003816100381610038161198960=

and

1198966

= 0

(16)

The equation (17) can be derived by formula (15) and (16)119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894] = 0

119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894]Δ119891119894= 0

119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894]Δ1198912

119894

= 0

119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894]Δ1198913

119894

= 0

119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894]Δ1198914

119894

= 0

119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894]Δ1198915

119894

= 0

119873

sum

119894=1

[(

and

1198960+

and

1198961Δ119891119894+

and

1198962Δ1198912

119894

+

and

1198963Δ1198913

119894

+

and

1198964Δ1198914

119894

+

and

1198965Δ1198915

119894

+

and

1198966Δ1198916

119894

) minus 119865119894]Δ1198916

119894

= 0

(17)

Equation (18) can be derived from formulas (14) and (17)Consider

119873and

1198960+and

1198961

119873

sum

119894=1

Δ119891 +and

1198962

119873

sum

119894=1

Δ1198912

+and

1198963

119873

sum

119894=1

Δ1198913

+and

1198964

119873

sum

119894=1

Δ1198914

+and

1198965

119873

sum

119894=1

Δ1198915

+and

1198966

119873

sum

119894=1

Δ1198916

=

119873

sum

119894=1

119865119894

and

1198960

119873

sum

119894=1

Δ119891 +and

1198961

119873

sum

119894=1

Δ1198912

+and

1198962

119873

sum

119894=1

Δ1198913

+and

1198963

119873

sum

119894=1

Δ1198914

+and

1198964

119873

sum

119894=1

Δ1198915

+and

1198965

119873

sum

119894=1

Δ1198916

+and

1198966

119873

sum

119894=1

Δ1198917

=

119873

sum

119894=1

119865119894Δ119891119894

6 Mathematical Problems in Engineering

and

1198960

119873

sum

119894=1

Δ1198912

+and

1198961

119873

sum

119894=1

Δ1198913

+and

1198962

119873

sum

119894=1

Δ1198914

+and

1198963

119873

sum

119894=1

Δ1198915

+and

1198964

119873

sum

119894=1

Δ1198916

+and

1198965

119873

sum

119894=1

Δ1198917

+and

1198966

119873

sum

119894=1

Δ1198918

=

119873

sum

119894=1

119865119894Δ1198912

119894

and

1198960

119873

sum

119894=1

Δ1198913

+and

1198961

119873

sum

119894=1

Δ1198914

+and

1198962

119873

sum

119894=1

Δ1198915

+and

1198963

119873

sum

119894=1

Δ1198916

+and

1198964

119873

sum

119894=1

Δ1198917

+and

1198965

119873

sum

119894=1

Δ1198918

+and

1198966

119873

sum

119894=1

Δ1198919

=

119873

sum

119894=1

119865119894Δ1198913

119894

and

1198960

119873

sum

119894=1

Δ1198914

+and

1198961

119873

sum

119894=1

Δ1198915

+and

1198962

119873

sum

119894=1

Δ1198916

+and

1198963

119873

sum

119894=1

Δ1198917

+and

1198964

119873

sum

119894=1

Δ1198918

+and

1198965

119873

sum

119894=1

Δ1198919

+and

1198966

119873

sum

119894=1

Δ11989110

=

119873

sum

119894=1

119865119894Δ1198914

119894

and

1198960

119873

sum

119894=1

Δ1198915

+and

1198961

119873

sum

119894=1

Δ1198916

+and

1198962

119873

sum

119894=1

Δ1198917

+and

1198963

119873

sum

119894=1

Δ1198918

+and

1198964

119873

sum

119894=1

Δ1198919

+and

1198965

119873

sum

119894=1

Δ11989110

+and

1198966

119873

sum

119894=1

Δ11989111

=

119873

sum

119894=1

119865119894Δ1198915

119894

and

1198960

119873

sum

119894=1

Δ1198916

+and

1198961

119873

sum

119894=1

Δ1198917

+and

1198962

119873

sum

119894=1

Δ1198918

+and

1198963

119873

sum

119894=1

Δ1198919

+and

1198964

119873

sum

119894=1

Δ11989110

+and

1198965

119873

sum

119894=1

Δ11989111

+and

1198966

119873

sum

119894=1

Δ11989112

=

119873

sum

119894=1

119865119894Δ1198916

119894

(18)

Equation (18) can be written as

119873and

1198960+ 119860and

1198961+ 119861and

1198962+ 119862and

1198963+ 119863and

1198964+ 119864and

1198965+ 119865and

1198966= 119872

119860and

1198960+ 119861and

1198961+ 119862and

1198962+ 119863and

1198963+ 119864and

1198964+ 119865and

1198965+ 119866and

1198966= 119875

119861and

1198960+ 119862and

1198961+ 119863and

1198962+ 119864and

1198963+ 119865and

1198964+ 119866and

1198965+ 119867and

1198966= 119876

119862and

1198960+ 119863and

1198961+ 119864and

1198962+ 119865and

1198963+ 119866and

1198964+ 119867and

1198965+ 119868and

1198966= 119877

119863and

1198960+ 119864and

1198961+ 119865and

1198962+ 119866and

1198963+ 119867and

1198964+ 119868and

1198965+ 119869and

1198966= 119878

119864and

1198960+ 119865and

1198961+ 119866and

1198962+ 119867and

1198963+ 119868and

1198964+ 119869and

1198965+ 119870and

1198966= 119879

119865and

1198960+ 119866and

1198961+ 119867and

1198962+ 119868and

1198963+ 119869and

1198964+ 119870and

1198965+ 119871and

1198966= 119880

(19)

where

119860 =

119873

sum

119894=1

Δ119891119894 119861 =

119873

sum

119894=1

Δ1198912

119894

119862 =

119873

sum

119894=1

Δ1198913

119894

119863 =

119873

sum

119894=1

Δ1198914

119894

119864 =

119873

sum

119894=1

Δ1198915

119894

119865 =

119873

sum

119894=1

Δ1198916

119894

119866 =

119873

sum

119894=1

Δ1198917

119894

119867 =

119873

sum

119894=1

Δ1198918

119894

119868 =

119873

sum

119894=1

Δ1198919

119894

119869 =

119873

sum

119894=1

Δ11989110

119894

119870 =

119873

sum

119894=1

Δ11989111

119894

119871 =

119873

sum

119894=1

Δ11989112

119894

119872 =

119873

sum

119894=1

119865119894 119875 =

119873

sum

119894=1

119865119894Δ1198911

119894

119876 =

119873

sum

119894=1

119865119894Δ1198912

119894

119877 =

119873

sum

119894=1

119865119894Δ1198913

119894

119878 =

119873

sum

119894=1

119865119894Δ1198914

119894

119879 =

119873

sum

119894=1

119865119894Δ1198915

119894

119880 =

119873

sum

119894=1

119865119894Δ1198916

119894

(20)

