Ansoft High Frequency
Structure Simulator (HFSS)
Training
Version 7, with OptimetricsTM
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Ansoft HFSS Version 7
Training
Section 1: Introduction to
HFSS and the Finite
Element Method
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Synopsis of Introduction
General FEM Introduction, Usage, and Definitions
FEM in Electromagnetics
Positioning vs. Other Solution Techniques
Possible Applications
High Frequency Structure Simulator Introduction
The HFSS Field Equation and Matrix Solution
HFSS “Adaptive” Convergence
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What is Finite Element Method (FEM)
Software?
FEM software is a design tool for engineers and
physicists, utilizing rapid computations to solve
large problems insoluble by analytical, closed-form
expressions
The “Finite Element Method” involves subdividing a large
problem into individually simple constituent units which
are each soluble via direct analytical methods, then
reassembling the solution for the entire problem space as
a matrix of simultaneous equations
FEM software can solve mechanical (stress,
strain, vibration), aerodynamic or fluid flow,
thermal, or electromagnetic problems
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FEM Problem Constraints
Geometry can be arbitrary, 3-dimensional
Model ‘subdivision’ is generally accomplished by use of
tetrahedral or hexahedral (brick) elements which are
defined to fill any arbitrary 3D volume
Boundary Conditions within and without problem
can be varied to account for different
characteristics, symmetry planes, etc.
Size constraints are predominantly set by
available memory and disk space for storage and
solution of the problem matrix
Solution created is in the frequency domain,
assuming steady-state behavior
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Major Industries using FEM Software
Communications/Telecom
Aerospace/Aviation
Automotive
Power
Consumer Electronics (Audio/Visual, Computer)
Medical (Imaging, Electrical Equipment)
Universities (Research and Instructional)
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Commonly Used Terms in FEM
An FEM “Element” is a single subdivided ‘unit’ of
the overall problem to be solved.
HFSS uses tetrahedral elements, with triangular faces.
The “Mesh” is the mapping of tetrahedral elements
to the 3D geometry for which a solution is desired.
Meshing is the process of defining the position of vertices
which comprise all the tetrahedral locations in a problem
space.
The “Matrix” is the assembly of simultaneous
equations related to the mesh which permit
solution of behavior in a defined solution space
HFSS’s matrix equations are formulated to solve for
electromagnetic field behavior
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Different Methods of
Electromagnetic Analysis
MOM
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When is an FEM solver appropriate for Electromagnetic
Problems (Lower Bound)?
Example: Finding Signal Integrity
impacts of a Via in the signal path
0
λ/100
Example: Coax to WG Transformer
λ/10
Use a Quasi-Static Solver (OVERLAP)
■
■
■
Use a FEM Full-Wave Solver
When the Electrical Length (in wavelengths) requires phase consideration
■
■
Problem Scale
λ/10 is a guideline; there are exceptions
When radiation from the device must be considered
When S-Parameters are the desired output
When lossy dielectric materials have significant effects
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When is a FEM solver appropriate for Electromagnetic
Problems (Upper Bound)?
When the structure under evaluation is not too large to be
reasonably solved with available resources
■
■
This limit is VERY problem and hardware dependent
ROUGH rule-of-thumb: Projects should be within 5 x 5 x 5
wavelengths in volume
When the structure’s aspect ratio does not exceed manythousands to one
■
■
Example: extremely long, thin wire antennas might be more
efficiently solved using a Wire-MoM (e.g. NEC)
Entirely ‘planar’ structures with stratified dielectrics might be more
efficiently solved using a 2.5D MoM (e.g. Ensemble)
When the structure’s behavior is not more easily
approximated using Optical (GTD or Ray-Tracing) Techniques
■
■
Example: Parabolic Dish antenna, generally many 10’s of
wavelengths in diameter
Example: Radar Cross Section of a large vehicle body, such as an
aircraft or helicopter
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Some Typical High-Frequency
Electromagnetic Applications
Waveguide Components
RF Integrated Circuits
Antenna
EMC
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High Frequency Structure Simulator (HFSS)
Flowchart of General Design Process
Input Model Parameters
Define Solution Criteria
Geometry
Material Properties
Boundary Conditions
Frequency
Adaptive? Convergence Parameters?
Sweep? Sweep Parameters?
Perform Initial Solution
Generate Mesh
Solve Excitations
Solve 3D Fields
Adaptive?
NO
YES
NO
YES
Iterate on Solution
SOLUTION
Sweep?
Evaluate vs. Convergence Parameters
Refine Mesh and Resolve
Exit only when Conv. Parameters Met
Perform Sweep Solution
Define Excitation across band
Solve 3D Fields across band
Review Results
S-Parameters
(Tabular and Plotted)
Field Visualization
Data Output/Exportation
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HFSS Solution Process
Subdivide model into Elements (tetrahedra)
Define basis functions per tetrahedra
■
■
Basis functions, Wn define conditions between nodal locations in
the overall mesh of tetrahedra, based on problem inputs
Functions are simple and nonzero only within the tetrahedra
Multiply Basis Functions by Field Equation
■
HFSS Solves Field Equation Derived from Maxwell’s Equations:
æ 1
ö
∇ × çç ∇ × E − k o2ε r E = 0
è µr
Integrate result over Volume
é
ù
æ 1
ö
Wn ⋅ ∇ × çç ∇ × E ÷÷ − ko2ε rWn E dV = 0
ê
V
è µr
ø
ë
■
Integration replicated in thousands of equations for n=1, 2, ...N
Intent is to obtain N equations with N unknowns for solution
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HFSS Solution Process, cont.
