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Updated April, 2005 |
Lectures and Short Courses of
Dr. A.S.Rukhlenko
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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
incurred while lecturing at your site.
SAW filter course can be organized at Neuchatel (Switzerland) for
an individual or for a group, at a special request.
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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]
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Contents
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Frequency response of a periodic SAW transducer
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Basic properties and classification of SAW transducers
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Synchronous and asynchronous SAW transducers
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Overlap- and finger-length weighted transducers
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Array and element factors and their properties
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Impulse model and discrete Fourier transform
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Frequency sampling interpolation and properties of the basis functions
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Time domain interpolation
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Reduction of the parameters in the time domain: baseband and bandpass response
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Reduction of the parameters in the frequency domain: oversampling and
undersampling
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Transformations of the SAW filter response (frequency scaling and shifting)
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Z-transform and its properties.
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Classification of the Z-transform roots.
[Abstract]
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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]
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Contents
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Optimum design of SAW linear phase bandpass filters: statement of the problem
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Chebyshev approximation and its properties
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Optimization methods:
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Linear programming
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Remez exchange algorithm
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Suboptimum synthesis of SAW filters
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Frequency sampling technique and linear programming optimization
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Application of the Remez exchange algorithm to optimum and suboptimum
synthesis
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Factorizational synthesis of SAW filters
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Design of SAW filters with prescribed magnitude and phase response
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Linearization schemes
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Iterative techniques
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Chebyshev approximation of the complex-valued function
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Weighted-least-mean-squares approximation
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Design examples
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Conclusions
[Abstract]
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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]
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Contents
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Z-transform and its properties
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Classification of the Z-transform roots:
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monozeros
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couples of zeros
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linear-phase quadruplets
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Properties of Z-transform roots in stopband and passband
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Basic features of the roots solving program for high-order polynomials
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Factorizational synthesis algorithm for linear- and nonlinear-phase SAW filters
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Suboptimum and optimum synthesis of minimum-phase SAW filters
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Factorizational synthesis design examples:
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bandpass linear-phase SAW filter
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SAW filter with prescribed magnitude and phase response
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suboptimum and optimum minimum-phase SAW filter design
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Conclusions
[Abstract]
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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]
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Contents
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Definition of the Acoustoelectric Conversion Function
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Generalized Wave Amplitude and Surface-Wave Potential
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Acoustoelectric Conversion in the Quasi-Static Approximation
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Unapodized Periodic SAW Transducers
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Basic structure and Guard Electrodes
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Array Factor and Element Factor
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Contribution of the Guard Electrodes to the Acoustoelectric Conversion
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Finger (Potential) and Gap (Voltage) Taps
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Element Factor Properties
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Example of Misusing Finger Taps
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Apodized Periodic SAW Transducers
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Basic Assumptions
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Generalization of the Finger and Gap Taps
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Conclusions
[Abstract]
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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]
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Contents
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Nodal Admittance Matrix of a SAW Transducer
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Definition of the Admittance Matrix
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Modeling Assumptions in the Quasi-Static Approximation
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Elemental Nodal Admittance
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Self- and Mutual Elemental Admittances
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Properties of the Admittance Matrix
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Admittance of an Unapodized SAW Transducer
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Definition of the Admittance Matrix
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Admittance Calculation in Terms of Finger Potentials
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Nodal Admittance Matrix in Terms of Gap Voltages
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Admittance Calculation in Terms of Gap Voltages
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Example of the Admittance Calculation and Relation to the Known Results
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Correction due to the Contribution of Guard Electrodes
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Admittance of an Apodized SAW Transducer
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Admittance Calculation in Terms of Finger Taps
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Admittance Calculation in Terms of Gap (Overlap) Taps
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Physical Meaning of Weighting the Elemental Admittances
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Computational Implementation of the Algorithm
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Calculation Example and Experimental Results
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Conclusions
[Abstract]
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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]
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Contents
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Introduction
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Statement of the electrostatic problem for a periodic SAW transducer
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Phased array periodic transducer and basic analytic equations
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Surface charge density distribution calculation
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Interrelation of the electrode charges and voltages
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Capacitance and potential matrices. Interelectrode capacitors
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Static capacitance of a SAW transducer
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Mixed electrostatic problem and its solution
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SAW transducers with separate and interconnected floating electrodes
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Calculation examples
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Conclusion
[Abstract]
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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]
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Contents
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Basic approximations and equations
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General closed-form solution of the wave propagation problem
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Modelling of the periodic reflective array
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Modelling of SAW transducers
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Closed-form mixed scattering matrix of a SAW transducer
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Determination of COM- parameters
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Self-coupling
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Cross-coupling
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Excitation function
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Static capacitance
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COM-analysis applications
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SAW reflectors
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Self-matched SAW transducers
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Long SAW transducers with internal reflections
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One- and two-port SAW resonators
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Conclusions
[Abstract]
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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]
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Contents
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Statement of the analysis problem