Coefficients 1198960to 1198966in (13) can be obtained and the input

and output variable regression of the SAW based micro forcesensor can be calculated by solving (18)

5 Testing and Analysis of the SAW BasedMicro Force Sensor

51 Actual Circuit Detection Results The output frequencyof the SAW based micro force sensor is conducted by usingthe network analyzer equipment E5061A (Figure 7) Force-measuring elements employ a cantilever beam loaded with0ndash20 kPa pressure and add 2 kPa to this beam at each time[20]

Figure 8 shows the test schematic The SAW based microforce sensor has been designed with a single channel For theinductive components the electromagnetic field interferenceis more sensitive two inductors have been placed at 90∘to reduce interference between these components Figure 9shows the actual circuit In the process of real production thedevice location and the connection between our devices aremore important

Mathematical Problems in Engineering 7

Table 1 Difference in frequency data for various pressures

(kPa)119865119898

0 2 4 6 8 10 12 14 16 18 20119891 (MHz) 49255389 49255391 49255378 49255393 49255434 49255459 49255474 49255481 49255447 49255486 49255497119891 (MHz) 49255321 49255312 49255298 49255296 49255338 49255343 49255357 49255359 49255319 49255361 49255363Δ119891 (Hz) 68 79 80 97 96 116 117 122 128 125 134

Network analyzerE5061A

Input IDT Output IDT

Piezoelectric substrate

Fn

Figure 7 Schematic of the SAW based micro force sensor

DC power Output ScopeThe micro

force sensor of SAW device

Figure 8 Test schematic diagram

52 The Fitting Curve for the Measured Frequency Figure 10shows the actual test waveform diagram [21]

To eliminate the system instability the experimental datahas been averaged in Table 1

Frequency experiment data samples have been gener-ated from (18) according to the different micro pressurereading and the estimated regression coefficients

and

1198960and

1198961and

1198962

and

1198963and

1198964and

1198965andand

1198966can be calculated The method of least

squares can reduce the error due to measurement inaccu-racies caused by the SAW device based micro force sensorThrough the minimization of squared errors of our actualdata the least squares method has the ability to find the bestmatching function data Additionally the fitting curve of theexperimental data shows that the circuit design is reasonableand the device exhibits good linearity (Figure 11) The pres-sure 119865

119898is proportional to the output frequency119891 which has

proved that the SAW detection and pierce oscillator circuithave correct logic function

Based on (13) the available in differentmicro force sensoroutput difference frequency transfer function is

119865119898(Δ119891) = 31441 times 10

minus1

+ 59057 times 10minus2

Δ119891119894

minus 23012 times 10minus4

Δ1198912

119894

+ 54127 times 10minus7

Δ1198913

119894

Table 2 Oscilloscope measurement results

Measurement parameter Averagevalue

Minimumvalue

Maximumvalue

Voltage output (mV) 320 314 326Frequency output(MHz) 492553965 49255296 49255497

minus 60364 times 10minus10

Δ1198914

119894

+ 30200 times 10minus13

Δ1198915

119894

minus 50540 times 10minus17

Δ1198916

119894

(21)

Because of the load impedance having affected the ampli-tude output of the micro force sensor the impedance of theoscilloscope probe during testing is set at 1mΩ to stabilize theoscillator amplitude The working circuit voltage and currentare 3V and 10mA Using the difference in frequency data forvarious pressures in Table 1 the Oscilloscope measurementresult has been calculated in Table 2

6 Conclusion

This paper has addressed three problems in designing theSAW based micro force sensor namely the envelope of IDTthe variable regression and the fitting curve analysis forthe measured frequency which are according to the wavelettransform method SAW detection and pierce oscillatorcircuits

The paper has also proposed themixing frequency circuitfor the reference oscillator and the detector circuit Thechanges between the oscillator frequency and the mea-surement of the parameters can be obtained through thepierce oscillator circuits and the difference in frequency datafor various pressures also can be established by the linearregression model By affecting the production of amplitudeof impedance and parasitic capacitance the output frequencyof 50MHz still has stabilized features and performance Theparameters of frequency amplitude frequency stability andamplitude stability have been measured during the deviceresponse and the sensor simulation

According to the Morlet wavelet transform SAW detec-tion and pierce oscillator circuits the experimental resultshave confirmed that the SAW based micro force sensor canimplement high reproducibility When the input transducerof our device has been designed with the envelope of theconducting strips our device performs well linearity Inaddition the device uses the piezoelectric properties and thetemperature stability of the crystal as well as the frequency

8 Mathematical Problems in Engineering

Figure 9 The actual circuit testing diagram

Figure 10 The actual test waveform diagram

Figure 11 The experimental data fitting curve

signal instead of the conventional pressure sensor withvoltage signal which has made the signal processing of thisdevice more digital and possessed more stable performancesThe SAW based micro force type can be fabricated and has

high performance in either mobile micro robots or a precisepositioning device under the control of mechanical system

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the National Natural ScienceFoundation of China (Grant no 61274078) the ResearchInnovation and Project of the Shanghai Municipal EducationCommission (Grant no 13ZZ049) the Doctoral ScientificFundProject of theMinistry of Education ofChina (Grant no20120075110006) and the Foundation of Shanghai Universityof Engineering Science (Grant no nhky-2013-10)

References

[1] I Daubechies ldquoThe wavelet transform time-frequency local-ization and signal analysisrdquo IEEE Transactions on InformationTheory vol 36 no 5 pp 961ndash1005 1990

