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why not try other simulation tools . I know Micro-strips which use transmission line matrix method is a good choice.you said "My initial geometry is an inhomogeneous dielectric plate. " I think this software is suitable for you, it is a time domain method hence inherently wideband .
I only know that if you set ground radius is about to quater wavelength , the dipole antenna's radiation pattern is ideal.but as to patch antenna, I don't know,you can try with different size!
impedance calculator insert feed
my master graduation paper is to design a kind of multi-layer microstrip antenna . During the simulation I found that if the length of the feed line(whether microstrip or stripline) isn't long enough then the response of the system will include high-order...
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