1-1 Getting Started: Ansoft HFSS 8.0 Baofu Jia Physical Electronics Institute University of Electronic Science and Technology of China

1-2 Section 1: Introduction to HFSS and the Finite Element Method Getting Started: Ansoft HFSS 8.0

1-3 Synopsis of Introduction ò General FEM Introduction, Usage, and Definitions ò FEM in Electromagnetics ò Positioning vs. Other Solution Techniques ò Possible Applications ò High Frequency Structure Simulator Introduction ò The HFSS Field Equation and Matrix Solution ò HFSS “Adaptive” Convergence

1-4 What is Finite Element Method (FEM) Software? ò FEM software is a design tool for engineers and physicists, utilizing rapid computations to solve large problems insoluble by analytical, closed-form expressions ò 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 ò FEM software can solve mechanical (stress, strain, vibration), aerodynamic or fluid flow, thermal, or electromagnetic problems

1-5 FEM Problem Constraints ò Geometry can be arbitrary, 3-dimensional ò Model ‘subdivision’ is generally accomplished by use of tetrahedral or hexahedral (brick) elements which are defined to fill any arbitrary 3D volume ò Boundary Conditions within and without problem can be varied to account for different characteristics, symmetry planes, etc. ò Size constraints are predominantly set by available memory and disk space for storage and solution of the problem matrix ò Solution created is in the frequency domain, assuming steady-state behavior

1-6 Major Industries using FEM Software ò Communications/Telecom ò Aerospace/Aviation ò Automotive ò Power ò Consumer Electronics (Audio/Visual, Computer) ò Medical (Imaging, Electrical Equipment) ò Universities (Research and Instructional)

1-7 Commonly Used Terms in FEM ò An FEM “Element” is a single subdivided ‘unit’ of the overall problem to be solved. ò HFSS uses tetrahedral elements, with triangular faces. ò The “Mesh” is the mapping of tetrahedral elements to the 3D geometry for which a solution is desired. ò Meshing is the process of defining the position of vertices which comprise all the tetrahedral locations in a problem space. ò The “Matrix” is the assembly of simultaneous equations related to the mesh which permit solution of behavior in a defined solution space ò HFSS’s matrix equations are formulated to solve for electromagnetic field behavior

1-8 Different Methods of Electromagnetic Analysis MOM

1-9 When is an FEM solver appropriate for Electromagnetic Problems (Lower Bound)?  0 Use a Quasi-Static Solver n When the Electrical Length (in wavelengths) requires phase consideration n /10 is a guideline; there are exceptions n When radiation from the device must be considered n When S-Parameters are the desired output n When lossy dielectric materials have significant effects Use a FEM Full-Wave Solver Problem Scale Example: Finding Signal Integrity impacts of a Via in the signal path  (OVERLAP) Example: Coax to WG Transformer

1-10 When is a FEM solver appropriate for Electromagnetic Problems (Upper Bound)? ò When the structure under evaluation is not too large to be reasonably solved with available resources n This limit is VERY problem and hardware dependent n ROUGH rule-of-thumb: Projects should be within 5 x 5 x 5 wavelengths in volume ò When the structure’s aspect ratio does not exceed many- thousands to one n Example: extremely long, thin wire antennas might be more efficiently solved using a Wire-MoM (e.g. NEC) n Entirely ‘planar’ structures with stratified dielectrics might be more efficiently solved using a 2.5D MoM (e.g. Ensemble) ò When the structure’s behavior is not more easily approximated using Optical (GTD or Ray-Tracing) Techniques n Example: Parabolic Dish antenna, generally many 10’s of wavelengths in diameter n Example: Radar Cross Section of a large vehicle body, such as an aircraft or helicopter

1-11 Some Typical High-Frequency Electromagnetic Applications Waveguide Components Antenna RF Integrated CircuitsEMC

1-12 High Frequency Structure Simulator (HFSS) Flowchart of General Design Process Input Model Parameters Geometry Material Properties Boundary Conditions Define Solution Criteria Frequency Adaptive? Convergence Parameters? Sweep? Sweep Parameters? Review Results S-Parameters (Tabular and Plotted) Field Visualization Data Output/Exportation Perform Sweep Solution Define Excitation across band Solve 3D Fields across band Adaptive? Sweep? Iterate on Solution Evaluate vs. Convergence Parameters Refine Mesh and Resolve Exit only when Conv. Parameters Met YES NO YES NO Perform Initial Solution Generate Mesh Solve Excitations Solve 3D Fields SOLUTION

