Resonant frequency of a microstrip patch in the vicinity of an identical radiator

The resonant frequency of a microstrip patch (rectangular, square, and circular) changes as soon as an identical patch is brought closer than 0.2λ to it. Closed-form expressions are presented for the H-plane-coupled configuration (the two adjacent patches are excited by same phase excitation) from which this altered resonant frequency may be easily computed. From the same expression the resonant frequency of an isolated patch antenna may also be calculated. A procedure utilizing these closed-form expressions for the design of microstrip patch antennas which will resonate at the desired frequency is also outlined. These expressions may be readily used in the computer-aided design of microstrip antenna arrays.