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This paper presents a thin absorbing structure comprising an array of finitely conductive terminal-loaded dipoles spaced about half a wavelength apart and located above a ground plane. We show that if the antennas are terminated with proper load impedance, instead of a conjugate-matched one, a perfect absorption can be attained even when the array lies close to the ground plane. We also identify a threshold height below which the absorption efficiency rapidly drops and perfect absorption cannot be realized. The idea is illustrated via a concrete example of array of dipoles printed with conductive ink technology on a Kapton HN flexible film backed by a rigid Rogers 4350B substrate. The array is designed for perfect absorption at 3.45 GHz when it is located one-tenth of a wavelength above the ground plane. Good agreement between simulation and measurement results is demonstrated. [ABSTRACT FROM AUTHOR]