Lectures and Short Courses of

Dr. A.S.Rukhlenko

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SAW filter course can be organized at Neuchatel (Switzerland) for an individual or for a group, at a special request.

Looking for a SAW professional, on-site lecturer on various aspects of the state-of-the-art SAW filter computer-aided design?

Dr. Alexander S. Rukhlenko, a SAW researcher and designer with 24 years experience in the field, is offering a cycle of lectures, shourt courses, and comprehensive demonstration of his state-of-the-art SAWCAD software at your company or organization. This is the unique chance to to get insight in SAWCAD software, evaluate the modeling and computational algorithms, compare with your own SAW design capabilities, if any.

Please find attached the list of lectures. You can also request ?for a customized lecture, at your most need.

New lectures on MATLAB SAW Filter Analysis Toolbox (SAWFAT) in the quasi-static approximation which is now commercially available (you can download the Demo version) and on designing SPUDT/RSPUDT SAW filters have been recently included.

In addition to the lecture fee (negotiable), a company or organization is expected to pay for or reimburse the instructor's basic travel expenses including

• airline round-trip tickets
• lodging
• meal
• rental car (optional)

incurred while lecturing at your site.

1. Basics of SAW Filter Design

Abstract

Basic properties of linear- and nonlinear-phase periodic SAW transducers with a constant pitch and metallization ratio (duty factor) are considered in quasi-static approximation, i.e. neglecting interelectrode reflections. It is shown that a SAW transducer frequency response can be represented as the product of the array factor which is basically responsible for the shape of the frequency response in the passband and the element factor which accounts for the metallization ratio and describes harmonic behavior of the response. The classification of SAW transducers with respect to symmetry type, sampling rate in time and frequency domain, and number of electrodes (even or odd) is given. Symmetry properties of the magnitude and phase response are discussed. Basic properties of the array and element factors are considered and the difference between overlap- and finger-length weighted SAW transducers is investigated and explained. Advantages and disadvantages of each method of weighting are discussed and practical recommendations how to correctly apply overlap- and finger-weighting are given. It is shown that the element factor results in the slant of the passband magnitude response which may be significant for wide-band SAW transducers. In many practical cases, the passband distortion of the frequency response due to the element factor is negligible and the quasi-static model is reduced to the ideal impulse model where the frequency response and transducer taps are related via Fourier transform, with a SAW transducer frequency response described as a trigonometric polynomial. Properties and limitations of the impulse model are considered and different forms of frequency response representation in time domain, frequency domain, and on Z-plane are considered. The equivalence and interrelation of three basic forms of the frequency response representation is discussed. Basis function properties in time and frequency domain are considered. Properties of the Z-transform are discussed and classification of Z-transform roots is given with respect to their phase characteristics and partial contribution to an overall frequency response. Stopband and passband properties of the Z-transform roots are considered. Methods of the reduction of the number of parameters to describe frequency response practically without sacrificing approximation accuracy are discussed. The lecture material is illustrated with design and modelling results.

Contents

• Frequency response of a periodic SAW transducer
• Basic properties and classification of SAW transducers
• Synchronous and asynchronous SAW transducers
• Overlap- and finger-length weighted transducers
• Array and element factors and their properties
• Impulse model and discrete Fourier transform
• Frequency sampling interpolation and properties of the basis functions
• Time domain interpolation
• Reduction of the parameters in the time domain: baseband and bandpass response
• Reduction of the parameters in the frequency domain: oversampling and undersampling
• Transformations of the SAW filter response (frequency scaling and shifting)
• Z-transform and its properties
• Classification of the Z-transform roots.

