In this article, the frequency-selective rasorber (FSR) built on multilayer resistive sheets, which achieves a broad absorption band, was proposed. First, the detailed analysis of the absorption and transmission performance for FSR with the single-layer/multilayer resistive sheets based on the equivalent circuit model (ECM) was demonstrated, which proved that the FSR with the multilayer resistive sheets can obtain a broader absorption band. Second, the multilayer resonator (MR) of a smaller size and higher design freedom compared with single-layer resonator was proposed. Then, the FSR on the basis of multilayer resistive sheets using MR was designed. It consists of the three-layered metallic structures and separated by an air spacer. For the top and middle layers, the lumped-resistor-loaded metallic dipole with the MR inserted into the center was applied to generate a wide absorption band and transparent window, respectively. For the bottom layer, the square-slot frequency-selective surface was optimized to match the transmission band of the resistive sheet. Simulated and measured results show that the broad absorption band and transmission band with low insertion loss have been realized, and the proposed FSR yields the widest relative bandwidth <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\vert S_{11}\vert \le -10$ </tex-math></inline-formula> dB of 145.2%.
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