RF & Microwave Simulation with the Finite Integration Technique
- From Component to System Design
Irina Munteanu
CST GmbH
Bad Nauheimer Str. 19, 64289 Darmstadt, Germany
irina.munteanu@cst.com
Abstract— The paper presents a historical review and the
current state-of-the-art of the Finite Integration Technique (FIT),
method which has been successfully used for almost 30 years for
the solution of electromagnetic field problems. The presented
applications are in the range of high-end RF and microwave
technologies.
Keywords— Finite Integration Technique, FEM, 3D field
simulation, microwaves, high-frequency, numerical techniques
I.
laboratories with the goal to develop of an FIT-based, general
software package, for the solution of electromagnetic
problems. The result of the 10 years of existence of this
consortium was a full electromagnetic, thermal and particle
tracking software, distributed to (and widely used in) research
facilities from 26 countries.
More details on the FIT equations and algorithm will be
presented in the full paper. The present abstract summarizes
the variety of applications to RF and microwave simulations.
A SHORT HISTORICAL REVIEW
Almost 30 years ago, one of the most successful numerical
methods for the simulation of electromagnetic fields and of
various coupled problems appeared : the Finite Integration
Technique, for short FIT [1]. The key idea FIT was to use, in
the discretization, the integral, rather than the differential form
of Maxwell’s equations. FIT generates exact algebraic
analogues to Maxwell’s equations, which guarantee that the
physical properties of fields are maintained in the discrete
space, and lead to a unique solution.
This early intuition proved to be correct and to have
numerous theoretical, algorithmic and numerical advantages.
Moreover, recently the same viewpoint seems to become
predominant also in a historically completely different method,
the finite element method (FEM) [2].
FIT was first proposed with application to the solution of
Maxwell’s equations in frequency domain (Fig. 1). It was the
first eigenmode algorithm able to reliably eliminate all
spurious modes – whereas for other methods, such as the
FEM, a solution to this issue could be found only 10 years
later.
The first application of FIT to eddy current problems was
presented one year after the first paper (1978), followed by (to
mention just a few) the extension of FIT to FDTD-like
schemes, including the extension to r--z coordinate system
(1980), application to triangular meshes (1987), waveguide
boundary conditions to allow accurate S-parameter extraction
from time domain simulations (1988), stable subgridding
algorithm (1995), application to non-orthogonal grids,
including triangular fillings (1998, 1999), model order
reduction in conjunction with FIT (2000).
Around 1980, the FIT gained instantaneous fame in the
international accelerator physics community, as the first code
ever which was able to calculate transient field of charged
particles at ultra-relativistic energies. This was the starting
point of the MAFIA Collaboration (an acronym for “solving
MAxwell’s equations with the Finite Integration Algorithm”),
a consortium of universities, research institutes, accelerator
Fig. 1. High accuracy mode computation for a 22 Gap IH Ion Accelerator
designed entirely based on FIT simulations; the mesh of the 20m – long
structure contained 3 million cells (simulation and experimental model).
The success of the Finite Integration Technique is probably
mainly due to three factors. First, it is an algorithm with a
sound theoretical foundation (among others, stability,
orthogonality of numerically computed modes, energy and
charge conservation were demonstrated in a very early stage).
Second, it is applicable not only in frequency, but also in time
domain, allowing thus the simulation of very large or very
complex structures. Last but not least, it is applicable to a
variety of mesh types. On Cartesian grids, whereas the
classical FDTD has the disadvantage of the staircase
approximation of complex boundaries, the Perfect Boundary
Approximation (PBA)™ technique and its extension Thin
Sheet Technique™ (TST), maintain all the advantages of the
structured Cartesian grids, while allowing an accurate
modeling of curved boundaries (Fig. 2). The PBA algorithm is
implemented in CST MICROWAVE STUDIO™, the
commercial software package based on FIT [3].
needed: PCBs, integrated circuit components, etc. This is due
to the partial failure of the circuit design techniques, when
operating frequencies of e.g. integrated circuits grow. Figure 4
presents such an example: the surface currents on a Ball Grid
Array Package, at a quite high frequency, 10 GHz. The field
effects are clearly visible, and would not be captured by any
circuit simulation.
Fig. 2. Thin Sheet Technique applied to a curved patch antenna array.
Staircase approximations, as well as too small mesh steps are avoided.
II. RF AND MICROWAVE APPLICATIONS
The needs of today’s industry go more and more in the
direction of computer simulation: operating frequencies grow
and make existing design techniques difficult to apply; device
complexity increases every year; prototyping becomes more
expensive and time-consuming.
High-frequency
electromagnetic
simulation
today
continues of course to be needed in the classical areas of
microwave applications: filters, connectors, waveguide
structures, antennas. The characteristic of this area of
applications is that the models become very large, requiring
very efficient algorithms in terms of computational complexity
and memory requirements. As an example, Fig. 3 shows the
results of the full 3D simulation of a 30 meter-long airplane
illuminated by a plane wave at 500 MHz. Although quite large
(9 million cells), with the efficient FIT/PBA time domain
algorithm it takes under two hours to simulate on a common
PC.
Fig. 4.
Surface currents on an IC package at 10 GHz.
Whereas 3D field simulation is perfectly suited for
simulating components and devices of high complexity, it
would be inefficient to apply to the simulation of entire
systems: the numerical effort for obtaining a desired accuracy
would simply be too large. For such applications, a hybrid
approach is needed. FIT has been successfully integrated in
such a design environment, in which numerical methods may
be arbitrarily mixed: one may e.g. easily combine fully three
dimensional blocks with planar solution tools, analytical
solution or mode matching techniques, or virtually with any
other technique that is capable of describing an element by
some port behavior. Most importantly, this open architecture
approach allows including best-in-class elements, and thus
eliminates the dependence on single proprietary software.
ACKNOWLEDGEMENT
´The valuable advice and support of Prof. Thomas Weiland
is gratefully acknowledged.
III.
[1]
[2]
Fig. 3.
Surface currents (at 500 MHz) on an airplane illuminated by a plane
wave
A new tendency is to apply field simulation to domains in
which until recently only circuit-simulation techniques were
[3]
REFERENCES
1] T. Weiland: “A Discretization Method for the Solution of Maxwell's
Equations for Six-Component Fields,” Electronics and Communication
(AEÜ), Vol. 31, p. 116, 1977.
A. Bossavit, “’Generalized finite differences’ in computational
electromagnetics,” Progress In Electromagnetics Research, vol. PIER
32, pp. 45–64, 2001
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