In this reprot, we introduce a new technique for designing miniaturized-element frequency selective surfaces (MEFSSs) with bandpass responses and no spurious transmission windows over extremely large bandwidths. The proposed, harmonic-suppressed MEFSSs consist of multiple metallic and dielectric layers. Each metallic layer is in the form of a two-dimensional arrangement of capacitive patches or an inductive wire grid with extremely sub-wavelength periods. Harmonicfree operation in these structures is achieved by using multiple, closely-spaced capacitive layers with overlapping unit cells to synthesize a single, effective capacitive layer with a larger capacitance value. This allows for reducing the unit cell size of a conventional MEFSS considerably and moving the natural resonant frequencies of its constituting elements to considerably higher frequencies. Consequently, the spurious transmission windows of such MEFSSs, which are caused by these higher-order harmonics, can be shifted to very high frequencies and an extremely broad frequency band free of any spurious transmission windows can be obtained. Using this technique, an MEFSS with a second-order bandpass response is designed to operate at 3.0 GHz with 20% fractional bandwidth and be free of spurious transmission bands up to 27.0 GHz. A prototype of this harmonic-free MEFSS is fabricated and experimentally characterized in the lab. Measurement results confirm harmonic-free operation of the proposed FSS for incidence angles in the ±60• range for both the TE and TM polarizations of incidence.