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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
2
Electromagnetics problems: scalar and vector potentials
3
The Lorentz gauge and the vector wave equation
4
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
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