Antenna plays an important role in most of the RF and microwave applications. Intensifying applications of wireless communications now a day’s persist to challenge RF or microwave Antenna with ever more meticulous requirements- smaller size, lighter weight, high performance, economical and easy for fabrication. The advancement in the modern materials fabrication technologies and different research on novel materials, including monolithic microwave integrated circuits (MMIC), low-temperature cofired ceramics (LTCC), high-temperature superconductors (HTS), micro electro mechanic system (MEMS), and micromachining technology, have encouraged the fast strengthening of latest microstrip and supplementary Antenna for RF and microwave applications. The manuscript presented here is a representation of the H shape patch antenna design and effect of coupling of parasitic patch and discontinuities in radiating structure in order to achieve high gain and better bandwidth (-10 dB). A mathematical model is presented which has been established on the basis of result obtained. The working frequency range of the manuscript is from 1 GHz to 20 GHz.