2. Review of SAW Filter Optimization Techniques

Abstract

Problems of optimum and suboptimum synthesis of SAW bandpass filters with prescribed magnitude and phase (group delay) response including linear-, nonlinear-, and minimum-phase filters are considered. Two different approaches to the optimum synthesis problem of linear-phase SAW filters are discussed. In the first one, a SAW filter to be designed consists of two linear phase IDT, with the frequency response of one of them supposed to be given a priori while the other's optimized providing a Chebyshev (minimax) approximation of the desired magnitude response. There are no constraints on a magnitude shape imposed which may be symmetrical, non-symmetrical, multipassband, etc. Statement of the problem for optimum design which provides the best fit to a design target and leads to a minimum length SAW filter under the design constraints imposed is considered. It is shown how an original SAW filter FR approximation problem may be converted to an auxiliary one by the proper modifying of a desired magnitude function and a weight function. This auxiliary approximation problem is solvable by means of standard linear Chebyshev approximation techniques using the linear programming (simplex method) or the Remez exchange algorithm (the McClellan's computer program), for example. Both the element factor and/or multistrip frequency response might also be accounted for if necessary. The major drawback of optimum design is a considerable amount of computations due to a large number of optimized variables ) even if one uses the efficient McClellan's program. It is shown that given a band-limited frequency response, the number of variables to be optimized may be considerably reduced by applying the sampling theorem in the time or frequency domain. An original suboptimum synthesis technique based on the same McClellan's computer program is proposed, with the number of optimized variables considerably reduced without significant sacrificing approximation accuracy. This is accomplished by factorizing a priori an optimized function, with the majority of the stopband zeros prescribed and expressed in the closed-form. The storage and the computation time are greatly reduced if compared to the optimum synthesis with optimization over the complete set of optimized variables. The detailed suboptimal synthesis theory and practical design aspects are discussed.
Another approach uses factorizational approach where design starts from the optimum response synthesized without a priori constraints imposed to SAW transducers. Optimum or suboptimum techniques may be applied to the synthesis of the overall response. After converting an trigonometric polynomial to the algebraic polynomial using Z-transform , Z-transform roots are to be found by applying roots solving problem for high-order polynomials. Since all the Z-transform roots are found, they are shared in the systematic manner between input and output SAW transducers.
Three basic techniques for linear phase SAW filter optimization are considered and compared:?
??? 1) the Remez exchnge algorithm (REA)
??? 2) the linear programming
??? 3) the Weighted Least Mean Squares (WLMS) algorithm.
The synthesis of SAW filters with prescribed magnitude and phase response is also considered. The design schemes based on the independent optimization of the real and imaginary parts of the complex-valued frequency response are considered. It is shown that with respect to approximation accuracy better results can be obtained by applying more sophisticated iterative design algorithms based on the real and imaginary part optimization using the results of the previous iteration to specify tolerance field for the next iteration.
Chebyshev approximation of the complex-valued function with Euclidean metric is also considered. Iterative technique of alternative optimization of the real and imaginary part is proposed. Another technique is based on the weighted-least-mean-squares algorithm with dynamic reiteration of the weighting function.

All the optimization techniques (REA, LP,NLP, WLMS) are implemented in the author's software for designing bidirectional SAW filters and the design examples for each optimization technique are presented.

The lecture is followed by the demonstration of the optimization software of the author implementing all the aforementioned SAW filter optimization techniques.

Contents

• ?Optimum design of SAW linear phase bandpass filters: statement of the problem
• Chebyshev approximation and its properties
• Optimization methods:
  • Linear programming
  • Remez exchange algorithm
• Suboptimum synthesis of SAW filters
  • Frequency sampling technique and linear programming optimization
  • Application of the Remez exchange algorithm to ?optimum and suboptimum synthesis
• Factorizational synthesis of SAW filters
• Design of SAW filters with prescribed magnitude and phase response
  • Linearization schemes
  • Iterative techniques
  • Chebyshev approximation of the complex-valued function
  • Weighted-least-mean-squares approximation
• Design examples
• Conclusions

3. Factorizational Synthesis of SAW Bandpass Filters

Abstract

Design technique of surface acoustic wave (SAW) filters with prescribed magnitude and linear-, nonlinear-, and minimum-phase characteristics by factorizing (spliting) the overall filter frequency response is considered. The key point of the design procedure is the roots search of the Z-transform using the roots solving program for high-order polynomials. Separate responses of the interdigital transducers (IDT) are found by sharing the Z-transform roots in the systematic manner between input and output SAW transducers resulting in apodized transducers. Several roots separation algorithms are considered. For linear-phase design, both transducers have identical non-linear phase responses which cancel each other in the overall SAW filter response due to complex-conjugation. Apodized non-linear phase SAW transducers can be approximated by withdrawal-weighted SAW transducers where appropriate. Given the desired specifications, the algorithm leads uniquely to the minimum length SAW filter which is usually 20-30 % shorter if compared to the design where two identical apodized IDT are used. It is shown how the algorithm can be adopted to designing suboptimum and optimum minimum-phase SAW filters from the linear-phase prototype. To design suboptimum minimum-phase SAW filters, the only additional step is to invert outside Z-transform roots inside the unit circle. Such a minimum-phase design minimizes the filter time delay that could be useful in some applications. The length of such minimum-phase SAW filters may be further reduced by applying more sophisticated optimum design procedures which leads to the minimum-minimorum length SAW filters within prescribed magnitude shape specifications. Two different minimum-phase design algorithms from the linear-phase prototype are considered based on the removing stopband Z-transform off the unit circle. One is the known Hermann-Shuessler procedure, another is direct synthesis of the positive-valued prototype, with the desired minimum-phase response being a square root of the prototype response. Minimum-phase SAW filters may be used in the applications where the dispersionless requirements are not too severe. A reasonable compromise between linear-phase and minimum-phase designs may be attained in quasiminimum-phase SAW filters containing a small portion of zeros outside the unit circle. The design examples are presented.

