Extension of the Hansen–Woodyard Condition for Endfire Leaky-Wave Antennas

The Hansen-Woodyard condition is modified to include attenuation, making it applicable to leaky-wave antennas. The optimum phase constants are found for two cases, one based on the array factor only and the other including the element pattern. The optimum radiation efficiency for maximizing the endfire gain is also found in both cases. The effects of material loss on the optimization of endfire gain is also discussed.