Dabas, Sweety

Dhankar, Minal

Hussain, Dil muhammed Akbar

Mishra, Dipti

Singh, Abhishek

The frequency reliance of inter-digital transducer is analyzed with the help of MASON’s Equivalent circuit which is based on Smith’s Equivalent circuit which is further based on Foster’sNetwork. An inter-digital transducer has been demonstratedas a RLC network. The circuit is simulated by Simulation program with Integrated Circuit Emphasis (HSPICE), a well-liked electronic path simulator. The acoustic wave devices are not suitable to simulation through circuit simulator.In this paper, an electrical model of Mason’s Equivalent electricalcircuit for an inter-digital transducer (IDT) is projected which is well-suitedwith a broadlycast-offuniversalresolution circuit simulator SPICE built-in out with the proficiency to simulatethenegative capacitances and inductances. The investigationis done to prove the straightforwardness of establishing the frequency and time domain physical characteristics of the IDT and flexibility to simulate the IDT laterally with other peripheral circuit elements. Sensors with high Q for resonance provide a better stability

VBN (Videnbasen)  Aalborg Universitets forskningsportal

Proceedings of the 10thINDIACom; INDIACom-2016; IEEE Conference ID: 37465 2016 3rd International Conference on “Computing for Sustainable Global Development”, 16th - 18th March, 2016 Bharati Vidyapeeth’s Institute of Computer Applications and Management (BVICAM), New Delhi (INDIA)   Inter Digital Transducer Modelling through Mason Equivalent Circuit Model Design and Simulation Dipti Mishra Electronics and Communication Engineering Jaypee Institute of Information Technology Noida, India dipti.mishra28@gmail.com  D M Akbar Hussain Department of Energy Technology Aalborg University, Denmark akh@et.aau.dk Abhishek Singh Electronics and Communication Engineering Pranveer Singh Institute of Technology Kanpur, India abhisheksingh013@gmail.com  Sweety Dabas Maharaja SurajmalInstituteJanakpuri New Delhi, India sweety.dabas@gmail.com  Minal Dhankar Maharaja Surajmal Institute, Janakpuri, New Delhi, India minal.dhankar@gmail.com Abstract—Thefrequencyreliance of inter-digital transducer isanalyzed with the help of MASON’s Equivalent circuit which is based on Smith’s Equivalent circuit which is further based on Foster’sNetwork. An inter-digital transducer has been demonstratedas a RLC network. The circuit is simulated by Simulation program with Integrated Circuit Emphasis (HSPICE), a well-liked electronic path simulator. The acoustic wave devices are not suitable to simulation through circuit simulator.In this paper, an electrical model of Mason’s Equivalentelectricalcircuit for an inter-digital transducer (IDT) is projected which is well-suitedwith a broadlycast-offuniversalresolution circuit simulator SPICE built-in out with the proficiency to simulatethenegative capacitances and inductances. The investigationis done to prove the straightforwardness of establishing the frequency and time domain physical characteristics of the IDT and flexibility to simulate the IDT laterally with other peripheral circuit elements. Sensors with high Q for resonance provide a better stability.  Keywords—Mason, piezoelectric transducer, SAW, MEMS, Foster method,resonator I.  INTRODUCTION  There are numerous simulation design techniques for SAW devices like impulse response,coupling of modes,superpositiontheorem,field theory etc. Fromthese entire mentioned methods the equivalent circuit model providessuperior results than other methods.Surface Acoustic Wave (SAW) devices are not compatible to simulation through circuit simulatorsbecausetheyare mainly electro-acoustic in nature, whereas any electrical circuit simulation requires pure electrical model. The paper intelligence significant improvements in the previous model and proposes it for HSPICE circuitsimulation.On the other hand some finite element model (FEM) tools such as COMSOL provide 3D view simulation for SAW devices [1][2].An inter-digital transducer is a comb shaped like metallic structure having a fixed gap between its fingers having the combination of both acoustic and electric field. The Mason’s equivalent electrical circuit is or the three port system shown in fig 1.  