[2] D S Ballantine R M White S J Martin et al Acoustic WaveSensor Theory Design and Physico-Chemical ApplicationsAcademic Press New York NY USA 1997

[3] Y H Peng Wavelet Transform and Its Engineering ApplicationScience Press Beijing China 1999 (Chinese)

[4] W K Lu C C Zhu J H Liu and Q Liu ldquoImplementingwavelet transform with SAW elementsrdquo Science in China ETechnological Sciences vol 46 no 6 pp 627ndash638 2003

[5] W-K Lu C-C Zhu J-H Liu and P-Y Wei ldquoStudy onimplementation of surface-acoustic-wave type of the wavelet-transformation and reconstruction elementrdquo Acta ElectronicaSinica vol 30 no 8 pp 1156ndash1159 2002 (Chinese)

[6] K Andra C Chakrabarti and T Acharya ldquoA VLSI architecturefor lifting-based forward and inverse wavelet transformrdquo IEEETransactions on Signal Processing vol 50 no 4 pp 966ndash9772002

[7] K K Parhi and T Nishitani ldquoVLSI architecture for discretewavelet transformsrdquo IEEE Transactions on Very Large ScaleIntegration (VLSI) Systems vol 1 no 2 pp 191ndash202 1993

[8] X Chen X Zhang K Chen and Q Li ldquoOptical wavelet-matched filtering with bacteriorhodopsin filmsrdquoApplied Opticsvol 36 no 32 pp 8413ndash8416 1997

Mathematical Problems in Engineering 9

[9] M von Schickfus R Stanzel T Kammereck D Weiskat WDittrich and H Fuchs ldquoImproving the SAW gas sensor deviceelectronics and sensor layerrdquo Sensors andActuators B Chemicalvol 19 no 1ndash3 pp 443ndash447 1994

[10] M K Tan L Y Yeo and J R Friend ldquoRapid fluid flow andmixing induced inmicrochannels using surface acousticwavesrdquoEurophysics Letters vol 87 no 4 pp 537ndash563 2009

[11] W CWilson D CMalocha N Y Kozlovski et al ldquoOrthogonalfrequency coded SAWsensors for aerospace SHMapplicationsrdquoSensors Journal vol 9 no 11 pp 1546ndash1556 2009

[12] M Jungwirth H Scherr and R Weigel ldquoMicromechanicalprecision pressure sensor incorporating SAW delay linesrdquo ActaMechanica vol 158 no 3-4 pp 227ndash252 2002

[13] S Muntwyler F Beyeler and B J Nelson ldquoThree-axis micro-force sensor with sub-micro-Newtonmeasurement uncertaintyand tunable force rangerdquo Journal of Micromechanics and Micro-engineering vol 20 no 2 pp 3165ndash3170 2010

[14] Y C Kim Y S Ihn H Moon et al ldquoLow cost dual axismicro force sensor for robotic manipulationsrdquo MicrosystemTechnologies vol 17 no 5ndash7 pp 1197ndash1205 2011

[15] K J Singh O Elmazria F Sarry et al ldquoEnhanced sensitivityof SAW-based Pirani vacuum pressure sensorrdquo IEEE SensorsJournal vol 11 no 6 pp 1458ndash1464 2011

[16] C B Wen and C C Zhu ldquoTime synchronous dyadic waveletprocessor array using surface acoustic wave devicesrdquo SmartMaterials and Structures vol 15 no 4 pp 939ndash945 2006

[17] W K Lu C C Zhu J F Zhang C Shi and X Z Lu ldquoStudyof small size wavelet transform processor and wavelet inverse-transform processor using SAWdevicesrdquoMeasurement Journalof the International Measurement Confederation vol 44 no 5pp 994ndash999 2011

[18] Y Kang Design of Surface Acoustic Wave Devices and ItsApplication Oscillator Circuit Changrsquoan University 2011

[19] X Z Lu Interfacial Stress Sensor for Artificial Skin ApplicationDonghua University 2012

[20] Y Y Li W K Lu C C Zhu et al ldquoAcoustic electric generationfor morlet wavelet transform of surface acoustic wave devicerdquoResearch Journal of Applied Sciences Engineering and Technol-ogy vol 5 no 4 pp 1203ndash1207 2013

[21] Y Y Li W K Lu and C C Zhu ldquoPspice equivalent circuitmodel for implementation of surface acoustic wave filterrdquoJournal of Donghua University vol 29 no 2 pp 148ndash152 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Mathematical Problems in Engineering

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Differential EquationsInternational Journal of

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Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Mathematical PhysicsAdvances in

Complex AnalysisJournal of

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OptimizationJournal of

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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

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Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

