Corrugated horn - Radiation pattern problem...

[tiagojk]

The radiation pattern of a corrugated-horn is given by the function

g(?) = P1v(cos?)/sin? + dP1v(cos?)/d?

where
P1v(cos?)
is the associated Legendre function of the first kind and order v.

The problem is determine its order v.
I know that to find v I have to use g(?m) = 0, where ?m is the max angle (horn flare angle). If ?m = 20º or any other angle, how could I find the order v in a way that g(?m) = 0 ???

Someone can help me with a tip or a reference?

Thanks any help...

 

[VEBill]

If I understand your question (a risky assumption), then perhaps the principle of Conservation of Energy might be useful. Put another way: if the average gain over the sphere exceeds unity, then you're doing it wrong.

Is this an academic problem?

 

[tiagojk]

Yes, it is an academic problem.
I need to know this theoric radiation pattern then I will be able to use the principle of Conservation of Energy.
Anyway, thanks.

 

[Higgler]

An alternate is a brute force method to calculate the pattern, create an array of radiators that fill the aperture. Sum your radiators with vector math using voltage amplitude* e^jbndcos(theta) in Excel or MathCad.

If it's a good corrugated layout you know the amplitude in the aperture is a Cosine function and if you know the angle of the horn that provides the phase error in the aperture. Not sure if corrugations change that phase in the aperture since corrugations are a slow wave structure.

Is this to design a new horn or analyze a current horn?