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Computational Electromagnetics :

Antenna computations

Uday Khankhoje

Electrical Engineering, IIT Madras

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Topics in this module

1 Scalar and Vector Potentials

2 The Simplest Antenna

3 Finite Antennas & Integral Equations

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Table of Contents

1 Scalar and Vector Potentials

2 The Simplest Antenna

3 Finite Antennas & Integral Equations

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Electromagnetics problems: scalar and vector potentials

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The Lorentz gauge and the vector wave equation

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Flow of problem solving in antenna problems

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Table of Contents

1 Scalar and Vector Potentials

2 The Simplest Antenna

3 Finite Antennas & Integral Equations

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The Hertz Dipole: ~A

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The Hertz Dipole: ~H, ~E

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The Hertz Dipole: Far fields

~H = I∆z4π jk(1 +

1jkr )

e−jkr

r sin θφ̂

~E = I∆z4π jωµ[1 +

1jkr +

1(jkr)2

] e−jkr

r sin θθ̂

+ I∆z2π jωµ[

1jkr +

1(jkr)2

] e−jkr

r cos θr̂

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The Hertz Dipole: Near fields

~H = I∆z4π jk(1 +

1jkr )

e−jkr

r sin θφ̂

~E = I∆z4π jωµ[1 +

1jkr +

1(jkr)2

] e−jkr

r sin θθ̂

+ I∆z2π jωµ[

1jkr +

1(jkr)2

] e−jkr

r cos θr̂

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The Hertz Dipole: Visualizing fields

Cr: Stutzman [1]

Field pattern: F (θ, φ) = EθEθ(max

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Antenna patterns in general

Typical power pattern: Side lobe level (SLL)

SLLdB = 20 log F (SLL)F (max)

Broadside and endfire NF v/s FF: 2D2

λ

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Antenna modelling: the scattered field

Recall: φ = jωε0µ0

∇ · ~A and ~E = −jω ~A−∇φ

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Antenna modelling: Pocklington’s equation

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Pocklington’s equation: Solution using MoM

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Source Modelling

Delta-gap Magnetic Frill Incident wave

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Two antennas: any gain? (pun intended)

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Advantage of two antennas: beam forming

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Topics that were covered in this module

1 Scalar and Vector Potentials

2 The Simplest Antenna

3 Finite Antennas & Integral Equations

4 Mutual coupling between two antennas

References:

(1) Ch 1,10 of Antenna Theory & Design, Stutzman and Thiele, Wiley

(2) Ch 3,8 of Antenna Theory & Design, C A Balanis, Wiley

(3) Mutual coupling between a wire antenna of finite conductivity and a large object,

Vossen, Masters Thesis, Eindhoven University of Technology, 1997

https://pure.tue.nl/ws/portalfiles/portal/46983690/684720-1.pdf