Radiation Pattern and Directivity of an Antenna Array - Maple Programming Help

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Radiation Pattern and Directivity of an Antenna Array

Introduction

The application calculates the array factor and directivity for a uniform linear antenna array, and then plots the radiation pattern.

restart:withUnitsStandard:withplots:withScientificConstants:withColorTools:

Parameters

The number of elements in the uniform array:

N10:


Design frequency:

f__d1GHz:

Permittivity and permeability of free space:

ε__oevalfConstantpermittivity_of_vacuum,units;

8.85418781510−12Fm

(2.1)

μ__oevalfConstantpermeability_of_vacuum,units

1.25663706210−6Hm

(2.2)


Phase constant:

β__o2πf__dμ__oε__o

β__o20.958450221m

(2.3)


Wavelength:

λ__d2πβ__o

λ__d0.2997924580m

(2.4)

For a maximum at:

φ__mπ3.:


Inter-element spacing:

d λ__d3

d0.09993081933m

(2.5)


Progressive phase shift between elements:

ψβ__odcosφ__m

ψ1.047197551

(2.6)

Calculations

Array factor

AFφ1NsinN2β__odcosφψsin12β__odcosφψ:

 

polarplotAFφ,φ=0..2π,filled,size=700,700,color=ColorRGB,0/255,79/244,121/255,thickness=0,axesfont=Calibri,adaptive=false,numpoints=500,axis=gridlines=color=grey

The directivity for this array is calculated from the total power radiated.

P__tot2 intAFφ2,φ=0..2Pi,numeric

P__tot1.428780370

(3.1)

D__o4πP__tot

D__o8.795173059

(3.2)

Which, in dB, is:

10log10D__o

9.442443893

(3.3)

Reference

Iskander, Magdi F., Electromagnetic Fields and Waves, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1992.