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microstrip patch antenna dimension

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gmmahdinas

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hi friends
as mentioned in Balanis, ANTENNA THEORY AND ANALYSIS DESIGN, when an optimized width for an efficient radiator is W=(C0/2f)(√ (2/εr+1)) The resonant frequency for the TM100 mode is f=(C0/2Leff)(√ (1/εreff)). but when W is adjusted as above, W is larger than the L and this led to that dominate resinance frequency of the antenna detrmines by =(C0/2W)(√ (1/εr)). Now i amd confused please help me!
 

you should arrange the position of feed with a starting point of R_i=R_e 〖sin〗^4 πx/L at the middle of W.
 

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