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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