A geometrical theory for the resonant frequencies and Q-factors of some triangular microstrip patch antennas

Interest in the use of printed-circuit antennas for lightweight antenna arrays has led to studies of radiation and resonance properties of microstrip patches of many different shapes. The present investigation is concerned with the use of the solution of the canonical problem of plane-wave reflection from under the patch to obtain simple closed-form expressions for the resonant frequencies and radiation Q-factors of three types of triangular patch antennas. Attention is given to a 45 deg - 45 deg - 90 deg triangular patch, a 60 deg - 60 deg - 60 deg triangular patch, and a 30 deg - 60 deg - 90 deg triangular patch. It is believed that the presented formulas are sufficiently accurate for most engineering applications.