6 Mathematical Problems in Engineering

and

1198960

119873

sum

119894=1

Δ1198912

+and

1198961

119873

sum

119894=1

Δ1198913

+and

1198962

119873

sum

119894=1

Δ1198914

+and

1198963

119873

sum

119894=1

Δ1198915

+and

1198964

119873

sum

119894=1

Δ1198916

+and

1198965

119873

sum

119894=1

Δ1198917

+and

1198966

119873

sum

119894=1

Δ1198918

=

119873

sum

119894=1

119865119894Δ1198912

119894

and

1198960

119873

sum

119894=1

Δ1198913

+and

1198961

119873

sum

119894=1

Δ1198914

+and

1198962

119873

sum

119894=1

Δ1198915

+and

1198963

119873

sum

119894=1

Δ1198916

+and

1198964

119873

sum

119894=1

Δ1198917

+and

1198965

119873

sum

119894=1

Δ1198918

+and

1198966

119873

sum

119894=1

Δ1198919

=

119873

sum

119894=1

119865119894Δ1198913

119894

and

1198960

119873

sum

119894=1

Δ1198914

+and

1198961

119873

sum

119894=1

Δ1198915

+and

1198962

119873

sum

119894=1

Δ1198916

+and

1198963

119873

sum

119894=1

Δ1198917

+and

1198964

119873

sum

119894=1

Δ1198918

+and

1198965

119873

sum

119894=1

Δ1198919

+and

1198966

119873

sum

119894=1

Δ11989110

=

119873

sum

119894=1

119865119894Δ1198914

119894

and

1198960

119873

sum

119894=1

Δ1198915

+and

1198961

119873

sum

119894=1

Δ1198916

+and

1198962

119873

sum

119894=1

Δ1198917

+and

1198963

119873

sum

119894=1

Δ1198918

+and

1198964

119873

sum

119894=1

Δ1198919

+and

1198965

119873

sum

119894=1

Δ11989110

+and

1198966

119873

sum

119894=1

Δ11989111

=

119873

sum

119894=1

119865119894Δ1198915

119894

and

1198960

119873

sum

119894=1

Δ1198916

+and

1198961

119873

sum

119894=1

Δ1198917

+and

1198962

119873

sum

119894=1

Δ1198918

+and

1198963

119873

sum

119894=1

Δ1198919

+and

1198964

119873

sum

119894=1

Δ11989110

+and

1198965

119873

sum

119894=1

Δ11989111

+and

1198966

119873

sum

119894=1

Δ11989112

=

119873

sum

119894=1

119865119894Δ1198916

119894

(18)

Equation (18) can be written as

119873and

1198960+ 119860and

1198961+ 119861and

1198962+ 119862and

1198963+ 119863and

1198964+ 119864and

1198965+ 119865and

1198966= 119872

119860and

1198960+ 119861and

1198961+ 119862and

1198962+ 119863and

1198963+ 119864and

1198964+ 119865and

1198965+ 119866and

1198966= 119875

119861and

1198960+ 119862and

1198961+ 119863and

1198962+ 119864and

1198963+ 119865and

1198964+ 119866and

1198965+ 119867and

1198966= 119876

119862and

1198960+ 119863and

1198961+ 119864and

1198962+ 119865and

1198963+ 119866and

1198964+ 119867and

1198965+ 119868and

1198966= 119877

119863and

1198960+ 119864and

1198961+ 119865and

1198962+ 119866and

1198963+ 119867and

1198964+ 119868and

1198965+ 119869and

1198966= 119878

119864and

1198960+ 119865and

1198961+ 119866and

1198962+ 119867and

1198963+ 119868and

1198964+ 119869and

1198965+ 119870and

1198966= 119879

119865and

1198960+ 119866and

1198961+ 119867and

1198962+ 119868and

1198963+ 119869and

1198964+ 119870and

1198965+ 119871and

1198966= 119880

(19)

where

119860 =

119873

sum

119894=1

Δ119891119894 119861 =

119873

sum

119894=1

Δ1198912

119894

119862 =

119873

sum

119894=1

Δ1198913

119894

119863 =

119873

sum

119894=1

Δ1198914

119894

119864 =

119873

sum

119894=1

Δ1198915

119894

119865 =

119873

sum

119894=1

Δ1198916

119894

119866 =

119873

sum

119894=1

Δ1198917

119894

119867 =

119873

sum

119894=1

Δ1198918

119894

119868 =

119873

sum

119894=1

Δ1198919

119894

119869 =

119873

sum

119894=1

Δ11989110

119894

119870 =

119873

sum

119894=1

Δ11989111

119894

119871 =

119873

sum

119894=1

Δ11989112

119894

119872 =

119873

sum

119894=1

119865119894 119875 =

119873

sum

119894=1

119865119894Δ1198911

119894

119876 =

119873

sum

119894=1

119865119894Δ1198912

119894

119877 =

119873

sum

119894=1

119865119894Δ1198913

119894

119878 =

119873

sum

119894=1

119865119894Δ1198914

119894

119879 =

119873

sum

119894=1

119865119894Δ1198915

119894

119880 =

119873

sum

119894=1

119865119894Δ1198916

119894

(20)

Coefficients 1198960to 1198966in (13) can be obtained and the input

and output variable regression of the SAW based micro forcesensor can be calculated by solving (18)

5 Testing and Analysis of the SAW BasedMicro Force Sensor

51 Actual Circuit Detection Results The output frequencyof the SAW based micro force sensor is conducted by usingthe network analyzer equipment E5061A (Figure 7) Force-measuring elements employ a cantilever beam loaded with0ndash20 kPa pressure and add 2 kPa to this beam at each time[20]

Figure 8 shows the test schematic The SAW based microforce sensor has been designed with a single channel For theinductive components the electromagnetic field interferenceis more sensitive two inductors have been placed at 90∘to reduce interference between these components Figure 9shows the actual circuit In the process of real production thedevice location and the connection between our devices aremore important

Mathematical Problems in Engineering 7

Table 1 Difference in frequency data for various pressures

(kPa)119865119898

0 2 4 6 8 10 12 14 16 18 20119891 (MHz) 49255389 49255391 49255378 49255393 49255434 49255459 49255474 49255481 49255447 49255486 49255497119891 (MHz) 49255321 49255312 49255298 49255296 49255338 49255343 49255357 49255359 49255319 49255361 49255363Δ119891 (Hz) 68 79 80 97 96 116 117 122 128 125 134

Network analyzerE5061A

Input IDT Output IDT

Piezoelectric substrate

Fn

Figure 7 Schematic of the SAW based micro force sensor

DC power Output ScopeThe micro

force sensor of SAW device

Figure 8 Test schematic diagram

52 The Fitting Curve for the Measured Frequency Figure 10shows the actual test waveform diagram [21]

To eliminate the system instability the experimental datahas been averaged in Table 1

Frequency experiment data samples have been gener-ated from (18) according to the different micro pressurereading and the estimated regression coefficients

and

1198960and

1198961and

1198962

and

1198963and

1198964and

1198965andand

1198966can be calculated The method of least

squares can reduce the error due to measurement inaccu-racies caused by the SAW device based micro force sensorThrough the minimization of squared errors of our actualdata the least squares method has the ability to find the bestmatching function data Additionally the fitting curve of theexperimental data shows that the circuit design is reasonableand the device exhibits good linearity (Figure 11) The pres-sure 119865

119898is proportional to the output frequency119891 which has

proved that the SAW detection and pierce oscillator circuithave correct logic function

Based on (13) the available in differentmicro force sensoroutput difference frequency transfer function is