Contents

• Z-transform and its properties
• Classification of the Z-transform roots:
  • monozeros
  • couples of zeros
  • linear-phase quadruplets
• Properties of Z-transform roots in stopband and passband
• Basic features of the roots solving program for high-order polynomials
• Factorizational synthesis algorithm for linear- and nonlinear-phase SAW filters
• Suboptimum and optimum synthesis of minimum-phase SAW filters
• Factorizational synthesis design examples:
  • bandpass linear-phase SAW filter
  • SAW filter with prescribed magnitude and phase response
  • suboptimum and optimum minimum-phase SAW filter design
• Conclusions

4. Acoustoelectric Conversion Function: Properties and Computation

Abstract

Properties and calculation of the acoustoelectric (electroacoustic) conversion function for unapodized and apodized periodic SAW transducers are discussed in the quasi-static approximation. The basic equations for the acoustoelectric conversion function of an unapodized SAW transducer are deduced in terms of finger potentials and gap voltages. The results are generalized to the case of the apodized SAW transducers, with the finger and gap taps correctly defined. Merits of using the gap taps against the finger taps are discussed. It is shown that contrary to the wide-spread opinion guard fingers may give considerable contribution to the overall acoustoelectric conversion function calculated in terms of finger taps, in general case. The known equations are correct only in the particular case of the grounded guard fingers at both transducer ends. These equations fail to give the correct result for antisymmetric transducer structure, for example. As using the gap taps instead of the finger taps always gives zero contribution for the guard fingers, this fixes automatically the problem with guard finger contribution. The comparison of two different tap types is illustrated by examples of misusing finger taps in practical SAW filter design.

Contents

• Definition of the Acoustoelectric Conversion Function
  • Generalized Wave Amplitude and Surface-Wave Potential
  • Acoustoelectric Conversion in the Quasi-Static Approximation
• Unapodized Periodic SAW Transducers
• • Basic structure and Guard Electrodes
  • Array Factor and Element Factor
  • Contribution of the Guard Electrodes to the Acoustoelectric Conversion
  • Finger (Potential) and Gap (Voltage) Taps
  • Element Factor Properties
  • Example of Misusing Finger Taps
• Apodized Periodic SAW Transducers
  • Basic Assumptions
  • Generalization of the Finger and Gap Taps
• Conclusions

5. Closed-Form Admittance Calculation for Generalized Periodic SAW Transducers

Abstract


Analytic formulae for surface acoustic wave (SAW) transducer admittance calculation comprising both acoustic radiation conductance and susceptance are deduced neglecting multiple interelectrode SAW interactions (quasi-static approximation). For calculation, the concept of a nodal admittance matrix of a SAW transducer is introduced, with the self- and mutual elemental nodal admittances of a periodic SAW transducer with the uniform aperture deduced in the closed-form. Physical meaning of the elemental admittances is explained. Given the nodal admittance matrix and transducer electrode voltages, an analytic expression for the admittance of a transducer with uniform aperture and arbitrary polarity sequence is deduced. The admittance of the aperture-weighted (apodized) SAW transducer can be found by applying this formula to an arbitrary intersection of an apodized transducer and integrating in the closed-form over the total aperture. Within model constraints applied, an acoustic admittance of the aperture-weighted SAW transducer is treated as a weighted sum of the nodal interelectrode admittances, with the weights given by the effective apertures defined by the total overlaps of all the nearest, next nearest neighbour electrodes, and so on, respectively. The effective apertures depend on the SAW transducer apodization and the number of fingers and do not depend on the frequency. By applying a special summation technique for the apodized periodic SAW transducers with a fixed pitch and metallization ratio and taking into account the periodic properties of the nodal admittance matrix, the general formula is reduced to the compact form resulting in considerable reduction of the computation time if compared to the wide-spread aperture channelizing technique. According to this formula, an acoustic admittance comprising both conductance and susceptance is defined by the Fourier transform of the effective apertures, with effective apertures values being the total overlaps of all the nearest neighbour fingers, next nearest ones, and so on, respectively. Effective apertures are uniquely defined by finger overlaps and do not depend on the frequency. Assumed for the set of the effective apertures to be determined a priori, acoustic admittance calculation comprising both radiation conductance and susceptance takes no more time than frequency response calculation in quasi-static approximation. Fast Fourier transform can be effectively applied to calculate the admittance characteristic in the wide frequency range. The method is quite general and may be applied to capacitively-weighted, polarity-weighted, multi-phase, and other periodic SAW transducers having the central frequency away from the synchronous frequency. Results of admittance calculation for apodized SAW transducers with split (double) fingers are presented which agree well with the measured admittance characteristics.

Contents

• Nodal Admittance Matrix of a SAW Transducer
  • Definition of the Admittance Matrix?
  • Modeling Assumptions in the Quasi-Static Approximation
  • Elemental Nodal Admittance
  • Self- and Mutual Elemental Admittances
  • Properties of the Admittance Matrix
• Admittance of an Unapodized SAW Transducer
  • Definition of the Admittance Matrix
  • Admittance Calculation in Terms of Finger Potentials
  • Nodal Admittance Matrix in Terms of Gap Voltages
  • Admittance Calculation in Terms of Gap Voltages
  • Example of the Admittance Calculation and Relation to the Known Results
  • Correction due to the Contribution of Guard Electrodes
• Admittance of an Apodized SAW Transducer
  • Admittance Calculation in Terms of Finger Taps
  • Admittance Calculation in Terms of Gap (Overlap) Taps
  • Physical Meaning of Weighting the Elemental Admittances
• Computational Implementation of the Algorithm
• Calculation Example and Experimental Results
• Conclusions

