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The use of microstrip patch configuration in the 5th generation (5G) wireless network is expected to fulfill the demands of smartphone users by significantly increasing the capacity of communication technology. The main objective of this paper is to report the development of a mathematical model on the effects of conductor thickness on the center frequency for the performance of a low profile, cost-effective antenna in the application of 5G devices. This mathematical model is proposed for an antenna system incorporated with air substrate occupying a 5.43 × 4.54 × 0.5 mm3 volume which resonated at 28 GHz. The impacts of varying thickness of conductive material and substrate on the bandwidth, gain, and efficiency of the antenna in 5G applications were studied. The model is successfully developed. The fabricated antenna used in this study had provided a gain of 9.47 dBi, an impedance bandwidth of 1.72 GHz, and a performance efficiency of 90.1%.