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In this study, a new method for designing low profile frequency selective surfaces (FSS) with second-order bandpass responses is presented. The FSSs designed using this technique utilize non-resonant subwavelength constituting unit cells with unit cell dimensions and periodicities in the order of 0.15lambda0. It is demonstrated that using the proposed technique, second-order FSSs with an overall thickness of lambda0/30 can be designed. This is considerably smaller than the thickness of second-order FSSs designed using traditional techniques and could be particularly useful at lower frequencies with long wavelengths. To facilitate the design of this structure, an equivalent circuit based synthesis method is also presented in this paper. Two bandpass FSS prototypes operating at X-band are designed, fabricated, and tested. A free space measurement setup is used to thoroughly characterize the frequency responses of these prototypes for both the TE and TM polarizations and various angles of incidence. The frequency responses of these structures are shown to have a relatively low sensitivity to the angle of incidence. Principles of operation, detailed design and synthesis procedure, and measurement results of two fabricated prototypes are presented and discussed in this paper.