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Directivity Plot in HFSS

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Xionarc

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HFSS allows you to plot 2D & 3D Polar as well as Rectangular plots with a variety of variables. For transmitting antenna designs, apart from the actual E-Field pattern there is a variable called Dir (or directivity) which is DirTotal, DirPhi, DirTheta, DirX,Y,Z etc. What is this though? I thought directivity is a ratio so its a number. Directivity in terms of field pattern function [F(theta,Phi)] is a function of theta,phi. but plotting this in 2D Polar or rectangular? What is the meaning of that? Any clarification or math formula to help me understand would be great!

Thanks in advance
 

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