6. Charge Distribution and Capacitance Calculation for Generalized Periodic SAW Transducers

Abstract

Analytic formulae for the surface charge density, electrode charges, and capacitance of generalized periodic SAW transducers with uniform finger spacing are derived in the present paper. The initial electrostatic problem is approximated by an auxiliary one with periodic boundary conditions on the surface. To this end, a transducer containing N electrodes with arbitrary voltages Vi ?is treated as one generalized period of infinite periodic array derived by subsequential multiple repeating of the initial transducer. The closed-form electrostatic solution is derived using Floquet theorem, superposition principle, and the known analytic solution for the charge density in a periodic phased array of strips with the same voltages and the phase progressing uniformly along the array.
Electrode charges and voltages within one period are interrelated via closed-form capacitance and pseudo-inverse potential matrices. The general expression for the transducer static capacitance is derived in terms of weighted interelectrode capacitors between nearest neighbor electrodes, next nearest ones and so on. The derived formula for the capacitance is applicable both to uniform as well as to aperture-weighted transducers.
The general solution of the "mixed" electrostatic problem is also considered where each electrode is characterized either by its potential or by its charge. Unknown charges and potentials are determined in terms of a priori prescribed voltages and charges using capacitance or potential matrices. As a special case, the solution for SAW transducers with floating electrodes can be obtained by imposing charge neutrality condition to the floating sections including single floating electrodes.
Examples of charge distribution and capacitance calculations for some practical transducers are presented.

Contents

• Introduction
• Statement of the electrostatic problem for a periodic SAW transducer
• Phased array periodic transducer and basic analytic equations
• Surface charge density distribution calculation
• Interrelation of the electrode charges and voltages
• Capacitance and potential matrices. Interelectrode capacitors
• Static capacitance of a SAW transducer
• Mixed electrostatic problem and its solution
• SAW transducers with separate and interconnected floating electrodes
• Calculation examples
• Conclusions

7. COM-Analysis of SAW Devices

Abstract

The coupling-of-modes (COM) approximation is a closed-form technique to model systems with spatially varying properties which is a convenient tool for modelling low-loss SAW filters taking into account interelectrode reflections due to mass-electrical load effect. Basic COM-equations are deduced and applied to the analysis of SAW reflective arrays and transducers. Analytic solution of the reduced system of homogeneous differential equations for reflective grating is considered. Reflection and transduction properties of the reflecting grating are discussed. General solution of the linear system of inhomogeneous differential equations describing an interdigital transducer is considered, with an additional equation containing terminal current flowing into SAW transducer added. Radiation and reception characteristics of a SAW transducer are deduced from which the closed-form mixed scattering matrix (P-matrix) of a SAW transducer is constructed. COM equations involved in the model are characterized by four independent COM-model parameters (self- and cross-coupling coefficients, SAW excitation function, and static capacitance) to be determined a priori. Generally, these COM parameters depend on the frequency, substrate and electrode material, and transducer geometry (metallization ratio, pitch, and metal height). Derivation of COM-parameters from theory or experiment is considered and their physical meaning is explained. Application of the COM method is illustrated by analysis of SAW reflectors, self-matched SAW transducers, long resonant transducers with internal reflections, and one- and two-port resonators, with good agreement between theory and experiment observed.

Contents

• Basic approximations and equations
• General closed-form solution of the wave propagation problem
• Modelling of the periodic reflective array
• Modelling of SAW transducers
  • Transducer terminal current
  • SAW excitation mode
  • SAW detection mode
• Closed-form mixed scattering matrix of a SAW transducer
• Determination of COM- parameters
  • Self-coupling
  • Cross-coupling
  • Excitation function
  • Static capacitance
• COM-analysis applications
  • SAW reflectors
  • Self-matched SAW transducers
  • Long SAW transducers with internal reflections
  • One- and two-port SAW resonators
• Conclusions

8. Simulation of Multiport/Multitransducer Surface Acoustic Wave Devices

Abstract

Closed-form matrix approach to the analysis of multiport/multitransducer SAW devices of arbitrary complexity is presented, provided for the scattering matrices of SAW components to be known a priori. Active SAW components (SAW transducers) are described in terms of the mixed (electroacoustic) scattering matrices (P-matrices) while all ?the passive SAW components (multistrip couplers, reflective arrays, etc.) are characterized by the uniform (acoustic) wave scattering matrices. A complete mixed scattering matrix of a SAW system is deduced as the closed-form solution of the block-matrix equation to express all the currents on the electric ports and the reflected waves on the external acoustic ports in terms of the applied voltages and incident acoustic waves. In particular case of an isolated SAW system with no external incident waves, the mixed scattering matrix of a SAW system is reduced to the nodal admittance matrix and therefore the standard nodal analysis of the electrical networks can be applied. The approach is general and flexible taking into account all multiple acoustic interactions in an arbitrary SAW system. The proposed algorithm provides a systematic unified approach to the closed-form analysis of a variety of SAW devices. Separation of the tasks (first independent modeling of the SAW components of a system and then combining them into the overall SAW system) provides an excellent upgrade capability with respect to the modelling accuracy. It seems to be an attractive tool for modeling low-loss SAW filters for mobile communications? such as low-loss filters with interdigitated interdigital SAW transducers, dual track image impedance connected SAW filters, etc. The algorithm applications are illustrated by the analysis of one- and two-port SAW resonators.

