###### Abstract  
This paper presents a miniaturized frequency selective surface (FSS) based on the convoluted and interdigitated stripe with multiple narrow passbands/wide stopbands in the L-/S-/C-/X-/Ku-/K-band. By using the convoluted and interdigitated stripe, the coupling inside is well controlled, so that the spatial efficiency is maximized to provide a high miniaturization. An equivalent circuit model is presented to reveal the working mechanism of the proposed FSS. The proposed structure forms four transmission band rejections of 3 dB in 1-6.65 GHz, 8.35-16.9 GHz, 18.0-24 GHz, and 24.50-27.84 GHz. The size of the unit cell is \(0.09\lambda_{0}\times 0.09\lambda_{0}\), where \(\lambda_{0}\) is the wavelength of the first resonance frequency. The proposed FSS has a good angle stability and polarization stability in a scanning range up to 60\({}^{\circ}\). For verification, an FSS prototype has been fabricated and measured. The measured results were in agreement with the simulated results. The proposed FSS can be used in practical applications such as radomes, antenna reflectors, and spatial filters. frequency selective surface; quad-stopband; miniaturization; angle and polarization stability 20212027 1027 10.27. [[https://doi.org/10.3390/mi12091027](https://doi.org/10.3390/mi12091027)]([https://doi.org/10.3390/mi12091027](https://doi.org/10.3390/mi12091027))  
12 May 2021  
rejection characteristic for transverse magnetic (TM) polarization is relatively stable, for transverse electric (TE) polarization, as the incident angle increases, the first suppression band remains almost unchanged, while the second suppression band moves downward. In addition, [17] proposed a method of designing a dual-band miniaturized-element frequency selective surface (MEFSS). The proposed structure consists of grids and complementary capacitor patches arranged periodically in two dimensions, separated by a dielectric substrate. This structure is based on an inductively coupled MEFSS, which uses a capacitively loaded dielectric pad as its main resonator. The two operating frequency bands of the MEFSS correspond to the first and second resonance frequencies of the resonator. For TE and TM incident polarization, the incident angle is relatively stable in the range of 45\({}^{\circ}\). In [18], an FSS with a wide passband and ultra-wide stopband performance was studied. The proposed FSS is composed of three metal layers and a cascading multilayer dielectric substrate. In the L/S frequency band, a new type of inductance layer with a spiral zigzag line shape is proposed to synthesize a large inductance to increase the passband bandwidth. When the incident angle is in the range of 0\({}^{\circ}\) to 45\({}^{\circ}\), an ultra-wide reflection band with good and stable performance can be obtained. In [19], a thin multilayer polarization-independent FSS was proposed. The FSS includes three metal layers. One is a four-legged metal cross on the top surface, the other is on the bottom surface, and the middle layer is a Jerusalem cross. This structure reflects the bandpass characteristics of 7.15 GHz and 13.02 GHz and the bandstop response of 8.22 GHz. This structure is not sensitive to polarization. Under different incident angles, the frequency shift of the lower two frequency bands is less than 5%, while the frequency shift of the higher transmission frequency band is up to 12%. Although the tri-band FSS can achieve its operating characteristics, the filtering characteristics are singular, that is, all bandstop or all bandpass, which makes it easy to cause bandstop/bandpass of the whole frequency band. The design of the tri-band FSS can be implemented in a way that a ring structure is nested in itself. The authors of [20] mentioned a tri-band blocking FSS operating at 1.8 GHz, 3.5 GHz, and 5.5 GHz. The FSS has a single-sided FR4 substrate and a single metal layer. The metal layer is composed of a square ring, a dodecagonal ring, and a Jerusalem cross ring.