Text preview for : 5990-3225EN State of the Art in EM Software for Microwave Engineers - White Paper c20140829 [13].pdf part of
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Keysight Technologies
State of the Art in EM Software
for Microwave Engineers
White Paper
Introduction
The growing number and complexity of high frequency systems is leading to an increased need for
electromagnetic (EM) simulation to accurately model larger portions of the system. There are several
different technical approaches to EM simulation, and while no method is generally superior to the
others, each one of them is aligned with one or more application areas. This article will discuss the
three most established EM simulation technologies: Method-of-moments (MoM), inite element meth-
od (FEM) and inite difference time domain (FDTD), linking the simulation technology to
solving speciic applications.
Authors: Jan Van Hese, Keysight Technologies
Jeannick Sercu, Keysight Technologies
Davy Pissoort, Keysight Technologies
Hee-Soo Lee, Keysight Technologies
03 | Keysight | State of the Art in EM Software for Microwave Engineers - White Paper
The method Overview of the method-of-moments
of moments Among all techniques to solve EM problems, the method of moments (MoM)
is one of the hardest to implement because it involves careful evaluation of
Green's functions and EM coupling integrals. Maxwell's equations are
transformed into integral equations which upon discretization yield the
coupling matrix equation of the structure.
The advantage of this transform is that the current distributions on the metal
surfaces emerge as the core unknowns. This is in contrast to other techniques
which typically have the electric and/or magnetic fields (present everywhere
in the solution space) as the core unknowns. Only the surfaces of the metals,
where the currents flow, need to be taken into account in the meshing (Figure 1).
Hence the number of unknowns (or the size of the matrix) is much smaller.
This results in a very efficient simulation technique, able to handle
very complex structures.
This benefit comes with a price as the integral equations are not applicable
for general 3D structures. The key is the availability of the Green's functions.
Computation of the Green's functions is only available for free space or for
structures that fit in a layered stack up. These so-called 3D planar structures
can have any shape in the plane of the layered stack, but can only have
vertical geometry features (via's) in the normal direction. Many practical RF or
microwave structures fall into this category. Hence the method of moments is
a very wide-spread technique and commonly used for the simulation of printed
antenna's, MMIC's, RF boards, SiPs, RFIC, SI structures and RF modules.
Figure 1. MoM discretization of a 3D planar structure (PCB differential via stubs)
04 | Keysight | State of the Art in EM Software for Microwave Engineers - White Paper
Recent innovations in the method-of-moments
As data rates and signal frequencies keep on rising, the complexity of the
electronic circuits that require EM simulation has gone up to such levels that
existing MoM technology suffers from performance issues (both in capacity and
speed). The main bottlenecks are in the storage and the solution of the huge
dense coupling matrix. For a structure with N discrete elements, the memory
storage requirement scales with N2 and the matrix solve time scales with N3
(when using a direct solver) or with N2 (when using an iterative solver). These
scaling properties impose a roadblock on the performance to address very
large and complex structures. A major break-through that recently emerged is
the development of matrix compression techniques that reduce these scalings
to NlogN. The benefits of NlogN technology in terms or memory usage and
computation time are huge and grow with the complexity of the structures.
Application of the method-of-moments for printed circuit
board simulations
With the enhancement of an NlogN matrix compression technique, a method
of moments solver is very well prepared to handle very complex designs. As
an example, we consider the simulation of differential via stubs in a 16 layer
printed circuit board stack up (Figure 2). The example demonstrates the benefits
of the MoM integral formulation. Note that the mesh used for the ground planes
(Figure 1) contains only cells in the via anti-pad holes. The entire ground plane
metallization is taken up in the kernels of the integral equations. The resulting
matrix equation has only 5,539 unknowns.
Figure 2. Differential via stubs in 16 layer PCB (geometry is stretched in vertical direction)
05 | Keysight | State of the Art in EM Software for Microwave Engineers - White Paper
The broadband data for the simulated group delay and insertion loss are obtained
in less then 10 minutes using the momentum simulator on a standard 4 core
Linux machine. The correlation with measured data is shown in (Figure 3).
Group delay (Sdd12) Insertion loss (Sdd12)
1.0E-10 10
0
-10
1.0E-11
-20
-30
1.0E-12 -40
1E8
1E9
1E10
2E10
0 4 8 12 16 20
freq. Hz freq. GHz
Figure 3. Simulated (red) and measured (blue) group delay and insertion loss
The authors wish to acknowledge Gustavo Blando (SUN Microwave Systems)
for his aid in the preparation of this PCB example.
Finite element method Overview of FEM method
FEM field solver has several advantages over MoM. For example, FEM solver
can handle arbitrary shaped structures such as bondwires, conical shape vias,
solder balls/bumps where z-dimensional changes appear in the structure.
Moreover, FEM solvers can simulate dielectric bricks or finite size substrates.
Many applications such as cavity designs require this capability. But it is
generally slower than MoM especially for planar applications. (Figure 4)
illustrates an example where FEM has advantages over regular MoM,
particularly with respect to the general 3D nature of the structure.
Figure 4. 3D FEM application example for spiral inductors with bond wires