Contents

• Statement of the analysis problem
• Electrical and acoustical variables on the ports
• Mixed (electro-acoustic) scattering matrices and wave scattering matrices of the components
• Coupled and uncoupled acoustical ports
• Connection matrix
• Closed-form block-matrix solution of the problem
• Particular case: multiport SAW system loaded by acoustic two-port junctions
• Applications of the method:
  • one-port SAW resonator
  • two-port SAW resonator
• Conclusions

10. Multistrip Coupler Modeling: Two Mode Approach

Abstract

Basic properties and models of SAW multistrip couplers (MSC) are discussed, with the basic assumption of two rectangular orthogonal modes with symmetric and antisymmetric amplitude distribution propagating in the MSC (two-mode approach). It is shown that the symmetric and antisymmetric modes are essentially the waves propagating in the open- and short-circuit gratings. Therefore, known techniques for modeling reflective and non-reflective gratings can be applied to normal mode MSC analysis. Using the acoustical boundary conditions the MSC scattering parameters are expressed in terms of the modal scattring parameters.

The solutions for normal modes are obtained using the following techniques:

??? 1) quasi-static approximation (neglecting SAW reflections near the synchronous frequency);?
??? 2) reflective array model (RAM) based on the closed-form cascading of the elemental reflective cells;
??? 3) coupling-of-modes (COM) analysis;?
??? 4) field approach based on the closed-form equations for the fundamental and first backward space harmonics.

Basic MSC properties both in the passband and stopband are discussed. The modeled results are compared with the publsihed experimental results.

Contents

• Normal Mode Representation of a Multistrip Coupler
  • Concept of a Multistrip Coupler (MSC)
  • MSC Modeling Assumptions
  • Boundary Conditions
  • Two Modes Approximation
  • Physical Meaning of the Symmetric/Antisymmetric Modes
• Properties of the Normal Modes in the Periodic Gratings
  • Wavenumber and SAW Velocity
  • Reflection Coefficient
  • Dispersion Relation
• Multistrip Coupler Models
  • Reflective Array Model (RAM)
  • Coupling-of-Modes (COM) Model
  • Field Approach (Ingebrigtsen)
  • Quasi-Static Approximation (Morgan)
• MSC Modeled and Experimental Results
  • MSC Stopband and Passband Modeling
  • Comparison with Experimental Data
• Conclusions

11. Mixed Scattering Matrix: Properties and Applications

Abstract

The lecture provides a comprehensive overview of the mixed scattering matrix (P-matrix) theory. Properties of the admittance, wave scattering, and mixed scattering matrices of the arbitrary acoustoelectric multiport network are discussed where the mixed scattering matrix M is defined as a mixed units hybrid of the scattering matrix S and admittance matrix Y. Based on the relationship between acoustic and electric variables the equations for conversion between admittance, scattering, and mixed scattering matrices are deduced. Matrix implications due to the reciprocity and power conservation
are discussed.

The general results and equations are applied to SAW transducer modeling where a conventional unapodized SAW transducer is considered as a reciprocal and lossless three-port acoustoelectric network, with two acoustic and one electric ports. Properties and physical ?meaning of the matrix blocks and elements are discussed. The number of the independent P-matrix elements is determined and their physical meaning is explained. Conversion between the mixed scattring matrix M, mixed transmission matrix T, and wave scattering matrix S is considered. It is shown that in general case of a reciprocal and lossless SAW transducer the elements of the mixed scattering matrix must satisfy a self-consistent system of equations following from the reciprocity and power conservation.

As a particular case, the mixed scattering matrix of a SAW transducer is deduced in the quasi-static approximation where a short-circuit SAW transducer is supposed to be non-reflective. In practice, the quasi-static approximation is valid if the central frequency fo of a SAW transducer is far away from the synchronous frequency fs=v/2p where v is effective SAW velocity and p is the transducer period (pitch). In this case the mixed scattering matrix takes the simplest form. The relationship between the mixed scattering and transmission matrices of a SAW transducer is deduced. An important particular case of the conversion between scattering and transmission matrices in the quasi-static approximation completes consideration.

