Magnetless Nonreciprocal Metamaterial (MNM) Technology: Application to Microwave Components

Abstract

S 22 5S 11 5 Z in 250 Z in 150 S 21 5 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 12jS11j 2 q (5)The RF performance of the ECM is also verified by the circuit simulator in Ansoft Designer. The S-parameter results calculated by circuit simulator and from the analytic formulations (1) and (5) are shown in Figure 6. These results confirm the correct analytical formulation of the ECM with (1) and (5).The occurring discrepancies in the results are originating from the numerical inaccuracy. As deduced from Figures 3 and 6, the ECM describes the frequency dependence of scattering parameters and hence the operation principle of BPF even though there are some frequency shifts between both results. There are three main reasons. At first, the capacitive and inductive coupling between resonators 1 and 2 are neglected as first-order approximation. Second, the metallic loss, which degrades resonator Q, resonance frequency, and scattering parameters, is neglected for the model simplicity. This can be deduced from higher return loss and lower insertion loss calculated from ECM in comparison to the ones calculated from the numerical model. As a last reason, the circuit model is based on the calculation of circuit elements for k/4 resonance of both resonator types. This is, however, not true for the frequencies far from the resonance frequency, in which the electromagnetic wave feature of RF signal has to be modeled by the distributed circuit elements or additional reactive lumped elements in a more complex circuit model.The operation principle of BPF can be described with the help of ECM in Figure 5. The incoming field is transmitted in the passband with different phase shifts by the excitation of output metamaterialinspired resonator through the electric and magnetic coupling of the resonant field of the input resonator. The resulting field coupling from one resonator at the first port to another resonator at the second port is also enhanced by k/4 transmission line resonator. The oppositely directed magnetic moments of both resonators at the resonance frequency, Figure 4(a) is also correctly modeled in Figure 5. At the stopband frequencies, these two resonators are purely electrically and magnetically coupled in the form of 0 and p modes of coupled resonators as deduced from Figures 4(b) and 4(c), respectively. CONCLUSIONIn this article, the design of a compact BPF, composed of two metamaterial-inspired resonators and k/4 transmission line resonators surrounding these resonators, is explained. The filter operation is verified from the numerically and experimentally calculated scattering parameters. They show good agreement. The ECM is additionally derived with the corresponding lumped circuit elements to describe the filter operation principle. The proposed filter has satisfactory insertion loss, which is smaller than 1 dB in the frequency band between 3.9 and 4.54 GHz with the bandwidth of 640 MHz. The physical size of filtering section without the feeding line sections is k o /11 3 k o /14 at the lower pass ban...

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