Analytical CAD formulas for design of microstrip patch antennas based on numerical simulations

Analytical CAD formulas for design of square microstrip patch antennas (MPAs) are derived using results obtained by 3D EM simulations. The formulas are obtained by fitting the results of simulations performed at 3 GHz in a wide range of input data parameters: the thickness of substrate ranges from 0.5 to 4.5mm, the relative permittivity ranges from 1 to 9, and the radius of inner coaxial cable conductor ranges from 0.21 mm to 0.87 mm. The effectiveness of formulas is tested on a number of examples, which show that the patch length is predicted with error of maximum of 0.1 mm, resulting in the maximum error of resonant frequency of 0.1%. The position of coaxial feed is predicted with error of maximum 0.3 mm, resulting in the maximum error of bandwidth of 0.2%. For the given range of input data parameters: a) the formulas offer ability to have a fast yet accurate solution for square MPAs without using numerical simulations and optimization methods, and b) the formulas can be used as reference formulas for comparison with analytical CAD formulas based on approximate MPA models as well as other numerical solutions.