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Electrical and acoustical variables on the ports
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Mixed (electro-acoustic) scattering matrices and wave scattering matrices
of the components
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Coupled and uncoupled acoustical ports
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Connection matrix
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Closed-form block-matrix solution of the problem
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Particular case: multiport SAW system loaded by acoustic two-port junctions
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Applications of the method:
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one-port SAW resonator
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two-port SAW resonator
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Conclusions
[Abstract]
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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]
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Contents
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Normal Mode Representation of a Multistrip Coupler
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Concept of a Multistrip Coupler (MSC)
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MSC Modeling Assumptions
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Boundary Conditions
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Two Modes Approximation
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Physical Meaning of the Symmetric/Antisymmetric Modes
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Properties of the Normal Modes in the Periodic Gratings
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Wavenumber and SAW Velocity
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Reflection Coefficient
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Dispersion Relation
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Multistrip Coupler Models
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Reflective Array Model (RAM)
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Coupling-of-Modes (COM) Model
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Field Approach (Ingebrigtsen)
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Quasi-Static Approximation (Morgan)
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MSC Modeled and Experimental Results
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MSC Stopband and Passband Modeling
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Comparison with Experimental Data
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Conclusions
[Abstract]
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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]
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Contents
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Admittance, Wave Scattering, and Mixed Scattering Matrices of the Multi-Port
Network
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Definition of the Mixed Scattering Matrix
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Generalized Wave Amplitudes and Electric Variables
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Conversion between Admittance, Wave Scattering, and Mixed Scattering Matrices
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Reciprocity and Power Conservation
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Mixed Scattering Matrix of a SAW Transducer
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Three-Port Representation of a SAW Transducer
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Physical Meaning of the Mixed Scattering Matrix
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Mixed Scattering Matrix Elements
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Conversion to the Wave Scattering Matrix
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Properties of the reciprocal and lossless SAW transducer
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Conversion between Mixed Scattering and Transmission Matrices
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SAW Transducer Modeling in the Quasi-Static Approximation
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Mixed Scattering Matrix
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Transmission Matrix
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Conclusions
[Abstract]
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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]
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Contents
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Three-port representation of a SAW transducer
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Electrical and acoustical variables and their interrelation
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Mixed (electro-acoustic) scattering matrix and wave scattering matrix
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Properties of the mixed scattering matrix of a lossless SAW transducer
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Applications of the mixed scattering matrix
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Electrically-loaded SAW transducer
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Impedance-connected SAW transducer pair
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Multiport SAW devices
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SAW transducers with interelectrode reflections
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SPUDT transducers
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Conclusions
[Abstract]
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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 45o 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]
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Contents
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Concept of Single Phase Unidirectional SAW Transducer (SPUDT)
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SPUDT Features
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Basic Equations and SPUDT Properties
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Types and Properties of SPUDT Cells
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Resonant SPUDT Implementation
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Reflection Coefficient
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SPUDT Design
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Design Goal
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Design Assumptions and Simplifications
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SPUDT Synthesis Algorithm
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Insertion Loss Separation
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SPUDT Modeling
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Design Goal
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SPUDT Region Partition
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Cascading Elemental Cells
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SPUDT Design and Modeling Example
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SPUDT SAW Filter Specifications
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Input SPUDT Synthesis
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Output SPUDT Synthesis
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Modeled and Experimental Results
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Conclusions
[Abstract]
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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.
Download
SAWFAT Demo (MATLAB)
[Contents]
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Contents
 What is
the SAW Filter Analysis Toolbox (SAWFAT)
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Basic Modeling Assumptions
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SAW Filters to be Analyzed
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Toolbox Capabilities
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Toolbox Limitations
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Computational Algorithms
Toolbox
Organization
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Directory Structure
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File Naming Conventions
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IDT-Directory
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MSC-Directory
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EXAMPLES-Directory
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Building MEX-Files
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Fortran and C Compilers
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Step-by-Step MEX-Files Generating
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Troubleshooting
Tutorial Examples
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List of Tutorial Examples
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Data File Format
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Material Constants
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Tutorial Examples Limitations
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Software Generalization
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Test Results
[Abstract]
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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:
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admittance (radiation conductance and susceptance) calculation for unapodized
and apodized SAW transducers;
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static capacitance calculation;
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bandpass and harmonic evaluation of a SAW filter frequency response;
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baseband or bandpass impulse response calculation;
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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
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end effects due to the final length of a periodic SAW transducer;
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electrical circuit effects including external matching and triple transit
echo;
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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.
YOU CAN SEE NOW WITH YOUR OWN EYES HOW IT WORKS !
[Contents]
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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
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quasi-static approximation
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mass-electrical load (MEL) reflections
Insertion loss calculation
Scattering parameters calculation
Analysis of electrical circuits comprising SAW filters
Second-order effects simulation including
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end effects
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electrical circuit effects including external tuning
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triple transit echo
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SAW diffraction and attenuation
Iterative self-compensation of the second
order effects including
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SAW diffraction
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circuit effects.
Matching circuit synthesis and optimization
[Abstract]
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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.
Abstract]
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Lecture 1