119865119898(Δ119891) = 31441 times 10

minus1

+ 59057 times 10minus2

Δ119891119894

minus 23012 times 10minus4

Δ1198912

119894

+ 54127 times 10minus7

Δ1198913

119894

Table 2 Oscilloscope measurement results

Measurement parameter Averagevalue

Minimumvalue

Maximumvalue

Voltage output (mV) 320 314 326Frequency output(MHz) 492553965 49255296 49255497

minus 60364 times 10minus10

Δ1198914

119894

+ 30200 times 10minus13

Δ1198915

119894

minus 50540 times 10minus17

Δ1198916

119894

(21)

Because of the load impedance having affected the ampli-tude output of the micro force sensor the impedance of theoscilloscope probe during testing is set at 1mΩ to stabilize theoscillator amplitude The working circuit voltage and currentare 3V and 10mA Using the difference in frequency data forvarious pressures in Table 1 the Oscilloscope measurementresult has been calculated in Table 2

6 Conclusion

This paper has addressed three problems in designing theSAW based micro force sensor namely the envelope of IDTthe variable regression and the fitting curve analysis forthe measured frequency which are according to the wavelettransform method SAW detection and pierce oscillatorcircuits

The paper has also proposed themixing frequency circuitfor the reference oscillator and the detector circuit Thechanges between the oscillator frequency and the mea-surement of the parameters can be obtained through thepierce oscillator circuits and the difference in frequency datafor various pressures also can be established by the linearregression model By affecting the production of amplitudeof impedance and parasitic capacitance the output frequencyof 50MHz still has stabilized features and performance Theparameters of frequency amplitude frequency stability andamplitude stability have been measured during the deviceresponse and the sensor simulation

According to the Morlet wavelet transform SAW detec-tion and pierce oscillator circuits the experimental resultshave confirmed that the SAW based micro force sensor canimplement high reproducibility When the input transducerof our device has been designed with the envelope of theconducting strips our device performs well linearity Inaddition the device uses the piezoelectric properties and thetemperature stability of the crystal as well as the frequency

8 Mathematical Problems in Engineering

Figure 9 The actual circuit testing diagram

Figure 10 The actual test waveform diagram

Figure 11 The experimental data fitting curve

signal instead of the conventional pressure sensor withvoltage signal which has made the signal processing of thisdevice more digital and possessed more stable performancesThe SAW based micro force type can be fabricated and has

high performance in either mobile micro robots or a precisepositioning device under the control of mechanical system

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the National Natural ScienceFoundation of China (Grant no 61274078) the ResearchInnovation and Project of the Shanghai Municipal EducationCommission (Grant no 13ZZ049) the Doctoral ScientificFundProject of theMinistry of Education ofChina (Grant no20120075110006) and the Foundation of Shanghai Universityof Engineering Science (Grant no nhky-2013-10)

References

[1] I Daubechies ldquoThe wavelet transform time-frequency local-ization and signal analysisrdquo IEEE Transactions on InformationTheory vol 36 no 5 pp 961ndash1005 1990

[2] D S Ballantine R M White S J Martin et al Acoustic WaveSensor Theory Design and Physico-Chemical ApplicationsAcademic Press New York NY USA 1997

[3] Y H Peng Wavelet Transform and Its Engineering ApplicationScience Press Beijing China 1999 (Chinese)

[4] W K Lu C C Zhu J H Liu and Q Liu ldquoImplementingwavelet transform with SAW elementsrdquo Science in China ETechnological Sciences vol 46 no 6 pp 627ndash638 2003

[5] W-K Lu C-C Zhu J-H Liu and P-Y Wei ldquoStudy onimplementation of surface-acoustic-wave type of the wavelet-transformation and reconstruction elementrdquo Acta ElectronicaSinica vol 30 no 8 pp 1156ndash1159 2002 (Chinese)

[6] K Andra C Chakrabarti and T Acharya ldquoA VLSI architecturefor lifting-based forward and inverse wavelet transformrdquo IEEETransactions on Signal Processing vol 50 no 4 pp 966ndash9772002

[7] K K Parhi and T Nishitani ldquoVLSI architecture for discretewavelet transformsrdquo IEEE Transactions on Very Large ScaleIntegration (VLSI) Systems vol 1 no 2 pp 191ndash202 1993

[8] X Chen X Zhang K Chen and Q Li ldquoOptical wavelet-matched filtering with bacteriorhodopsin filmsrdquoApplied Opticsvol 36 no 32 pp 8413ndash8416 1997

Mathematical Problems in Engineering 9

[9] M von Schickfus R Stanzel T Kammereck D Weiskat WDittrich and H Fuchs ldquoImproving the SAW gas sensor deviceelectronics and sensor layerrdquo Sensors andActuators B Chemicalvol 19 no 1ndash3 pp 443ndash447 1994

[10] M K Tan L Y Yeo and J R Friend ldquoRapid fluid flow andmixing induced inmicrochannels using surface acousticwavesrdquoEurophysics Letters vol 87 no 4 pp 537ndash563 2009

[11] W CWilson D CMalocha N Y Kozlovski et al ldquoOrthogonalfrequency coded SAWsensors for aerospace SHMapplicationsrdquoSensors Journal vol 9 no 11 pp 1546ndash1556 2009

[12] M Jungwirth H Scherr and R Weigel ldquoMicromechanicalprecision pressure sensor incorporating SAW delay linesrdquo ActaMechanica vol 158 no 3-4 pp 227ndash252 2002

[13] S Muntwyler F Beyeler and B J Nelson ldquoThree-axis micro-force sensor with sub-micro-Newtonmeasurement uncertaintyand tunable force rangerdquo Journal of Micromechanics and Micro-engineering vol 20 no 2 pp 3165ndash3170 2010

[14] Y C Kim Y S Ihn H Moon et al ldquoLow cost dual axismicro force sensor for robotic manipulationsrdquo MicrosystemTechnologies vol 17 no 5ndash7 pp 1197ndash1205 2011

[15] K J Singh O Elmazria F Sarry et al ldquoEnhanced sensitivityof SAW-based Pirani vacuum pressure sensorrdquo IEEE SensorsJournal vol 11 no 6 pp 1458ndash1464 2011

