Alternative analytic expressions for the mutual inductance (Lm) and coupling coefficient (k) between circular loops are presented using more familiar and convenient expressions that represent the property of reciprocity clearly. In particular, the coupling coefficients are expressed in terms of structural dimensions normalized to a geometric mean of radii of two loops. Based on the presented expressions, various aspects of the mutual inductances and coupling coefficients, including the regions of positive, zero, and negative value, are examined with respect to their impacts on the efficiency of wireless power transmission. This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/ by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. ⓒ
This paper presents simple expressions for the effective permeability of bulk metamaterial consisting of ring resonators (RRs) or split ring resonators (SRRs) based on the convenient geometrical factors of the structure compared with wavelength. The resonant frequency dependence of the medium permeability, including loss effects, is analyzed in detail. Inverting the analysis equations, useful design (or synthesis) equations are derived for a systematic design process with some examples. This paper may particularly be useful for the design of a bulk metamaterial with a specific negative relative permeability at a desired frequency. The loss of metamaterials consisting of RRs (or SRRs) is also analyzed over a wide frequency band from 10 MHz to 10 THz. This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/ by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. ⓒ
Design equations for wideband single-layer absorbers based on the condition of zero slope reactance (or susceptance) at a specific centre frequency are presented. Using the design equations, a microwave absorber is realised employing a cross-shaped strip structure as a unit on an FR-4 substrate with a relative permittivity of 4.6 and height of 3.2 mm. At a design centre frequency of 10.93 GHz, the size of each unit is 9.6 × 9.6 × 3.2 mm and the overall size of the fabricated absorber is 336 × 336 × 3.2 mm. The EM-simulated and measured absorptions are close to 100% at the design centre frequency and their 90% bandwidths are about 47% (the limit for the case of the layer with ε r = 4.6). The absorption characteristics of the proposed absorber are shown to be almost unaffected by the polarisation angles of normally incident TEM waves.Introduction: Microwave absorbers are required for anechoic chambers, stealth technology and electromagnetic compatibility, among other applications. A conventional and popular absorber is the Salisbury screen [1]. It is basically a resistive sheet placed a quarter wavelength from a metallic plane. Despite its relatively simple structure, the absorption bandwidth of the Salisbury screen is limited by the frequency dependence of the sandwiched layer. Recent advancements in metamaterial research have suggested the possibility of metamaterial absorbers (MAs) [2][3][4]. However, the reported bandwidths of MAs are still far narrower than those of the Salisbury-type absorbers. An optimum design method was theoretically investigated for enhanced bandwidth at the cost of the reduced absorption rate in [5]. A multi-layer structure with loaded chip resistors was also proposed with a 99% absorption bandwidth of about 40% [6]. Recently, a triple-band planar absorber with a high-impedance surface was proposed with a theoretical derivation of the match condition requiring varied resistance as a function of frequency [7]. The reported 90% absorption bandwidth is roughly 85% at a centre frequency of 10 GHz, but with a mixture of different unit structures with varying surface resistance per square.In this Letter, we present simple design equations for wideband absorbers with complete absorption at a specific centre frequency. As an example, a microwave absorber at 10.93 GHz is designed on an FR-4 substrate with a relative permittivity of 4.6 and a thickness of 3.2 mm. The theoretical bandwidth of the proposed absorber is compared with the measured one.
This paper presents a design methodology for wideband single-layered microwave absorbers with arbitrary absorption at the design center frequency using reactive Salisbury screens. The bandwidth of the absorber increases when the flatness of the reflection response at the design center frequency is maximized. Based on this observation, closed-form design formulas for wideband absorbers are derived. As they are scalable to any design frequency, wideband reactive screens can be systematically realized using two-dimensional periodic crossed-dipole structures patterned on a resistive sheet. Based on this method, a single-layered absorber with a 90% bandwidth improved to 124% of the design center frequency is presented. For the purpose of physical demonstration, an absorber with a design center frequency of 10 GHz is designed and fabricated using a silver nanowire resistive film with a surface resistance of 30 Ω/square. The measured absorption shows a good agreement with both the calculation and the electromagnetic simulation.
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