The 14th Symposium on Accelerator Science and Technology, Tsukuba, Japan, November 2003

THE ADVANCED 3D-EM SIMULATION SOFTWARE AND
APPLICATIONS
Eiji Tanabe and Koichi Kanno
AET Japan, Inc.
URSIS Bldg. 9th Floor, 1-2-3 Manpukuji, Asaoku, Kawasaki-City, Kanagawa, 215-0004, Japan
Abstract
Most of the electromagnetic problems can be analyzed
and understood by 3D-EM (Electromagnetic) simulation
which is performed by solving Maxwell's equations
numerically. Recent advances in computer hardware
technology and EM simulation algorithm enable us tovisualize 3D EM wave propagation, even with personal
computers. This paper reviews the most recent status ofadvanced EM simulation technologies and their future.

representation of the original Maxwell’s equations.
Therefore it retains all analytical properties of the original
Maxwell’s equations as well as the physical andmathematical characteristics of EM fields. These features
are extremely important since numerical analysis maylead to incorrect solutions that do not exist physically.
The disadvantage of FDTD, and TLM compared withFEM, is the usage of Cartesian meshes, being quite
inflexible when discretizing non-orthogonal structures asshown in Fig 1.

INTRODUCTION
The
traditional
processfor
solving
EM(Electromagnetic) problems was to build a prototype,
accumulate performance test data by subjecting theprototype to various experiments, correct deficiencies,and retesting, which normally require several cycles.
While 3D-EM (Three Dimensional Electro-Magnetic)
simulation techniques existed, these methods weregenerally not economically feasible since they required
the use of supercomputers as well as a substantial
knowledge of EM theory and advanced numerical
techniques. During the last decade, the three dimensional
electromagnetic simulation capabilities have significantly
advanced due to the tremendous progress in computer
hardware technology combined with an improvement innumerical techniques.

3D-EM SIMULATION SOFTWARE
Various numerical methods have been used to solve EMproblems. These methods include the finite element
method (FEM), the finite-difference method (FDM), andthe moment method (MM). This discussion focuses on avariation of the finite-difference-time-domain (FDTD)
method, which is versatile and is applicable to nearly allEM problems. At the same time, the FDTD method’s
simple algorithm facilitates computational analysis.
FDTD is applied to the Maxwell equations by
discretizing the differential equations with respect to theoriginal Cartesian coordinates in time and space. Theseequations are then transformed into difference equations,which are solved step-by-step in time and apace. 1
This discussion focuses on a extension of the FDTD
method, that is the finite integration method (FIM) whichuses aset of Maxwell’s Grid Equations (MGE)transformed from the integral form of Maxwell’sequations. 2 The very important feature of MGE is that theset of matrix equations is a consistent and discrete

Fig.1. Mesh representation of a curved material boundary
by FEM (left) and FDTD (right).
A new approach called the Perfect Boundary
Approximation (PBA) technique was developed andimplemented in a new PC based 3D-EM simulation
software called MICROWAVE STUDIO (MWS). 3 Thismethod allows an accurate consideration of roundedmaterial boundaries without requiring the orthogonalmesh to be conformal. Instead, the sub-cellular
information is taken into account, leading to an algorithmwith second order accuracy for arbitrary shapedboundaries (Fig 2).

Fig.2. Mesh representation of a curved material boundaryby PBA.

SELECTION OF 3D-EM SIMULATIONSOFTWARE AND BENCHMARKThe process of selecting 3D-EM simulation software israther complicated since the optimum choice depends ona number of considerations that include the simulation

The 14th Symposium on Accelerator Science and Technology, Tsukuba, Japan, November 2003

goal, budget, schedule, number of users and available
computers. The following are very important criteria to beconsidered when selecting a 3D- EM software tool:1) Consistently reliable results,2) Relatively short computational time, compatible
with the development schedule,
3) Simplicity of operation, particularly the ease of CAD
input and mesh generation,4) Compatibility with your requirements,
5) Compatibility with other CAD tools,
6) Versatility and expandability,
7) Customer support and service.
When making the software selection, it is very important
for the user to generate benchmark results to check thesecriteria and to compare the various candidates.
It is highly desirable to use a benchmark problem forwhich the accurate experimental data has been obtained inorder to evaluate the computational results.