[16] C B Wen and C C Zhu ldquoTime synchronous dyadic waveletprocessor array using surface acoustic wave devicesrdquo SmartMaterials and Structures vol 15 no 4 pp 939ndash945 2006

[17] W K Lu C C Zhu J F Zhang C Shi and X Z Lu ldquoStudyof small size wavelet transform processor and wavelet inverse-transform processor using SAWdevicesrdquoMeasurement Journalof the International Measurement Confederation vol 44 no 5pp 994ndash999 2011

[18] Y Kang Design of Surface Acoustic Wave Devices and ItsApplication Oscillator Circuit Changrsquoan University 2011

[19] X Z Lu Interfacial Stress Sensor for Artificial Skin ApplicationDonghua University 2012

[20] Y Y Li W K Lu C C Zhu et al ldquoAcoustic electric generationfor morlet wavelet transform of surface acoustic wave devicerdquoResearch Journal of Applied Sciences Engineering and Technol-ogy vol 5 no 4 pp 1203ndash1207 2013

[21] Y Y Li W K Lu and C C Zhu ldquoPspice equivalent circuitmodel for implementation of surface acoustic wave filterrdquoJournal of Donghua University vol 29 no 2 pp 148ndash152 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 7

Table 1 Difference in frequency data for various pressures

(kPa)119865119898

0 2 4 6 8 10 12 14 16 18 20119891 (MHz) 49255389 49255391 49255378 49255393 49255434 49255459 49255474 49255481 49255447 49255486 49255497119891 (MHz) 49255321 49255312 49255298 49255296 49255338 49255343 49255357 49255359 49255319 49255361 49255363Δ119891 (Hz) 68 79 80 97 96 116 117 122 128 125 134

Network analyzerE5061A

Input IDT Output IDT

Piezoelectric substrate

Fn

Figure 7 Schematic of the SAW based micro force sensor

DC power Output ScopeThe micro

force sensor of SAW device

Figure 8 Test schematic diagram

52 The Fitting Curve for the Measured Frequency Figure 10shows the actual test waveform diagram [21]

To eliminate the system instability the experimental datahas been averaged in Table 1

Frequency experiment data samples have been gener-ated from (18) according to the different micro pressurereading and the estimated regression coefficients

and

1198960and

1198961and

1198962

and

1198963and

1198964and

1198965andand

1198966can be calculated The method of least

squares can reduce the error due to measurement inaccu-racies caused by the SAW device based micro force sensorThrough the minimization of squared errors of our actualdata the least squares method has the ability to find the bestmatching function data Additionally the fitting curve of theexperimental data shows that the circuit design is reasonableand the device exhibits good linearity (Figure 11) The pres-sure 119865

119898is proportional to the output frequency119891 which has

proved that the SAW detection and pierce oscillator circuithave correct logic function

Based on (13) the available in differentmicro force sensoroutput difference frequency transfer function is

119865119898(Δ119891) = 31441 times 10

minus1

+ 59057 times 10minus2

Δ119891119894

minus 23012 times 10minus4

Δ1198912

119894

+ 54127 times 10minus7

Δ1198913

119894

Table 2 Oscilloscope measurement results

Measurement parameter Averagevalue

Minimumvalue

Maximumvalue

Voltage output (mV) 320 314 326Frequency output(MHz) 492553965 49255296 49255497

minus 60364 times 10minus10

Δ1198914

119894

+ 30200 times 10minus13

Δ1198915

119894

minus 50540 times 10minus17

Δ1198916

119894

(21)

Because of the load impedance having affected the ampli-tude output of the micro force sensor the impedance of theoscilloscope probe during testing is set at 1mΩ to stabilize theoscillator amplitude The working circuit voltage and currentare 3V and 10mA Using the difference in frequency data forvarious pressures in Table 1 the Oscilloscope measurementresult has been calculated in Table 2

6 Conclusion

This paper has addressed three problems in designing theSAW based micro force sensor namely the envelope of IDTthe variable regression and the fitting curve analysis forthe measured frequency which are according to the wavelettransform method SAW detection and pierce oscillatorcircuits

The paper has also proposed themixing frequency circuitfor the reference oscillator and the detector circuit Thechanges between the oscillator frequency and the mea-surement of the parameters can be obtained through thepierce oscillator circuits and the difference in frequency datafor various pressures also can be established by the linearregression model By affecting the production of amplitudeof impedance and parasitic capacitance the output frequencyof 50MHz still has stabilized features and performance Theparameters of frequency amplitude frequency stability andamplitude stability have been measured during the deviceresponse and the sensor simulation

According to the Morlet wavelet transform SAW detec-tion and pierce oscillator circuits the experimental resultshave confirmed that the SAW based micro force sensor canimplement high reproducibility When the input transducerof our device has been designed with the envelope of theconducting strips our device performs well linearity Inaddition the device uses the piezoelectric properties and thetemperature stability of the crystal as well as the frequency

8 Mathematical Problems in Engineering

Figure 9 The actual circuit testing diagram

Figure 10 The actual test waveform diagram

Figure 11 The experimental data fitting curve

signal instead of the conventional pressure sensor withvoltage signal which has made the signal processing of thisdevice more digital and possessed more stable performancesThe SAW based micro force type can be fabricated and has

high performance in either mobile micro robots or a precisepositioning device under the control of mechanical system

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the National Natural ScienceFoundation of China (Grant no 61274078) the ResearchInnovation and Project of the Shanghai Municipal EducationCommission (Grant no 13ZZ049) the Doctoral ScientificFundProject of theMinistry of Education ofChina (Grant no20120075110006) and the Foundation of Shanghai Universityof Engineering Science (Grant no nhky-2013-10)

References

[1] I Daubechies ldquoThe wavelet transform time-frequency local-ization and signal analysisrdquo IEEE Transactions on InformationTheory vol 36 no 5 pp 961ndash1005 1990

[2] D S Ballantine R M White S J Martin et al Acoustic WaveSensor Theory Design and Physico-Chemical ApplicationsAcademic Press New York NY USA 1997

[3] Y H Peng Wavelet Transform and Its Engineering ApplicationScience Press Beijing China 1999 (Chinese)

[4] W K Lu C C Zhu J H Liu and Q Liu ldquoImplementingwavelet transform with SAW elementsrdquo Science in China ETechnological Sciences vol 46 no 6 pp 627ndash638 2003

