Analytical Formulas for Frequency-unbalanced Periodic Leaky-wave Antennas

Periodic leaky-wave antennas (P-LWAs) are usually optimized in terms of frequency balancing (w-balancing) and Q balancing, where the resonance frequencies of the series and shunt modes (ω
_se
, ω
_sh
) and their quality factors (Q
_se
, Q
_sh
) that contribute to radiation are equalized. This paper performs a general study of the four radiation regimes in P-LWAs (ω-balancing/ Q-unbalancing, ω-balancing/ Q-unbalancing, ω-unbalancing/ Q-balancing and ω-balancing/Q-balancing) and provide analytical formulas of 1D P-LWA based on a network model. Finally, analytical results of important P-LWA parameters, such as propagation constant, Bloch impedance and radiation efficiency, are provided and discussed for the four regimes.