B) Bluetooth Antenna
Another typical application for EM-Simulators is theanalysis and optimization of antennas. Fig.5 shows aninverted F-antenna typically used for Bluetooth projects.

APPLICATIONS OF 3D-EM SIMULATIONSOFTWARE

The antenna performance and resonance frequency canbe optimized by varying the measures d, h and L with thebuilt in automatic optimizer of MWS. Fig.6 shaws theS11 parameter of the initial design and optimized antenna.

A) Coupled Cavity Waveguide FilterFig.3 shows a coupled cavity waveguide filter (7cavities, iris loaded). Due to high Q of the cavity filter, itis rather difficult to accurately calculate S-parameters
within a reasonable time using FEM or MM.
Fig 4 shows a comparison of measurement andsimulation for S11 and S21 using MWS. The computation
requires 47,488 mesh nodes, 20 min. CPU time and 13
MB on a windows PC with a 1.4 GHz XEON CPU

Fig.5. Inverted F-antenna and measures used forautomatic optimization.

Fig.6. S11 parameter of the initial and optimized inverted
F-antenna.

Fig.3. Iris loaded waveguide filter with 7 cavities.

C) Design of RF Window
RF Windows are one of the major concerns in designinghigh power microwave tubes and ac-celerators. Most of
conventional RF Windows uses a pillbox like cavity
operating on the TE11 mode. Fig.7 shows the result ofS11-parameter for a SLAC Type RF Window for frequencies between 2.5 to 6GHz.

Fig.4. Measured and computed S-parameters of an irisloaded waveguide filter with 7 cavities.

Fig.7: Amplitude of S11-parameters of the SLAC TypeRF Window.

The 14th Symposium on Accelerator Science and Technology, Tsukuba, Japan, November 2003

The TM11 like mode which has E field components
normal to the surface of ceramic disc, may aggravate thebombardment of electrons. Fig.8 shows the |E| patterns on
the surface of the ceramic disc for both modes.

Fig.8: |E| of TE11 (left) and TM11 (right) like modes on
the surface of the ceramic disc in the SLAC Type RF
Window.
The total computational time was less than 30 min on a450MHz Pentium II PC using MWS.
D) Accelerator Design
The time domain calculation is very useful for designing
multiple cavity coupled structures such as linear
accelerators. Fig.9 shows the mesh model of a S-band, 6cell travelling Wave Accelerator and the magnetic fieldvectors at 2π/3 mode resonance in a cross section. The
rounded irises are considered very accurately by the PBAtechnique.

Fig.10: Amplitude of S21 of the 6-cell Traveling Wave
Accelerator.
Fig.10 shows the amplitude of the S21-parameter. Sparameters can be obtained from a single time domain
computation by using Discrete Fourier Transformation(DFT) or Auto Regressive Filter techniques that can speed
up S-parameter calculations for high Q structures
drastically.

CONCLUSIONS
The advanced EM simulation technique utilizes FIMand PBA is presented and various examples of the method
are discussed. The examples are taken from practicalapplications in research and industries. These results
indicate that even the most complicated calculation can be
performed within the reasonable computational time withPCs. In future, 3D-EM simulation tools, like MWS will
be commonly used in R&D, engineering and even inmanufacturing.

REFERENCES[1] K. S. Yee, “Numerical Solution of Initial Boundary
Value Problems Involving Maxwell’s Equations in
Isotropic Media” IEEE, Antenna and Propagation
AP-14 pp302-307, 1966
[2] T. Weiland, “Time Domain Electromagnetic Field
Computation with Finite Difference Methods” Int.
Journal of Numerical Modelling 9, 295-319, 1996
[3] B. Krietenstein, et al, “The Perfect Boundary
Approximation Technique Facing the Big Challengeof High Precision Field Computation”, Proceedingsof the X IX International Linear Accelerator
Conference (LINAC 98), Chicago, USA, pp860-862,
1998
Fig.9: Mesh model of a 6-cell Travelling Wave
Accelerator (above) and magnetic field of the 2π/3 modein a cross section (below).