Method of moments solution for a printed patch/slot antenna on a thin finite dielectric substrate using the volume integral equation

In this paper, a volume integral equation (VIE)-based modeling method suitable for a patch or slot antenna on a thin finite dielectric substrate is developed and tested. Two new key features of the method are the use of proper dielectric basis functions and proper VIE conditioning, close to the metal surface, where the surface boundary condition of the zero tangential E-component must be extended into adjacent tetrahedra. The extended boundary condition is the exact result for the piecewise-constant dielectric basis functions. The latter operation allows one to achieve a good accuracy with one layer of tetrahedra for a thin dielectric substrate and thereby greatly reduces computational cost. The use of low-order basis functions also implies the use of low-order integration schemes and faster filling of the impedance matrix. For some common patch/slot antennas, the VIE-based modeling approach is found to give an error of about 1% or less in the resonant frequency for one-layer tetrahedral meshes with a relatively small number of unknowns. This error is obtained by comparison with fine finite-element method (FEM) simulations, or with measurements, or with the analytical mode matching approach. Hence it is competitive with both the method of moments surface integral equation approach and with the FEM approach for the printed antennas on thin dielectric substrates.