[5] W-K Lu C-C Zhu J-H Liu and P-Y Wei ldquoStudy onimplementation of surface-acoustic-wave type of the wavelet-transformation and reconstruction elementrdquo Acta ElectronicaSinica vol 30 no 8 pp 1156ndash1159 2002 (Chinese)

[6] K Andra C Chakrabarti and T Acharya ldquoA VLSI architecturefor lifting-based forward and inverse wavelet transformrdquo IEEETransactions on Signal Processing vol 50 no 4 pp 966ndash9772002

[7] K K Parhi and T Nishitani ldquoVLSI architecture for discretewavelet transformsrdquo IEEE Transactions on Very Large ScaleIntegration (VLSI) Systems vol 1 no 2 pp 191ndash202 1993

[8] X Chen X Zhang K Chen and Q Li ldquoOptical wavelet-matched filtering with bacteriorhodopsin filmsrdquoApplied Opticsvol 36 no 32 pp 8413ndash8416 1997

Mathematical Problems in Engineering 9

[9] M von Schickfus R Stanzel T Kammereck D Weiskat WDittrich and H Fuchs ldquoImproving the SAW gas sensor deviceelectronics and sensor layerrdquo Sensors andActuators B Chemicalvol 19 no 1ndash3 pp 443ndash447 1994

[10] M K Tan L Y Yeo and J R Friend ldquoRapid fluid flow andmixing induced inmicrochannels using surface acousticwavesrdquoEurophysics Letters vol 87 no 4 pp 537ndash563 2009

[11] W CWilson D CMalocha N Y Kozlovski et al ldquoOrthogonalfrequency coded SAWsensors for aerospace SHMapplicationsrdquoSensors Journal vol 9 no 11 pp 1546ndash1556 2009

[12] M Jungwirth H Scherr and R Weigel ldquoMicromechanicalprecision pressure sensor incorporating SAW delay linesrdquo ActaMechanica vol 158 no 3-4 pp 227ndash252 2002

[13] S Muntwyler F Beyeler and B J Nelson ldquoThree-axis micro-force sensor with sub-micro-Newtonmeasurement uncertaintyand tunable force rangerdquo Journal of Micromechanics and Micro-engineering vol 20 no 2 pp 3165ndash3170 2010

[14] Y C Kim Y S Ihn H Moon et al ldquoLow cost dual axismicro force sensor for robotic manipulationsrdquo MicrosystemTechnologies vol 17 no 5ndash7 pp 1197ndash1205 2011

[15] K J Singh O Elmazria F Sarry et al ldquoEnhanced sensitivityof SAW-based Pirani vacuum pressure sensorrdquo IEEE SensorsJournal vol 11 no 6 pp 1458ndash1464 2011

[16] C B Wen and C C Zhu ldquoTime synchronous dyadic waveletprocessor array using surface acoustic wave devicesrdquo SmartMaterials and Structures vol 15 no 4 pp 939ndash945 2006

[17] W K Lu C C Zhu J F Zhang C Shi and X Z Lu ldquoStudyof small size wavelet transform processor and wavelet inverse-transform processor using SAWdevicesrdquoMeasurement Journalof the International Measurement Confederation vol 44 no 5pp 994ndash999 2011

[18] Y Kang Design of Surface Acoustic Wave Devices and ItsApplication Oscillator Circuit Changrsquoan University 2011

[19] X Z Lu Interfacial Stress Sensor for Artificial Skin ApplicationDonghua University 2012

[20] Y Y Li W K Lu C C Zhu et al ldquoAcoustic electric generationfor morlet wavelet transform of surface acoustic wave devicerdquoResearch Journal of Applied Sciences Engineering and Technol-ogy vol 5 no 4 pp 1203ndash1207 2013

[21] Y Y Li W K Lu and C C Zhu ldquoPspice equivalent circuitmodel for implementation of surface acoustic wave filterrdquoJournal of Donghua University vol 29 no 2 pp 148ndash152 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

8 Mathematical Problems in Engineering

Figure 9 The actual circuit testing diagram

Figure 10 The actual test waveform diagram

Figure 11 The experimental data fitting curve

signal instead of the conventional pressure sensor withvoltage signal which has made the signal processing of thisdevice more digital and possessed more stable performancesThe SAW based micro force type can be fabricated and has

high performance in either mobile micro robots or a precisepositioning device under the control of mechanical system

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the National Natural ScienceFoundation of China (Grant no 61274078) the ResearchInnovation and Project of the Shanghai Municipal EducationCommission (Grant no 13ZZ049) the Doctoral ScientificFundProject of theMinistry of Education ofChina (Grant no20120075110006) and the Foundation of Shanghai Universityof Engineering Science (Grant no nhky-2013-10)

References

[1] I Daubechies ldquoThe wavelet transform time-frequency local-ization and signal analysisrdquo IEEE Transactions on InformationTheory vol 36 no 5 pp 961ndash1005 1990

[2] D S Ballantine R M White S J Martin et al Acoustic WaveSensor Theory Design and Physico-Chemical ApplicationsAcademic Press New York NY USA 1997

[3] Y H Peng Wavelet Transform and Its Engineering ApplicationScience Press Beijing China 1999 (Chinese)

[4] W K Lu C C Zhu J H Liu and Q Liu ldquoImplementingwavelet transform with SAW elementsrdquo Science in China ETechnological Sciences vol 46 no 6 pp 627ndash638 2003

[5] W-K Lu C-C Zhu J-H Liu and P-Y Wei ldquoStudy onimplementation of surface-acoustic-wave type of the wavelet-transformation and reconstruction elementrdquo Acta ElectronicaSinica vol 30 no 8 pp 1156ndash1159 2002 (Chinese)

[6] K Andra C Chakrabarti and T Acharya ldquoA VLSI architecturefor lifting-based forward and inverse wavelet transformrdquo IEEETransactions on Signal Processing vol 50 no 4 pp 966ndash9772002

[7] K K Parhi and T Nishitani ldquoVLSI architecture for discretewavelet transformsrdquo IEEE Transactions on Very Large ScaleIntegration (VLSI) Systems vol 1 no 2 pp 191ndash202 1993

