General formulas for 2-D leaky-wave antennas

General formulas for a two-dimensional (2-D) leaky-wave antenna (LWA) are obtained, which are applicable to any general class of 2-D leaky-wave antenna that consists of a partially reflecting surface that is mounted on top of a grounded substrate, and excited by a simple source. Closed-form expressions are obtained for the radiated fields, the field peak values in the E- and H-planes, the beamwidths in the E- and H-planes, and the pattern bandwidth. The formulas are obtained from a simple transverse equivalent network model of the structure. An accurate formula for the substrate thickness necessary to give a beam at any desired angle is also obtained.