Method of Moments (MOM) and Familiarizing with FEKO

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 Task 1:

a) Method of Moments (MOM):

Integral Equation Approach: MOM starts with integral equations that desoibe the ek›ctromagnetic
behavior of antennas and scaaaers.
Approxima'tion with Basis Fu‹xtions: The unknown currents on the antenna or scattered ae
approximated using a set of basis furs:tions (eg., pulse, triangle, sinusoidal).
V\lighted Residuals: The integral equations are convertwl into a system of linear equations by
applying a weighted residual approach (eg., Galerkin meth‹xI).
Solution of Matrix Equation: The rœulting mapix equation is solvœl numerically to obtain the
œefficients of the basis functiors, which represem the approximate currenb.
field Cakula'tion: The calculated cwrents ae then used to compute various eIectrornygr›etic
quantitim, s‹xh as fa-rieId radiation patterns.

Versatile for various antenna and scaaeing problems

problems Limitations:

Can become computationally mpensive ter large-scale problems Requires careful sdection of basis
furxtions and discre“fixation
May encounter challenges for extremely thin str‹x:tures or sharp edge
a) Familiarizing with FEI4 Functions:
Conformal MoM

Traditional MoM
 Access Tutorial Files: Locale and open the provided FEKO tutorial files.
Explore Menus and Options: Carefully mamir›e the user interface, paying aaen"Oon to main
menus, t‹›oIbars, and workspace wirxlows.
Ark Through Examples: Follow the instructions in the bztorials, step by step, to understand
the workflow and functionality of different features.
Consult Dz›cumentation: Refer to the FEKO User Manual m online resource for detailed
explana"tions of specific furxtions ardcommands.
Experiment with Different Examples: Practice using FEKO with various antenna types an
sœna'ios to solidify your understariding.
b)Generaông Far-Field Radiaôon Paaœns:

Geneal Steps (specific steps will vay bæed on FEI version):

Model Antenna Geometry: Create the model of the X/2 dipole or born antenna InFEKO's
workspace. Set Simulation Parameters: Defir›e frequerxy, œcitation, t›ourdary conditions, and
other relevant
parameters.
Solve for Currents: Run the MOM simula‘oon to compute tbe antenna currents.
Cakulate Far-Field Radiation: Use FEKO’s post-prmessing tools to generate the far-field
radiation patterns in polar or rectangula plots.
Visualize arm Analyze: Inspect the radiation patterns to visualize the antenna's directional
characteristics and gain.

Task2
To œmplete Task 2, y‹æ need to familiarize yourself with the array antenna faculty h FEKO
and dœign a 4-element array antenna tsIrg either pdnt sourcœ or dipole elements. The
element spæIrg should be varied from 0.6y to 1k in 0.1k steps, and the effect on the far-field
p‹›vver radiation pattern sfx›uId be observed.

To Iæild a 4-element array antenna in FŒO, you œn follow these ueps:

1.Open FEXO and oeate a new projecŁ

To Introdœe a tilt angle into the main beam direction by apçàying a phase progression in the
feed, we œn use a phased array antenna. The phase progression equation ter a phæed array
antenna is giwn by:
ssetnnl - ethi‹w{xaiHNli>illss

where 5$e^{}\phi)ss is the ccmpIexezpor›entiaI term, $$nss is the element rximber, ard
5SNss is the total number ct elements In the array[1].

For œample, let's œnslder an array with 0.7y element space and wry the tilt angle from 0"
(&oadsi&) to 70• in 10º steps. We œn calculate the required phase progresdons fœ each tilt
angle using the above equation. The change In beam direction and shape can be analyæd by
œmparing the far-field radiaôon patterns fr different dit arçlœ.

At0• tllt angle (broa:lside), all elernems in the array are fed with equal phase, resulsng in a
broadside radiation pattern. As the bit argle inoeases, the phase ¡xcgression will change,
œusing the main beam to be steered in the desired directiœ. The œact phase ¡xogressions
reqdred fr each dit angle œn be œlcdated using the phased array antenna equation.

By analyzing the far-Feld radiation patterns ter 4fferent dlt anglœ, we can observe the
change in beam érection and shape. The main beam will be tilted from the array plane, and
the side lobes will also change accorôingly. The dit arme œn be adjusted tooptimize the
radation pattern, ma ing the main Idee more 4rœtive and the sidelobes smaller[2].

In ændusion, a pbased array antœna with a variaNe ôlt arme œn be used to cœtrol the main
beam érection and shape. By a¡qzIying a suitable phase ¡xcgression in the feed, we œn steer
the main beam to desired armes, opbmizing the radiation pattern tir wrious applications.
References
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and Propagation (EuCAP) (pp. 1-5). IEEE.

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