Closed-Form Analysis of Reflection Losses in Microstrip Reflectarray Antennas

Microstrip reflectarray antennas consist of a grounded quasi-periodic array of printed elements able to compensate the phase displacement of a non-coherent electromagnetic excitation generated by a feeder. The design of reflectarray antennas is usually accomplished by tracing the reflection phase diagram of the periodic version of the printed surface, which is analogous to a high-impedance surface (HIS). Reflection losses of this periodic structure are here analyzed through a simple equivalent transmission line model. The analytical expressions of the surface impedance offered by a HIS (real and imaginary part) as a function of the imaginary part of the dielectric permittivity of the substrate are derived through well justified approximations. Some useful practical examples are then presented both for verifying the accuracy of the derived closed-form expressions and for studying the effect of the geometrical and electrical parameters of the periodic surface on the reflection losses. The dependence of the input impedance on the capacitance associated with the printed pattern is highlighted, demonstrating that highly capacitive elements (tightly coupled subwavelength elements) are preferable for minimizing reflection losses.