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A method is introduced for designing bandpass frequency-selective surfaces (FSSs) using arrays of antenna-filter-antenna (AFA) modules. An AFA module is a filter with radiation ports, which is obtained by integrating two antennas and a nonradiating resonant structure in between. AFA modules are designed based on circuit models and microwave filter design techniques. Three types of these AFA modules are designed using microstrip antennas and coplanar-waveguide resonators, and are used to form FSSs with three- and four-pole shaped bandpass response at 35 GHz. FSS structures are formed by arraying these modules in a periodic grid with an optimal cell size. The proposed concept and the design method are validated using numerical simulation (finite-element method), as well as experimental results.