Analytical model for double split ring resonators with arbitrary ring width

Abstract

For the first time, the analytical model for a double split ring resonator with unequal width rings is developed. The proposed models for the resonators with equal and unequal widths are based on an impedance matrix representation and provide the prediction of performance in a wide frequency range. A phase compensation is implemented to adjust for the difference in length of the two rings, resulting in an accurate calculation of the resonant frequencies. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 511–515, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23104

Transmission line model for coupled rectangular double split‐ring resonators

“…The indicated geometrical parameters are used to define microstrip line and the DSRRs. Previous works [10, 12] have shown that the properties of the DSRR can be modeled by a series of impedance matrix network representing the single, coupled transmission lines, gap and corner effects as shown in Figure 2. The different types of impedance network fall into categories according to their position: Coupled line sections Z CL1 , Z CL2 , and Z Δ can be modeled by the four‐port impedance matrix.…”

“…The different types of impedance network fall into categories according to their position: Coupled line sections Z CL1 , Z CL2 , and Z Δ can be modeled by the four‐port impedance matrix. With symmetric conditions [10, 13]: R c = 1 and R π = −1 for even and odd mode analysis, the four‐port impedance network of asymmetric coupled line can be simplified to be where and Z o and Z e are the odd and even mode impedances, respectively; γ o and γ e are the corresponded odd and even mode propagation constants; l is the length of the coupled line, which equals a 1 − 2( W r + S r ) for Z CL1 , $ {(a_{2}-g) \over 2} $ for Z CL 2 , and W r + S r for Z Δ . Transmission line Z ΔG can be modeled by a two‐port matrix where Z 0 is the characteristic impedance of the line, γ is the propagation constant, and L is the length of transmission line, which equals g for Z Δ G . Gap and corner effect: Z G and Z C can be modeled by two port π and T networks, respectively, with their corresponding parasitic inductors and capacitors. In the case of microstrip technology, the calculation of these parasitics is based on well established empirical expressions [14–16].…”

“…Coupled line sections Z CL1 , Z CL2 , and Z Δ can be modeled by the four‐port impedance matrix. With symmetric conditions [10, 13]: R c = 1 and R π = −1 for even and odd mode analysis, the four‐port impedance network of asymmetric coupled line can be simplified to be where and Z o and Z e are the odd and even mode impedances, respectively; γ o and γ e are the corresponded odd and even mode propagation constants; l is the length of the coupled line, which equals a 1 − 2( W r + S r ) for Z CL1 , $ {(a_{2}-g) \over 2} $ for Z CL 2 , and W r + S r for Z Δ .…”

“…In this article, the analytical model proposed by Zhurbenko et al [10] is used. This method shows an alternative way to model the DSRR structure by using coupled lines formulation.…”

Analysis, simulation, and experimental verification of split‐ring resonator

“…Split‐ring resonator (SRR) , loop‐gap resonator , or open‐loop resonator finds its utility in various applications due to low‐phase noise, moderate quality ( Q ) factor, low cost, ease of fabrication, and so forth. SRR can have a number of variations including planar/nonplanar forms , geometrical shapes , multiple rings , and multiple gaps . Various design models are available , which use dimensional and other parameters to calculate resonant frequency and Q factor.…”