We compare the analytical model with the numerical simulations in the case when we have the same value of individual PDL i and PDG i . The crosstalk CX resulting from PDL and PDG effects is presented in Figure 2. In turn, Figures 3 and 4 show the value of R CX ratio as a function of PDL mean and PDG mean . Figures 3 and 4 reveal that the analytical predictions of the CX are in good agreement with the numerical simulations only for low values of PDL i and PDG i . If the mean values of PDL and PDG are less than 2 dB then the value of R CX is greater than 90%. Next, the impact of the pure PDL effect (g i ϭ 1) on R CX is investigated. Figure 5 shows the relationship between R cx and PDL mean . These results confirm good agreement between analytical and numerical results for PDL mean Ͻ 2 dB.
CONCLUSIONA simplified analytical model to evaluate the CX between two polarization channels has been presented. It allows a significant simplification of the CX calculation in polarization multiplexed transmission systems. This model gives good qualitative predictions of the CX for PDL and PDG mean values Ͻ 2 dB. In this study, split-ring resonator (SRR) is studied to achieve three pass bands for further filter design. SRR is proposed by Pendry to provide negative permeability [6] and used in many microwave components and antennas' applications [7][8][9][10]. Here SRRs are printed on the substrate with ground plane. By adding an inner open-loop with the opposite orientation into the outer openloop, the first resonant frequency is reduced and an additional resonant frequency is created. At the first frequency, SRR is considered as the effective medium with negative permeability, which size is much smaller than the wavelength. Comparing with the common open-loop, which offers two controllable passbands using the stepped-impedance resonator (SIR) technique [11], SRR can provide three controllable passbands in the similar frequency range with more compact size.We use the even/odd-mode method to analyze the SRR roughly. Then the full-wave simulation method is then used for accurate analysis. Through the simulation, the current distributions are clearly exhibited. By changing the geometry parameters of SRR, the resonant frequencies can be controlled. Several types of triple-mode resonators are designed and fabricated. Both simulation and measurement results are presented, which have excellent agreements, to show the good performance of the resonators.
THEORETICAL ANALYSISThe SRR is shown in Figure 1, in which the edge-coupled feed line is utilized. It is convenient for analysis by a simply even-and odd-mode method. The symmetrical plane is also shown in Figure 1.
Even/Odd-Mode AnalysisThe structure is cut by the vertically symmetrical plane, which can be defined as magnetic wall for even-mode, and as electric wall for odd-mode. The impedance and admittance of SRR without feed line can be studied in the even-mode and odd-mode, which equivalent circuits are shown in Figures 2(a) and 2(b), respectively. The structure is partitioned into ...