Transmission Phase Limit of Multilayer Frequency-Selective Surfaces for Transmitarray Designs

Many transmitarray antennas are designed with multilayer frequency-selective surface (M-FSS) type elements. The goal of this paper is to reveal the transmission phase limit of M-FSS for transmitarray antenna designs. An analytical study of the transmission coefficient of multiple conductor layers separated by dielectric materials has been carried out, and the maximum transmission phase range has been determined according to the number of layers, substrate permittivity, and separation between conductor layers. It is revealed that the -1-dB transmission phase limits are 54°, 170°, 308°, and full 360 ^°for single-, double-, triple-, and quad-layer FSS consisting of identical layers, respectively. Furthermore, it is shown that if -3-dB criteria is used, a triple-layer FSS is sufficient to achieve the full 360 ^° phase range. The effectiveness of the analytical study has been validated through numerical simulations of several representative FSS examples.