moment of method
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Moment of Method
MoM Tareq Son Zeyad
Asem ShtayaBara’ Jml
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Integral Equation (IE)
The obe!ti"e of the Integral Equation (IE) methodfor radiation or s!attering is to !ast the solution forthe un#no$n !urrent density% $hi!h is indu!ed onthe surfa!e of the radiator&s!atterer% in the form ofan integral equation $here the un#no$n indu!ed!urrent density is 'art of the integrand
here is a #no$n linear o'erator% is a #no$ne*!itation fun!tion% and is the res'onse fun!tion
•
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,umeri!al Te!hnique(Moment of Method)
The moment of method (MoM)numeri!al te!hniques is thenused to sol"e the integralequation for the un#no$n!urrent density-oint.Mat!hing
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Matri* ,otation
/sing matri* notation to sol"e for theun#no$n
here0
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Basis 1un!tions
2Subdomain functions% $hi!h arenon3ero only o"er a 'art of the domainof the fun!tion g(*)
4Entire-domain functions% thate*ist o"er the entire domain of theun#no$n fun!tion
“pulse” function
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eighting (Testing)1un!tions
• To im'ro"e the 'oint.mat!hingsolution for the (MoM)% an inner'rodu!t !an be used
• A ty'i!al% but not unique% inner'rodu!t is
• A''lying to our solution% $e $ill ha"e
•
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5aussian quadrature
• A numeri!al te!hnique% that is used toe"aluate the inner 'rodu!t% is !alled65aussian 7uadrature8 and it is stated as
$here is the $eights% and is the 'ositionof that $eight
•
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9urrent :istribution
• Boundary 9ondition0
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5oing for the Solution
• At the surfa!e of the $ire ( ; )% andthe $ire is 'erfe!tly !ondu!ting% thetotal tangential ele!tri! <eld
"anishes0
and $e #no$ that0
•
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Mathemati!al Mani'ulation
• Substituting equation into equation%and using di=!ult mathemati!almani'ulation% sol"ing for % $e ha"e
to$ solution02 ->9?@I,5T>,’S E7/ATI>,
4 A@@ E,’S E7/ATI>,
•
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Sour!e Modeling
• To use% for e*am'le% -o!#lington’sintegro.diCerential equation% $eneed to #no$ ho$ to e*'ress
• Traditionally $e ha"e t$o methods touse to model the e*!itation tore'resent at all 'oints on the surfa!e
of the di'ole
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The delta.ga' sour!e
• The delta.ga' sour!emodeling is the sim'lestand most $idely used of
the t$o% but it is also theleast a!!urate% es'e!iallyfor im'edan!es
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Magneti!.1rill 5enerator
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Magneti!.1rill 5enerator
• by using this model% $e areeCe!ti"ely modeling a di'ole $ith thefeed system of a mono'ole
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->9?@I,5T>,’S E7/ATI>,
1or the se!ond term
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->9?@I,5T>,’S E7/ATI>,
• 1or the <rst term% $e ha"e to$!ases0
2 Self term0
4 ,on Self term0
•
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A@@E,’S E7/ATI>,
• 1or A@@E,’s equation% $e also ha"eto$ !ases0
2 Self term0
4 ,on Self term0
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A@@E,’S E7/ATI>,
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MAT@AB
• 1inally% !odes for sol"ing theequations
2 -o!#lington-ulseSolution
4 allen-ulseSolution
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Any 7uestion D