In this paper, a novel ultra-compact metamaterial unit-cell is introduced. The proposed unit-cell consists of one modified rings which has been designed based on the fractal technique and meander technique. These techniques are used to reduce the physical size of the conventional complementary split ring resonators (CSRRs). In the proposed metamaterial unit-cell which is called the fractal/meander CSRR (FMCSRR), the slot lines in the conventional CSRRs are replaced by the fractal and meander slots, simultaneously. The FMCSRR unit-cell is a planar metamaterial element which exhibits negative permittivity and is considered as electric dipole when excited by an axial electric field. Thus, the FMCSRR unit-cell is modeled as a shunt resonator tank. Therefore, by using the proposed FMCSRR configuration, all of the interior space of the ring has been used and the slot lines have been increased. Consequently, the higher inductance has been achieved and the resonance frequency of the proposed FMCSRR unit-cell becomes lower compared with the conventional CSRR. That’s mean the electrical size of the introduced unit-cell FMCSRR unit-cell is smaller than the conventional CSRR with the same physical sizes. A microstrip notch band filter, a microstrip band-pass filter, a half mode substrate integrated waveguide (HMSIW) band-pass filter and three HMSIW filtering power dividers (FPDs) with different power division ratios of 1:1, 1:4, and 1:8 have been designed to illustrate the ability of the proposed FMCSRR unit-cell in the size reduction. All of the designed devices operated at 2.4 GHz which are suitable for WLAN applications. For verification the performance of the utilized techniques in miniaturization of the dimension, the designed equal/unequal HMSIW FPDs have been fabricated and tested. A reasonable agreement between simulated and measured results has been achieved. The results confirmation that a miniaturization about 79% has been obtained. The total size of the proposed HMSIW FPDs are about 0.09λ g × 0.09λ g. The proposed HMSIW FPDs have many advantages in terms of compact size, low insertion loss, high selectivity, easy integration with the other planar circuits, and controllable bandwidth.

中文翻译：

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使用超紧凑超材料单元的等/不等半模衬底集成波导滤波功率分配器

在本文中，介绍了一种新型的超紧凑超材料晶胞。所提出的晶胞由一个改进的环组成，该环是基于分形技术和曲折技术设计的。这些技术用于减小传统互补开口环谐振器 (CSRR) 的物理尺寸。在被称为分形/曲折 CSRR (FMCSRR) 的超材料晶胞中，传统 CSRR 中的槽线同时被分形和曲折槽所取代。FMCSRR 晶胞是一种平面超材料元件，具有负介电常数，当被轴向电场激发时被认为是电偶极子。因此，FMCSRR 单元被建模为并联谐振回路。因此，通过使用建议的 FMCSRR 配置，环的所有内部空间都已被使用，并且槽线已增加。因此，与传统的 CSRR 相比，所提出的 FMCSRR 单元的谐振频率已经实现了更高的电感，并且谐振频率变得更低。这意味着引入的晶胞 FMCSRR 晶胞的电气尺寸小于具有相同物理尺寸的传统 CSRR。一个微带陷波带滤波器、一个微带带通滤波器、一个半模衬底集成波导（HMSIW）带通滤波器和三个不同功率分配比的HMSIW滤波功率分配器（FPD）1:1、1:4和1:8 的设计旨在说明所提议的 FMCSRR 单元在减小尺寸方面的能力。所有设计的设备均工作在 2.4 GHz，适用于 WLAN 应用。为了验证所用技术在尺寸小型化方面的性能，设计的等/不等 HMSIW FPD 已被制造和测试。模拟结果和测量结果之间取得了合理的一致性。结果证实已经获得了约79%的小型化。提议的 HMSIW FPD 的总大小约为 0.09λ G× 0.09λ G. 所提出的 HMSIW FPD 在尺寸紧凑、插入损耗低、选择性高、易于与其他平面电路集成以及带宽可控等方面具有许多优点。