Contents

• Admittance, Wave Scattering, and Mixed Scattering Matrices of the Multi-Port Network
• Definition of the Mixed Scattering Matrix
• • Generalized Wave Amplitudes and Electric Variables
  • Conversion between Admittance, Wave Scattering, and Mixed Scattering Matrices
  • Reciprocity and Power Conservation
• Mixed Scattering Matrix of a SAW Transducer
  • Three-Port Representation of a SAW Transducer
  • Physical Meaning of the Mixed Scattering Matrix
  • Mixed Scattering Matrix Elements
  • Conversion to the Wave Scattering Matrix
  • Properties of the reciprocal and lossless SAW transducer
  • Conversion between Mixed Scattering and Transmission Matrices
• SAW Transducer Modeling in the Quasi-Static Approximation
  • Mixed Scattering Matrix
  • Transmission Matrix
• Conclusions

12. Mixed Scattering Matrix (P-matrix) in SAW Filter Modeling

Abstract

Concept of the mixed scattering matrix (P-matrix) plays an important role in modelling SAW devices because its structure and ?independent variables most closely correspond to the ?very physical nature of a SAW interdigital transducer having two acoustic and one electric ports. It is shown how the mixed scattering matrix can be converted to the wave scattering one and vice versa using the interrelation between generalized electric and wave variables on the ports. General properties of the mixed scattering matrix are discussed for a loslless reciprocal SAW transducer based on the energy conservation law and known properties of the wave scattering matrix. For analysis, the mixed scattering matrix is conveniently separated into acoustic, acousto-electric, electro-acoustic, and electric blocks and the interrelation between different blocks is deduced in the matrix form. Physical meaning of each matrix element is explained.
Supposed for the mixed scattering matrix of a SAW transducer to be known a priori, important applications of the mixed scattering matrix are considered. It is shown how to use the mixed scattering matrix for simulation electrical source/load effects including triple transit echo. Scattering properties of the impedance-connected SAW transducer pair are also investigated. Given the mixed and wave scattering matrices of SAW components, modelling of the multitransducer SAW devices is discussed. The application of the mixed scattering matrix to the modelling of SAW transducers in quasi-static approximation (neglecting interelectrode reflections) and taking into account interelectrode reflections due to the mass-electrical load effect is considered. Finally, given the mixed scattering matrix of the elemental cell, modelling of the single-phase unidirectional transducers (SPUDT) is considered.
Applications of the mixed scattering matrix are illustrated by simulation examples. Good agreement between simulated and experimental results is observed.

Contents

• Three-port representation of a SAW transducer
• Electrical and acoustical variables and their interrelation
• Mixed (electro-acoustic) scattering matrix and wave scattering matrix
• Properties of the mixed scattering matrix of a lossless SAW transducer
• Applications of the mixed scattering matrix
  • Electrically-loaded SAW transducer
  • Impedance-connected SAW transducer pair
  • Multiport SAW devices
  • SAW transducers with interelectrode reflections
  • SPUDT transducers
• Conclusions

13. Design of SPUDT/RSPUDT SAW Filters

Abstract

The lecture reviews basic properties and design principles of the SAW filters using Single Phase Unidirectional Transducers (SPUDT). Based on the general properties of the mixed scattering (P-matrix) of a SAW transducer as a three-port reciprocal and lossless network, it is shown that acoustoelectric conversion is related to the transducer short-circuit reflection. A condition of the transducer global directivity is deduced from the condition of the net zero reflection coefficient at the forward (backward) acoustic port of a SAW transducer that ncludes both mechanical (mass-electrical loading, short-circuit SPUT) and regenerated reflections (transducer terminated by the electrical load). As can be shown, the global directivity condition reduces to the 45^o phase shift between the global transduction and reflection centers of a SAW transducer. Local directivity condition applied to each SPUDT elemental cell is also discussed.

Basic type of the SPUDT elemental cells are considered, in particular, DART - Distributed Acoustic Reflector Transducer, EWC - Electrode Width Controlled Transducer, and Hunsinger's structure. The positions of the reflection and transduction centers are evaluated by the numeric calculations.

Concept of the reflective SPUDT (RSPUDT) is discussed, with the elemental SPUDT cells generalized to the RSPUDT implementation. Conversion between standard SPUDT cells with positive reflectivity and inversed SPUDT cells with negative reflectivity is considered. Superiority of the RSPUDT design over the conventional SPUDT design is demonstrated by some examples.

Practical aspects of SPUDT design based on the bidirectional split-finger prototype are discussed. Contrary to the conventional bidirectional SAW filters, both the weighted transduction (SAW excitation) and the weighted reflection functions are to be simultaneously synthesized that greatly complicates the synthesis problem of SPUDT SAW filters. A simplified SPUDT synthesis algorithm is discussed which is modification of the auto-correlation technique for synthesizing the weighted reflection function.

The problem of the RSPUDT optimum synthesis is discussed using the Chebyshev non-linear approximation. The general non-linear programming optimization is used to solve the porblem.

SPUDT/RSPUDT SAW filter modeling is discussed using the matrix cascading the elemental cells. The recurrent cascading relations are given. The estimated data on the reflection coefficient for the basic SPUDT elemental cells are presented.