Fig.1. SAW IDT as a 3 port system Copy Right © INDIACom-2016; ISSN 0973-7529; ISBN 978-93-80544-20-5 8216Proceedings of the 10thINDIACom; INDIACom-2016; IEEE Conference ID: 37465 2016 3rd International Conference on “Computing for Sustainable Global Development”, 16th - 18th March, 2016    Fig.2. Cascading configuration for N electrode Transducer   Fig.3. Mason’s ECMfor one pair of fingers for Cross field model. Figure 2 shows the equivalent circuit model for N number of fingers and figure 3 shows the Mason’s ECM for one pair of finger. However higherthe count of fingers, the more time it take for simulation, and more computational resources are required. Then there is a problem to find a compromise allowing them to reduce the computational complexity of the desired FEM simulation.The second problem can occur when the fingers are too large.Thesimilarities between the electrical and mechanical elements are described by W. P. Mason in[4].As SAW devices are generally composed of several periodic sections,each section consists of a pair of fingers so Mason’s ECM can be easily applied on any one of the periodic sections [5].  Fig. 4(a) Mixed Circuit Model representation of an IDT  Fig.4 (b).Mixed Circuit model representation for two fingers-Mason Modified Model [6] 0 tan2TANEQ jZ , 0 cscCSCEQ jZ  ,0ff , 0 201SZk C f , 00vfL  Here K is the electromechanical coupling coefficient or factor,SC  is electrode capacitance per finger pair, 0v is the acoustic velocity for free region,L is the length of one pitch or period.  II. BACKGROUND  Copy Right © INDIACom-2016; ISSN 0973-7529; ISBN 978-93-80544-20-5 8217Inter Digital Transducer Modelling through Mason Equivalent Circuit Model -Design and Simulation  We know that a transmission line can be equated and designed as a distributed LC circuit and lumped circuit model as shown in fig.5(a) and(b). Reflect on a transmission line of length l. We wish to treat it as a two- port network and describe it in terms of its terminal parameters. One way is to use the amplitudes V   and V   of the waves travelling in the positive and negative z directions, respectively. This gives us 4 quantitities, 1V, 1V, 2V and 2V; any two of these can be treated as dependent variables and expressed in terms of the other two through a 2*2 matrix. Hence selecing the outgoing wave amplitudes 1V and 2V as the dependent variables, the scattering matrix [S] is given as: 1,2 1,2 1,2V V V   (1)      Fig.5(a). Transmission line of length l (b) lumped circuit equivalent 1,2 1,2 1,201( )I V VZ    (2)  𝑉1−𝑉2+ =  𝑆11 𝑆12𝑆21 𝑆22  𝑉1+𝑉2−  It is concluded that:  𝑆 =  0 𝑒−𝑗𝑘𝑙𝑒−𝑗𝑘𝑙 0   A linear two port network is completely described by a 2*2 matrix. It is frequently more convinient to use the voltage V and the current I rather than the wave amplitudes V   and V  . V= V   + V    (3) I= 01Z(V  - V  ) (4) Using the voltages as the dependent variables, we get the impedance matrix [Z]:  𝑉1𝑉2 =  𝑍11 𝑍12𝑍21 𝑍22  𝐼1𝐼2   Now there is a point to visualise the equivalence between thelumped circuit and the transmission line segment by showing that their [Z] matrices are equal[21]. From [S] matrix we have 1V= jkle 2V   (5) 2V= jkle 1V   (6) Hence 2 2 2V V V     (7) 1 1jkl jkle V e V        1 0 1cos sinV kl jZ I kl           (8) Similarly,  0 2 2 2Z I V V   0 1 1cos sinZ I kl jV kl  (9) This gives us the transmission matrix:   𝑉2𝐼2 =  𝑐𝑜𝑠𝑘𝑙 −𝑗𝑍0 sin𝑘𝑙−𝑗𝑠𝑖𝑛𝑘𝑙𝑍0cos𝑘𝑙  𝑉1𝐼1  Now the [Z] matrix with some arrangements is  given as   𝑉1𝑉2 = 𝑍0  −𝑗 cot 𝑘𝑙 𝑗 csc𝑘𝑙−𝑗 csc 𝑘𝑙 𝑗 cot 𝑘𝑙  𝐼1𝐼2  Here we have chosen the reference direction for both 1I  and 2I  in the positive Z direction. Copy Right © INDIACom-2016; ISSN 0973-7529; ISBN 978-93-80544-20-5 8218Proceedings of the 10thINDIACom; INDIACom-2016; IEEE Conference ID: 37465 2016 3rd International Conference on “Computing for Sustainable Global Development”, 16th - 18th March, 2016   III. MODELLING OF MASON EQUIVALENT CIRCUIT The absolute geometry or the model is shown in fig 4(a) and (b). The SAW IDTby means of aphase length (p) of the  same circuit corresponds substantially to the midpoint to midpoint spacing sandwich between two contiguous fingers each of width W.  is the transit angle of one periodic length section and is given by0ww  where w0 is the center frequency. The characteristic impedance R0of the transmission lineis dependent  on CS, the static capacitance per unit period.  The paper used Foster’s circuit which states that the locaton and behaviour of the zeros and poles,and the understanding of the impedance at one other frequency is appropriate to decide the complete network. Specifically, the elements 0 tan( / 2)jR   and 0 cosjR ec can be behaviorallygiven by networks,shown in fig 6 and 7.Totally the modules of the IDT equivalent circuit of Figure 4(a) are therefore known in terms of R,L and C and are required for circuit analysis in a simulator such as HSPICE.It is known that HSPICE considernegative inductance and capacitance values for circuit simulation to be valid[2,3].     