In this paper a closed-form expression is introduced to calculate slot shape of long slot leaky wave waveguide antennas at its fundamental mode of operation with minimum side lobe level (SLL). The derived equation is a function of geometrical parameters of the structure. This is an advantage because they show a clear relationship between geometrical parameters of the antenna and radiated field that allows intelligent modification of the pattern. The Gaussian slot is used to obtain the best radiation pattern with lowest SLL. The results obtained by introduced formula are compared with the full wave commercial simulator such as HFSS software which confirms the accuracy of the introduced equations.

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