SPUDT/RSPUDT design is illustrated by the CDMA SAW filter with the central frequency f₀=85.38 MHz. The classical SPUDT design and optimized RSPUDT design are presented and compared. Both filters have good triple transit echo suppression and low insertion loss when properly matched. ?However, while the CDMA SPUDT SAW filter fits the long SMD package 19 x 5 mm, ?RSPUDT SAW filter has almost twice shorter die size fitting the much shorter package 13.3 x 6.5 mm..

Good correspondence between modeled and measured SPUDT/RSPUDT SAW filter characteristics is observed.

Contents

• Concept of Single Phase Unidirectional SAW Transducer (SPUDT)
• SPUDT Features
• Basic Equations and SPUDT Properties
• Types and Properties of SPUDT Cells
• Resonant SPUDT Implementation
• Reflection Coefficient
• SPUDT Design
  • Design Goal
  • Design Assumptions and Simplifications
  • SPUDT Synthesis Algorithm
  • Insertion Loss Separation
• SPUDT Modeling
  • Design Goal
  • SPUDT Region Partition
  • Cascading Elemental Cells
• SPUDT Design and Modeling Example
  • SPUDT SAW Filter Specifications
  • Input SPUDT Synthesis
  • Output SPUDT Synthesis
• Modeled and Experimental Results
• Conclusions

14. MATLAB SAW Filter Analysis Toolbox (SAWFAT):
Structure, Organization, Algorithms, Examples

Abstract

This lecture covers the detailed description of the SAW Filter Analysis Toolbox (SAWFAT) uncluding the directory structure and organization. SAWFAT is a collection of the software tools for comprehensive analysis of the in-line or dual-track SAW filters in the quasi-static approximation. An accurate MSC modeling can be included in the analysis of the dual-track SAW filters if necessary (optional).

Basic modeling assumption is that bidirectional SAW interdigital transducers (IDT) are supposed to be periodic and non-reflective if short-circuited (quasi-static approximation). Two-mode approach (expansion into symmetric and antisymmetric first order rectangular modes) is applied to MSC modeling.

Modeling assumptions, toolbox capabilities, software limitations, and principles of the computational algorithms are discussed in the lecture. Purpose, synopsis, argument description, algorithm, and use of the basic computational subroutines are considered.

Compiling, linking and building MEX-files that enables to call C and/or Fortran computational subroutines directly from MATLAB is discussed with the necessary information to get up and run so that one can configure his system to build MEX-functions from the supplied source codes of the gateway programs and computational subroutines.

Tutorial examples and test results are given. The format of the input data is explained. Samples of data files are given that allows the user to effectively adopt these examples to the user's needs or compose own data files for analysis of the customized SAW filters.

Contents

• What is the SAW Filter Analysis Toolbox (SAWFAT)
  • Basic Modeling Assumptions
  • SAW Filters to be Analyzed
  • Toolbox Capabilities
  • Toolbox Limitations
  • Computational Algorithms
• Toolbox Organization
  • Directory Structure
  • File Naming Conventions
  • IDT-Directory
  • MSC-Directory
  • EXAMPLES-Directory
• Building MEX-Files
  • Fortran and C Compilers
  • Step-by-Step MEX-Files Generating
  • Troubleshooting
• Tutorial Examples
  • List of Tutorial Examples
  • Data File Format
  • Material Constants
  • Tutorial Examples Limitations
  • Software Generalization
  • Test Results

15. SAW Filter Computer-Aided Design (SAWCAD) Demonstration

Abstract

Basic features of the SAWCAD software developped by the author in 1987-1997 for IBM compatible personal computers are demonstrated. SAW filters to be designed consist of two bidirectional interdigital transducers (IDT) or single-phase unidirectional transducers (SPUDT) cascaded in the following combinations:
? ? 1) two unapodized (regular or withdrawal-weighted) transducers;
? ? 2) in-line uninform and apodized SAW transducers;
? ? 3) dual-track identical or different SAW transducers coupled via a multistrip coupler.
SAWCAD provides the entire design function starting from the SAW filter specifications and completing with photomask design. The effective and flexible optimum and suboptimum optimization techniques based on the Remez exchange algorithm are used for SAW filter synthesis with prescribed magnitude and phase (group delay) specifications. Suboptimum design allows to reduce considerably thecomputation time practically without sacrificing the approximation accuracy.
Both non-factorizational and factorizational design approaches are implemented. In non-factorizational design, one of the SAW transducers should be specified a priori, while another is optimized to meet overall SAW filter frequency response specifications. The element factor as well as the multistrip coupler transfer function can be correctly accounted for if necessary for broadband filters. Design of SAW filters containing two identical SAW transducers is also possible. Factorizational synthesis does not impose a priori specifications on SAW transducers comprised in a SAW filter and allows to reduce the SAW filter length. The design procedure starts from the optimization of the overall SAW filter frequency response to meet prescribed design specifications. The next step is to find Z-transform roots using roots searching program for high-order polynomials. To reduce the polynomial order, synthesis of the baseband prototype can be applied with the subsequent frequency transformation. Found Z-transform roots are shared in the systematic manner between input and output SAW transducers, with the acoustic taps reconstructed from the roots attributed to each transducer.
Two withdrawal-weighted synthesis techniques are implemented for designing high-performance SAW filters with encreased stop-band attenuation. For broad-band SAW filters with number of electrodes up to 100-150, the optimum synthesis technique based on the integer linear programming algorithm (branch and bound algorithm) must be applied. For narrow-band SAW filters with large number of fingers, the suboptimum design based on the step-wise approximation of the prototype apodization function has been developped. The approximation algorithm is quite general and can be applied to synthesis of the wide class of linear- and nonlinear-phase SAW filters. This suboptimum algorithm is applicable to the withdrawal-weighted factorizational synthesis.
The design of non-periodic SAW filters based on the non-equidistant sampling of the prototype bandpass impulse response is also implemented resulting in apodized quasi-solid or quasi-split finger SAW transducers.
Prototype withdrawal-weigted transducers can be converted to the SPUDT with the same ideal transfer function and synthesized reflective function to suppress electrical regeneration in the passband. Three basic SPUDT types are implemented: Hanma SPUDT containing lambda/16 fingers, DART (distributed acoustic reflection transducer) and EWC (electrode width control) transducer, both with lambda/8 fingers. After the SPUDT structure synthesis, a complete SPUDT SAW filter simulation in frequency and time domain as well as one- or two-component matching circuit optimization is possible.
Separate analysis of bidirectional SAW filters in quasi-static approximation with advanced capabilities is included. For tutorial purpose, ?computation of the charge density distribution and net charges on the electrodes of the generalized SAW transducers having arbitrary polarity sequence and single or interconnected floating electrodes is also included in SAWCAD. Other analysis capabilities using quasi-static appoximation comprise:

