Transversal Asymmetry in Periodic Leaky-Wave Antennas for Bloch Impedance and Radiation Efficiency Equalization Through Broadside

This paper demonstrates that unit cell asymmetry with respect to the transversal axis —or transversal asymmetry— is an essential design parameter in periodic leaky-wave antennas (P-LWAs). Specifically, it shows that transversal asymmetry can be leveraged to fully and systematically solve the well-known radiation degradation of P-LWAs at broadside, where it provides both open-stopband closure and efficiency equalization. The problem is addressed via a generic equivalent circuit model composed of a series resonator, a shunt resonator and ideal transformers for modeling asymmetry by a single and simple parameter, namely the transformation ratio. Once the series and shunt frequencies have been balanced (frequency-balancing), equalization is ensured by adjusting the degree of asymmetry in the unit cell so to match the at-broadside Bloch impedance to the off-broadside Bloch impedance. This equalization condition is referred to as quality factor balancing (
${\rm Q}$
-balancing) and it is related to the Heaviside condition (distortionless propagation) in homogeneous transmission lines. Based on this theory, optimization schemes for employing commercial fullwave eigenmode and drivenmode solvers are proposed to design unit cells with equalized efficiencies. Finally, two examples of P-LWAs are presented, a composite right/left-handed (CRLH) P-LWA and a series-fed coupled patch (SFCP) P-LWA, and verified to fully confirm the predictions of the theory obtained by circuit modeling.