1-13 HFSS Solution Process ò Subdivide model into Elements (tetrahedra) ò Define basis functions per tetrahedra n Basis functions, W n define conditions between nodal locations in the overall mesh of tetrahedra, based on problem inputs n Functions are simple and nonzero only within the tetrahedra ò Multiply Basis Functions by Field Equation n HFSS Solves Field Equation Derived from Maxwell’s Equations: ò Integrate result over Volume n Integration replicated in thousands of equations for n=1, 2,...N ò Intent is to obtain N equations with N unknowns for solution

1-14 HFSS Solution Process, cont. ò Rewrite Equations, Using Green’s and Divergence Theorems: n Set Equal to Excitation/Boundary Terms n Write E field as summation of unknowns, x m, times same basis functions used in generating the initial series of equations: ò Resulting Equations allow solution of unknowns, x m, to find E n Note: Equation has the basic form Ax=B, where n A is the basis functions and field equation, in a known N x N matrix n ‘x’ is the unknowns to be solved for n B is the excitation

1-15 Properties of the Solution Matrix ò The Finite-Element Solution Matrix has a number of known characteristics n Size: Matrix is generally large, N on the order of tens of thousands n Density: Matrix is generally sparse, with a large number of zero entries n Only basis functions in the same tetrahedra result in nonzero entries n Banding: Intelligent ordering of the mesh results in nonzero entries being clustered along the diagonal ò Different Types of Problems have different mesh characteristics as well n Lossless problems will have only real nonzero entries n Lossy problems will have complex nonzero entries n Problems with standard excitations (‘ports’) will have symmetric matrices n Problems with certain boundary conditions (e.g.‘linked’) may have asymmetric matrices

1-16 Solving the Matrix ò Due to its sparse and banded nature, the matrix can be solved using mathematical matrix decomposition techniques n HFSS Version 8 uses an iterative Multifrontal Matrix Solver ò Constructing and Decomposing this Matrix form the bulk of the computational load in HFSS n Significant effort is also spent in generating a good mesh, which will result in a well-behaved matrix n Tetrahedra “aspect ratio” is one driver of mesh acceptability n A good mesh results in a well-conditioned matrix ò For each excitation defined, only the right-hand side of the Ax=B equation changes n Therefore Matrix Decomposition must be performed only once n Resolving the entire E-field result to view different excitations takes minimal effort by comparison

1-17 Known Approximations in the Finite Element Method ò Discretization: the accuracy with which the solution space may be subdivided n Tetrahedra are good at ‘filling’ curved shapes n Nevertheless, some facetization of the solution space can result ò Accuracy of the Excitation Solution n 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 n Any inaccuracies in the 2D solution will therefore impact 3D results ò Finite Size Limitations on “Free Space” Models n Termination of modeled space with an ‘absorbing boundary condition’ mimics continued radiation into free space, but will have limitations ò 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!

1-18 HFSS Adaptive Refinement Process ò The FEM problem’s first mesh is generated with respect to solution wavelength n “Lambda refinement” results in tetrahedra of about /4 in free space ò However, for many field behaviors this may not be sufficient mesh density to properly solve for rapid fluctuations or extremely localized effects ò The adaptative refinement process addresses this issue n Field solution is obtained for initial mesh n Mesh is refined based on error analysis and/or field strength localization n Field is re-solved and compared with prior solution. n If user-specified criteria for convergence are not met, process continues

1-19 HFSS Adaptive Refinement Criteria ò Adaptive Refinement has two logical “OR” exit criteria n Number of Passes: The maximum number of times to run and refine the solution before quitting n Delta-S: The worst-case vector magnitude difference of any S-parameter, as compared between the current and previous pass results. n More specific S-parameter convergence criteria per parameter are also available ò Adaptation is performed at a single excitation frequency n Implication: For best accuracy in swept solutions, the adaptive procedure should be done at a sufficiently small representative wavelength to capture high-end behavior n (More detail about solution frequency selection will be presented later)

1-20 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

1-21 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)