# Numerically efficient techniques for the analysis of MMIC structures

Abstract (Summary)

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The method of moments (MoM) has been widely used for the full-wave
electromagnetic analysis of layered structures. It has been gaining in popularity because
the conventional equivalent circuit based simulation techniques have difficulty in
producing accurate results for circuits with complex geometry and high operating
frequency. However, the MoM is a computationally intensive process and requires
considerable computer resources to perform the analysis. This thesis proposes and
validates several techniques to speed up different stages of the MoM process.
We first consider the computation of impedance matrix for layered structures. It is
time-consuming since each element requires the evaluation of quadruple integrals. To
increase the efficiency, we propose a technique, referred to as the Fast Matrix Generation
(FMG). In this method, conventional and rigorous numerical methods are still used for
generating the impedance matrix elements that are associated with the near-field
interactions, while a more efficient scheme is employed where the separation distance
between basis and testing functions exceeds a threshold value. A significant saving in
computation time, sometimes over 90%, can be achieved via the application of this
approach, as is demonstrated by numerical results for a number of typical microwave
circuits.
The frequency response of microwave passive structures often involves one or
more resonances, and this, in turn, requires the use of small frequency steps for their
analysis. This imposes an enormous computational burden when computing their
frequency response via the MoM process. We introduce an impedance matrix
interpolation technique that serves to reduce the computation time for the impedance
matrix quite considerably, especially if the frequency band of interest is wide. In this
approach, the frequency variation of the matrix element is expressed in term of
interpolating polynomials with or without extracting the phase factor
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, depending on
the separation distance between the source and field points. Although the concept of
matrix interpolation is not entirely new, the accuracy has been improved in this work
over those published previously. Furthermore, our algorithm has the added advantage that
it can be readily incorporated into existing codes. The efficiency of this approach is
validated by considering a variety of layered structure problems.
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Next, the Characteristic Basis Function Method (CBFM) is proposed to reduce the
matrix solution time for MoM analysis of large and/or complex geometries. The CBFs
are special types of high-level basis functions, defined over domains that encompass a
relatively large number of conventional subdomain bases, e.g., triangular patches or
rooftops. In this approach, we define two kinds of CBFs that represent different kinds of
interactions between the conventional subdomain bases contained in the CBFs. The
primary CBF for a particular block is associated with the solution for the isolated block,
while the secondary ones account for the mutual coupling effects between this block and
others. Efficiency of the CBFM is demonstrated with several numerical examples
Finally, we present an iterative process for solving the matrix equation by using
an extrapolated initial guess in conjunction with the Conjugate Gradient (CG) method.
The initial guess is computed from the orthonormalized version of the solutions at
previous frequencies. The number of iterations needed to make the residual error smaller
than a tolerance is reduced via the application of the extrapolated initial guess. The
effectiveness of this approach is illustrated via several numerical examples.
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Bibliographical Information:

Advisor:

School:Pennsylvania State University

School Location:USA - Pennsylvania

Source Type:Master's Thesis

Keywords:

ISBN:

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