Calculation of the impedance characteristics of a microstrip loop antenna with a metallized dielectric substrate

In connection with the intensive development of electronic technology, an urgent task is the development of antennas in a microstrip way, the advantages of which are small dimensions, a relatively simple manufacturing technology, and the ability to control their characteristics by using various materials and forms of radiators in their design. Currently, there are many mathematical models of microstrip antennas with vibrator radiators located on dielectric substrates, while models of microstrip antennas with other radiator shapes are presented much less often. As a rule, the calculation of the characteristics of such antennas is performed in electrodynamic modeling systems based on the use of «closed» algorithms. In this regard, there is a need to develop rigorous mathematical models of microstrip antennas with radiators of various shapes. This work is dedicated to the development of a rigorous model of a microstrip antenna with a frame radiator located on a dielectric substrate, based on the use of the method of integral equations. An integral equation is obtained for the unknown distribution function of the radial component of the current density over a frame radiator, the numerical solution of which is a correct mathematical problem. In addition, the numerical results of calculating the current density distribution, as well as the input impedance of such an antenna for various parameters of the radiator and substrate, are presented.