• admittance (radiation conductance and susceptance) calculation for unapodized and apodized SAW transducers;
• static capacitance calculation;
• bandpass and harmonic evaluation of a SAW filter frequency response;
• baseband or bandpass impulse response calculation;
• insertion loss evaluation.

Separate program for nodal analysis of the electrical networks comprising SAW filters or SAW components is also included. The program allows to compose an acousto-electric circuit comprising both electrical and/or SAW components which are modelled in-place in quasi-static approximation or described by the modelled or experimental S-parameters to be imported. The transfer function at any node of the network can be calculated, with the insertion loss evaluated.

Second order effects are included in SAWCAD simulation, particularly

• end effects due to the final length of a periodic SAW transducer;
• electrical circuit effects including external matching and triple transit echo;
• SAW diffraction (in parabolic approximation) and attenuation.

Iterative self-compensation of SAW diffraction and circuit effects is possible by perturbaion of the apodization function unless they are not too severe to completely distort a frequency response.

The programming languages are Fortran, C. Some recent design options are implemented using MatLab interfaced with Fortran programs.

Comprehensive demo design examples on all basic features are included in demonstration.

Contents

• Optimum and suboptimum synthesis of SAW bandpass filters with prescribed magnitude and phase (or group delay) specifications including linear-, nonlinear-, or minimum-phase characteristics
• Factorizational SAW filter synthesis based on the Z-transform roots searching and sharing
• Optimum design of broadband withdrawal-weighted (WW) linear phase SAW transducers with prescribed magnitude specifications
• Suboptimum design of narrowband withdrawal-weighted SAW transducers with high out-of-band attenuation and linear or nonlinear phase from the apodized periodic prototype SAW transducer
• Design of non-periodic (non-equidistant) SAW transducers based on the apodized periodic prototype SAW transducer
• Single phase unidirectional transducer (SPUDT) SAW filter synthesis and simulation
• Bandpass and harmonic evaluation of a SAW filter frequency response
• Baseband or bandpass impulse (time) ideal response calculation
• Impulse (time) response modelling
• Calculation of the charge density distribution and net charges on the electrodes of the generalized SAW transducers having arbitrary polarity sequence and single or interconnected floating electrodes.
• Static capacitance calculation for generalized periodic SAW transducers.
• Admittance (acoustic conductance and susceptance) calculation
• quasi-static approximation
• mass-electrical load (MEL) reflections
• Insertion loss calculation
• Scattering parameters calculation?
  • Cartesian
  • Smith chart
• Analysis of electrical circuits comprising SAW filters
• Second-order effects simulation including
  • end effects
  • electrical circuit effects including external tuning
  • triple transit echo
  • SAW diffraction and attenuation
• Iterative self-compensation of the second order effects including
  • SAW diffraction ?
  • circuit effects.
• Matching circuit synthesis and optimization

16. Short Course "Computer-Aided Design of SAW Filters"

Abstract


Short ?course consists of the four principal parts:

1. SAW Filter Modeling (Mixed Scattering Matrix: Properties and Applications)

2. Review of SAW Filter Optimization Techniques (Remez Exchange Algorithm, Linear Programming, ?Non-Linear Programming, Weighted Least Mean Squares (WLMS) .

3. Factorizational synthesis of SAW bandpass filters.

4. Design of low loss SPUDT/RSPUDT SAW filters.

Please contact the author for more details. Please bookmark and check and the updated information on the short course shall be posted.