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Tutorial in

Electromagnetics #1

DRAFT

Sponsored by NSF Grant #05-559: Finite Element Method

Exercises for use in Undergraduate Engineering Programs

The Probe Feed Patch Antenna

Prepared By: Dr. Vladimir A Labay, Department of Electrical and Computer Engineering

Gonzaga University, Spokane, Washington

Estimated time to complete

This tutorial: 60 minutesOutline of Tutorial

1. Introduction

2. Overview of computational electromagnetics (CEM)

– Maxwell’s Equations and their numerical approximation

–F ul-wave CEM techniques

• The method of moments (MoM)

• The finite difference time domain (FDTD) Method

• The finite element method (FEM)

3. The CEM modeling process

–Overiew

– Methods of CEM

– Problems and Limitations

4. Finite Element Method (FEM)

– Introduction and Overview

– Strengths and Weaknesses

–Weakness

2(con’t)

Outline of Tutorial

5. Ansoft’s High Frequency Structure Simulator (HFSS)

–Introduction

– Using HFSS to create and improve designs

6. Problem Definition: The Probe Feed Patch Antenna

– Basic Characteristics of Microstrip/Patch Antennas

– Design Equations based on the Transmission Line Model

–S ample Design

7. Step-by-Step Solution

–L aunching Ansoft HFS

– Set up the Design

– Creating a Model

– Set up and Generate Solutions

– Analyze and display results

8. Further Reading and References

3Tutorial Objectives

• Understand the basis of FE theory for three-dimensional electromagnetic analysis.

(PEO #1)

• Understand the fundamental basis of the radiation field pattern in a patch

antenna beam through the use of Ansoft’s High Frequency Structure Simulator

(HFSS)™ three-dimensional finite element software. (PEO #2)

• Be able to construct a correct solid model using the build in 3-D solid modeler and

perform a correct three-dimensional finite element analysis using HFSS solution

engine. (PEO #3)

• Be able to interpret and evaluate finite element solution quality including verifying

convergence criterion and field plots. (PEO #4)

4Overview of Computational

Electromagnetics (CEM)

•Electromagnetics

– The study of electrical and magnetic fields and their interaction

– Governed by Maxwell’s Equations (Faraday’s Law, Ampère’s Circuital Law, and Gauss’ Laws)

• Maxwell’s Equations relate the following Vector and Scalar Fields

E: the Electric Field Intensity Vector (V/M)

H: the Magnetic Field Intensity Vector (A/m)

2

D: the Displacement Flux Density Vector (C/m )

B: the Magnetic Flux Density Vector (T)

2

J: the Current Density Vector (A/m )

3

ρ: the Volume Charge Density (C/m )

μ: is the Permeability of the medium (H/m)

ε: the Permittivity of the medium (F/m)

5Maxwell’s Equations

Faraday’s Law: Ampère’s Circuital Law:

∂

∂

∇ × E = − B

∇ × H = J+ D

∂t

∂t

Constitutive Equations:

Gauss’ Laws:

B = μ H D = ε E

∇ ⋅ B =0 ∇ ⋅ D = ρ

• Actual solution complex and for realistic problems require approximations

• Numerical approximations of Maxwell’s equations is known as computational

electromagnetics (CEM)

6Applications of CEM

• Over the past five decades CEM has been successfully applied to several engineering

areas, including:

– Antennas

– Biological electromagnetic (EM) effects

– Medical diagnosis and treatment

– Electronic packaging and high speed circuits

– Superconductivity

– Microwave devices and circuits

– Law enforcement

–E nvironmental isues

–Avionics

– Communications

– Energy generation and conservation

– Surveillance and intelligence gathering

–H omeland Security

– Signal Integrity

7Full-wave CEM techniques

• Approximations of Maxwell’s equations may be classified into several categories, e.g.,

low-frequency, quasi-static, full-wave, lumped element equivalent, etc.

• This tutorial deals with the finite element method a full-wave technique. Full-wave

techniques have the potential to be the most accurate of all numerical

approximations because they incorporate all higher order interactions and do not

make any initial physical approximations

•E xamples include:

– Finite difference time domain (FDTD) Method

– Method of Moments (MoM) Method

– Finite Element (FEM) Method

– Transmission Line Matrix (TLM) Method

– The Method of Lines (MoL)

– The Generalized Multipole Technique (GMT)

The FDTD, MoM and FEM are the most popular today!

8(con’t)

Full-wave CEM techniques

• Central to all methods is the idea of discretizing some unknown electromagnetic

property, for example:

– MoM: the Surface Current

– FE: the Electric Field

– FDTD: the Electric and Magnetic Field

• Discretization is also known as meshing that subdivides the geometry in a large

number of elements

– Two dimensional elements: triangles

– Three dimensional elements: tetrahedral

• Within each element, a simple functional dependence (basis functions) is assumed

for the spatial variation of the unknown

• The amplitude and phase of the unknown quantity is determined by the application

of the particular CEM

9Limitations of Full-wave CEM

techniques

• CEM is a modeling process and therefore a study in acceptable approximation

• In other words, CEM replaces a real field problem with an approximate one which

causes limitations and problems that one must keep in mind

• Limitations of the mathematical model and Simplifications in the formulation

– Assumptions are generally made, e.g., assuming an infinite ground plane in an antenna

structure. Are the assumption valid?

– Have you made simplifications on the design that are not valid? For example, simplifying a

thin wire by a current filament.

• Tolerances and Manufacturing deviations

– Tolerances are a part of all manufactured devices. How do small changes in dimensions or

material properties affect the performance?

– Do other manufacturing considerations, other that tolerances, affect the performance?

• Finite Discretization

– Is the mesh fine enough to properly so that the basis functions can adequately represent the

fields?

• Numerical approximations and Finite machine precision

– Does double precision provide enough accuracy for your problem, especially if it is ill

conditioned?

10