A Q-band low-profile FSS with controllable numbers of the band is proposed in this paper. Using the complementarity principle, the branched strip lines are complemented as slots, and the FSS with controllable numbers of the band is designed. Then its working mechanism is analyzed by using the equivalent circuit method. Finally, the model is solved by incidenting Floquet mode using CST. The simulation result is fitted by the equation derived from the equivalent circuit method and shows that there are four center frequencies of the bands (or i.e. four FTZs): 36 GHz, 44 GHz, 47.5 GHz, and 48.2 GHz, respectively. By designing the two and three slots, the controllability of the numbers of the bands has been verified. By analyzing the parameters p, p, of the unit of FSS, the controllability of the position of bands has been verified. In addition, the horizon size of the unit is x=2.24 mm, y=2.02 mm, and the profile is z=0.82 mm which is a small size design. It achieves the design purpose of miniaturization and low profile.
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