[8] X Chen X Zhang K Chen and Q Li ldquoOptical wavelet-matched filtering with bacteriorhodopsin filmsrdquoApplied Opticsvol 36 no 32 pp 8413ndash8416 1997

Mathematical Problems in Engineering 9

[9] M von Schickfus R Stanzel T Kammereck D Weiskat WDittrich and H Fuchs ldquoImproving the SAW gas sensor deviceelectronics and sensor layerrdquo Sensors andActuators B Chemicalvol 19 no 1ndash3 pp 443ndash447 1994

[10] M K Tan L Y Yeo and J R Friend ldquoRapid fluid flow andmixing induced inmicrochannels using surface acousticwavesrdquoEurophysics Letters vol 87 no 4 pp 537ndash563 2009

[11] W CWilson D CMalocha N Y Kozlovski et al ldquoOrthogonalfrequency coded SAWsensors for aerospace SHMapplicationsrdquoSensors Journal vol 9 no 11 pp 1546ndash1556 2009

[12] M Jungwirth H Scherr and R Weigel ldquoMicromechanicalprecision pressure sensor incorporating SAW delay linesrdquo ActaMechanica vol 158 no 3-4 pp 227ndash252 2002

[13] S Muntwyler F Beyeler and B J Nelson ldquoThree-axis micro-force sensor with sub-micro-Newtonmeasurement uncertaintyand tunable force rangerdquo Journal of Micromechanics and Micro-engineering vol 20 no 2 pp 3165ndash3170 2010

[14] Y C Kim Y S Ihn H Moon et al ldquoLow cost dual axismicro force sensor for robotic manipulationsrdquo MicrosystemTechnologies vol 17 no 5ndash7 pp 1197ndash1205 2011

[15] K J Singh O Elmazria F Sarry et al ldquoEnhanced sensitivityof SAW-based Pirani vacuum pressure sensorrdquo IEEE SensorsJournal vol 11 no 6 pp 1458ndash1464 2011

[16] C B Wen and C C Zhu ldquoTime synchronous dyadic waveletprocessor array using surface acoustic wave devicesrdquo SmartMaterials and Structures vol 15 no 4 pp 939ndash945 2006

[17] W K Lu C C Zhu J F Zhang C Shi and X Z Lu ldquoStudyof small size wavelet transform processor and wavelet inverse-transform processor using SAWdevicesrdquoMeasurement Journalof the International Measurement Confederation vol 44 no 5pp 994ndash999 2011

[18] Y Kang Design of Surface Acoustic Wave Devices and ItsApplication Oscillator Circuit Changrsquoan University 2011

[19] X Z Lu Interfacial Stress Sensor for Artificial Skin ApplicationDonghua University 2012

[20] Y Y Li W K Lu C C Zhu et al ldquoAcoustic electric generationfor morlet wavelet transform of surface acoustic wave devicerdquoResearch Journal of Applied Sciences Engineering and Technol-ogy vol 5 no 4 pp 1203ndash1207 2013

[21] Y Y Li W K Lu and C C Zhu ldquoPspice equivalent circuitmodel for implementation of surface acoustic wave filterrdquoJournal of Donghua University vol 29 no 2 pp 148ndash152 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 9

[9] M von Schickfus R Stanzel T Kammereck D Weiskat WDittrich and H Fuchs ldquoImproving the SAW gas sensor deviceelectronics and sensor layerrdquo Sensors andActuators B Chemicalvol 19 no 1ndash3 pp 443ndash447 1994

[10] M K Tan L Y Yeo and J R Friend ldquoRapid fluid flow andmixing induced inmicrochannels using surface acousticwavesrdquoEurophysics Letters vol 87 no 4 pp 537ndash563 2009

[11] W CWilson D CMalocha N Y Kozlovski et al ldquoOrthogonalfrequency coded SAWsensors for aerospace SHMapplicationsrdquoSensors Journal vol 9 no 11 pp 1546ndash1556 2009

[12] M Jungwirth H Scherr and R Weigel ldquoMicromechanicalprecision pressure sensor incorporating SAW delay linesrdquo ActaMechanica vol 158 no 3-4 pp 227ndash252 2002

[13] S Muntwyler F Beyeler and B J Nelson ldquoThree-axis micro-force sensor with sub-micro-Newtonmeasurement uncertaintyand tunable force rangerdquo Journal of Micromechanics and Micro-engineering vol 20 no 2 pp 3165ndash3170 2010

[14] Y C Kim Y S Ihn H Moon et al ldquoLow cost dual axismicro force sensor for robotic manipulationsrdquo MicrosystemTechnologies vol 17 no 5ndash7 pp 1197ndash1205 2011

[15] K J Singh O Elmazria F Sarry et al ldquoEnhanced sensitivityof SAW-based Pirani vacuum pressure sensorrdquo IEEE SensorsJournal vol 11 no 6 pp 1458ndash1464 2011

[16] C B Wen and C C Zhu ldquoTime synchronous dyadic waveletprocessor array using surface acoustic wave devicesrdquo SmartMaterials and Structures vol 15 no 4 pp 939ndash945 2006

[17] W K Lu C C Zhu J F Zhang C Shi and X Z Lu ldquoStudyof small size wavelet transform processor and wavelet inverse-transform processor using SAWdevicesrdquoMeasurement Journalof the International Measurement Confederation vol 44 no 5pp 994ndash999 2011

[18] Y Kang Design of Surface Acoustic Wave Devices and ItsApplication Oscillator Circuit Changrsquoan University 2011

[19] X Z Lu Interfacial Stress Sensor for Artificial Skin ApplicationDonghua University 2012

[20] Y Y Li W K Lu C C Zhu et al ldquoAcoustic electric generationfor morlet wavelet transform of surface acoustic wave devicerdquoResearch Journal of Applied Sciences Engineering and Technol-ogy vol 5 no 4 pp 1203ndash1207 2013

[21] Y Y Li W K Lu and C C Zhu ldquoPspice equivalent circuitmodel for implementation of surface acoustic wave filterrdquoJournal of Donghua University vol 29 no 2 pp 148ndash152 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of