Pyramidal Horn Design - Maple Programming Help

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Pyramidal Horn Design

Introduction

This application calculates the optimum design parameters for an X-band pyramidal horn.

 

 

Reference:
Based on example 13.6, page 782 of Antenna Theory, Analysis and Design, Constantine A. Balanis, 3rd Edition.

 

restart:withplots:withColorTools:

Parameters

The design equations require that the gain be unitless and that the wavelength, l, be in cm.  So our first equations which address design criteria (1) and (2), are


Gain in dB at design frequency:

G__odB22.6:


Hence

G__o10G__odB10

G__o181.9700859

(2.1)


Frequency (s-1):

f11.0109.: 

Geometrical constraints (cm):

a2.286:b1.016:

 

Speed of light (cm/s):

c31010:

 

Wavelength (in cm):

λcf

λ2.727272727

(2.2)

Governing Equations

These equations are extracted from the reference, and are derived therein.

 

We require the following for optimum directivity.

cons1G__o=2πλ2a__1b__1:

cons2a__1=3λρ__h:

cons3b__1=2λρ__e:


The dimensions pe and ph are equal.

cons4p__e=b__1bρ__eb__1214:

cons5p__h=a__1aρ__ha__1214:

cons6p__e=p__h:

Numerically Solve the Governing Equations

resfsolvecons1,cons2,cons3,cons4,cons5,cons6

resa__1=16.55573668,b__1=13.01154178,p__e=27.97911838,p__h=27.97911838,ρ__e=31.03837357,ρ__h=33.50018428

(4.1)

Plot the E-Plane Radiation Pattern

assignres

ρ__1ρ__e2b__122:

t__1θ2λρ__1b__12ρ__1sinθ:

t__2θ2λρ__1b__12ρ__1sinθ:

FθFresnelCt__2θFresnelCt__1θIFresnelSt__2θFresnelSt__1θ:


Radiation Pattern

E__θθ20log101+cos(θ)F(θ)F(0):

plotE__θθ,θ=π2..π2,thickness=7,color=ColorRGB,0,79/255,121/255,axes=frame

polarplotE__θθ+70,θ=0..2 π, thickness=0,color=ColorRGB,0,79/255,121/255,filled=true,transparency=0,title=E-Plane Radiation Pattern,size=800,800