Figure6. Functional behaviour and  networks for (a) 0 tan( / 2)jR   (b) 0 cosjR ec     Fig.7.Mason Modified Crossed field model where 000 tan2TAN jZ , 0 00 cscCSC jZ  ,tan2mmTANM jZ , cscm mCSCM jZ  ,004ff  , 4mmff  , 0 201SZk C f , 21mS mZk C f , 00vfL , mmvfL  IV. DESIGNING AND SIMULATION  Considering the 20 finger pair IDT made up of aluminum with a 1.5 µm thickness on 640Y-Z LiNbO3 with finger width or aspect ratio of 0.5 with an aperture of 0.020100257091454, operating at a center frequency of 850MHz.Allof the circuit simulations are performed using HSPICE and MATLAB. Here C01 i.e. oxide capacitance is considered as 4.6 pF and the circuit admittance is 3.6152 mS.An IDT is having a total static capacitance of 0.09pF. The full description is shown in fig.8 and 9. T-network elements represent lossless transmission lines consisting of N periodic section which is cascaded acoustically and in parallel electrically. In the equivalent circuit model, the impedances TANEQ,CSCEQ,TAN0,TANM,CSC0,and CSCM are independent of frequency. The proposed model substitute the above terms by LC network obtained using Foster’s reactance theorem.  Copy Right © INDIACom-2016; ISSN 0973-7529; ISBN 978-93-80544-20-5 8219Inter Digital Transducer Modelling through Mason Equivalent Circuit Model -Design and Simulation   Fig.8. ExtendedMason representation of an IDT for single finger pair     Fig.9. Corresponding complete circuit representation  of one pair of finger including energy storage V. RESULTS AND DISCUSSION  A 20 finger pair IDT presentation has been simulated by HSPICE at a centre frequency of 850MHz with a 3 dB bandwidth of 38 MHz(fig. 10 and 11). The source impedance is taken out to be 50 Ω. For simulation, up to 80 finger pairs have been magnificently handled by HSPICE without any convergence problem. The frequency response curve is showing very high quality factor when it resonates on its centre frequency i.e. 850 MHz.  Fig.10 HSPICE Simulation of a resonator at 850MHz frequency with 38 MHz bandwidth Figure.11.  HSPICE Simulation of a resonator at 850MHz frequency with 38 MHz bandwidth VI. CONCLUSION  Copy Right © INDIACom-2016; ISSN 0973-7529; ISBN 978-93-80544-20-5 8220Proceedings of the 10thINDIACom; INDIACom-2016; IEEE Conference ID: 37465 2016 3rd International Conference on “Computing for Sustainable Global Development”, 16th - 18th March, 2016   An HSPICE and MATLAB compatible Mason’s Macro model has been proposed. HSPICE is used as it can handle negative capacitances and inductances. The proposed model is showing highest amplitude at eigen frequency with a very high quality factor. The present model which is simulated by HSPICE and MATLAB is capable of managing the second order edge effects. From the simulation result of frequency response,very high quality factor is obtained.Sensors with high Quality factor Q for resonance provide a better stability.   REFERENCES  [1] A. B. Bhattacharya, S. Tuli, S. Majumdar, “SPICE smulation of surface acoustic wave interdigital transducers,” IEEE Trans. Sonics. Ultrason., vol. 42,pp.784-786,July 1995. [2] J. Munshi,S. Tuli, “ A Circuit Simulation Compatible Surface Acoustic Wave Interdigital Transducer acro-Model,” IEEE Trans. On Ultrasonics,Ferroelectrics,and Frequency Control, Vol. 51,No. 7,July 2004. [3] A. B. Bhattacharya, S. Tuli, S. Majumdar, “SPICE smulation of surface acoustic wave interdigital transducers,” IEEE Trans. Ultrasonics., vol. 42, No. 4,July 1995. [4] W. P. Mason,”Physical Acoustics”, vol. 1A,Academic Press,New York,1964. [5] A. H. Rasolomboahanginjatovo, F. Domingue, A. O. Dahmane , “A New SAW Device Simulator Based on Mason’s Equivalent Circuit Model” , SENSORDEVICES 2013 : The Fourth International Conference on Sensor Technologies and Applications, IARIA,2013, ISBN: 978-1-61208-297-4. [6] W. R. Smith,H. M. Gerard W. R. Jones, “ Analysis and Design of Dispersive Interdigital Surface Wave Trnsducers,” IEEE Transactions on Microwave Theory and Techniques,Vol. MTT-20,No. 7,July 1972. [7] W. R. Smith,H. M. Gerard,J. H. Collins,T. M. Reeder,H. J. Shaw, “Analysis of Interdigital Surface Wave Transducers by Use of an Equivalent Circuit Model,” IEEE Trans. On Microwave Theory and Techniques,Vol. MTT-17,No. 11.Nov 1969. [8] W. R. Smith,H. M. Gerard,J. H. Collins, T. M. Reeder,H. J. Shaw, “Design of Surface Wave Delay lines with Interdigital Transducers,” IEEE Transactions on Microwave Theory and Techniques,Vol. MTT-17,No. 11,Nov 1969.    Copy Right © INDIACom-2016; ISSN 0973-7529; ISBN 978-93-80544-20-5 8221

Inter Digital Transducer Modelling through Mason Equivalent Circuit Model

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Inter Digital Transducer Modelling through Mason Equivalent Circuit Model

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VBN (Videnbasen) Aalborg Universitets forskningsportal