Rewrite Equations, Using Green’s and Divergence Theorems:
■
Set Equal to Excitation/Boundary Terms
é
ù
æ 1
ö 2
ç
÷
ê(∇ × Wn ) • ç ∇ × E ÷ − ko ε rWn E dV = (boundary term)dS
V
è µr
ø
S
ë
■
Write E field as summation of unknowns, xm, times same basis
functions used in generating the initial series of equations:
E=
N
m =1
xmWm
Resulting Equations allow solution of unknowns, xm, to find E
æ é
ù ö
ö 2
æ 1
ç
÷
ç
(
)
−
x
⋅
∇
×
W
•
∇
×
W
k
ε
W
W
ê
å
m
n
m÷
o r n m dV = (boundary term ) dS
çµ
ç
m =1
ø
è r
S
èV ë
N
■
Note: Equation has the basic form Ax=B, where
■
■
■
A is the basis functions and field equation, in a known N x N matrix
‘x’ is the unknowns to be solved for
B is the excitation
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Properties of the Solution Matrix
The Finite-Element Solution Matrix has a number of known
characteristics
■
■
Size: Matrix is generally large, N on the order of tens of thousands
Density: Matrix is generally sparse, with a large number of zero
entries
■
■
Only basis functions in the same tetrahedra result in nonzero entries
Banding: Intelligent ordering of the mesh results in nonzero entries
being clustered along the diagonal
Different Types of Problems have different mesh characteristics
as well
■
■
■
■
Lossless problems will have only real nonzero entries
Lossy problems will have complex nonzero entries
Problems with standard excitations (‘ports’) will have symmetric
matrices
Problems with certain boundary conditions (e.g.‘linked’) may have
asymmetric matrices
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Solving the Matrix
Due to its sparse and banded nature, the matrix can be solved
using mathematical matrix decomposition techniques
■
HFSS Version 7 uses an iterative Multifrontal Matrix Solver
Constructing and Decomposing this Matrix form the bulk of the
computational load in HFSS
■
Significant effort is also spent in generating a good mesh, which will
result in a well-behaved matrix
■
■
Tetrahedra “aspect ratio” is one driver of mesh acceptability
A good mesh results in a well-conditioned matrix
For each excitation defined, only the right-hand side of the Ax=B
equation changes
■
■
Therefore Matrix Decomposition must be performed only once
Resolving the entire E-field result to view different excitations takes
minimal effort by comparison
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Known Approximations in the Finite
Element Method
Discretization: the accuracy with which the solution space may
be subdivided
■
■
Tetrahedra are good at ‘filling’ curved shapes
Nevertheless, some facetization of the solution space can result
Accuracy of the Excitation Solution
■
■
The ‘port’ excitation (or B, in the Ax=B equation) is first solved using a
2D field equation, before being used as an input into the 3D solution
Any inaccuracies in the 2D solution will therefore impact 3D results
Finite Size Limitations on “Free Space” Models
■
Termination of modeled space with an ‘absorbing boundary condition’
mimics continued radiation into free space, but will have limitations
Finite number of decimals available for calculation
...if there were no limits on the size of the matrix and on the
number of digits for computation, there would be no limit to the
accuracy of the Finite Element Method!
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HFSS Adaptive Refinement Process
The FEM problem’s first mesh is generated
with respect to solution wavelength
■
“Lambda refinement” results in tetrahedra of
about λ/4 in free space
However, for many field behaviors this may
not be sufficient mesh density to properly
solve for rapid fluctuations or extremely
localized effects
The adaptative refinement process
addresses this issue
■
■
■
■
Field solution is obtained for initial mesh
Mesh is refined based on error analysis
and/or field strength localization
Field is re-solved and compared with prior
solution.
If user-specified criteria for convergence are
not met, process continues
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HFSS Adaptive Refinement Criteria
Adaptive Refinement has two logical “OR” exit
criteria
■
■
Number of Passes: The maximum number of times to run
and refine the solution before quitting
Delta-S: The worst-case vector magnitude difference of any
S-parameter, as compared between the current and
previous pass results.
■
More specific S-parameter convergence criteria per parameter
are also available
Adaptation is performed at a single excitation
frequency
■
Implication: For best accuracy in swept solutions, the
adaptive procedure should be done at a sufficiently small
representative wavelength to capture high-end behavior
■
(More detail about solution frequency selection will be
presented later)
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Example of Adaptive meshing
Waveguide Filter at right (symmetry along top
face) shows effect of mesh adaptation. The
region between posts has a denser mesh,
due to the superposition of reflected energy
found in the solution process.
Post
Post
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Limitations of Adaptive Meshing
Some structures and solution types do not
lend themselves well to adaptive meshing
convergence. In these cases, manual
meshing and mesh seeding allow the user to
provide meshing guidance to the software for
better solution results
Specific model or solution types for which manual or
seeded meshing is recommended will be discussed in
the presentation on Solution Setup (Section 6)
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