Yan n Li

Two-Dimensional Metallic Photonic Crystal with Point Defect Analysis Using Modified Finite-Difference Frequency-Domain Method

We have derived a modified finite-difference frequency-domain (FDFD) algorithm for two-dimensional (2-D) metallic photonic crystal (MPC) analysis. Using this method, the numerical results for the transverse-electric (TE) and transverse-magnetic (TM) modes in square and triangular lattices are in excellent agreements with those from other method. Then the correspondence of the band gaps between a unit cell and a supercell is demonstrated. Furthermore, by comparing the field distributions of the defect modes in a point defected MPC and a point defected dielectric photonic crystal (DPC), it is found that the defect MPC has a higher degree of localization, which means that MPC is preponderant for resonator and waveguide applications in millimeter wave and sub-millimeter wave bands.

Vectorial Solution to Double Curl Equation With Generalized Coulomb Gauge for Magnetostatic Problems

In this paper, a solution to the double curl equation with generalized Coulomb gauge is proposed based on the vectorial representation of the magnetic vector potential. Traditional Coulomb gauge is applied to remove the null space of the curl operator and hence the uniqueness of the solution is guaranteed. However, as the divergence operator cannot act on edge elements (curl-conforming) directly, the magnetic vector potential is represented by nodal elements, which is too restrictive, since both the tangential continuity and the normal continuity are required. Inspired by the mapping of Whitney forms by mathematical operators and Hodge (star) operators, the divergence of the magnetic vector potential, as a whole, can be approximated by Whitney elements. Hence, the magnetic vector potential can be expanded by the edge elements, where its vectorial nature is retained and only the tangential continuity is required. Finally, the original equation can be rewritten in a generalized form and solved in a more natural and accurate way using finite-element method.

Full-Wave Semi-Analytical Modeling of Planar Spiral Inductors in Layered Media

In this paper, we present a full-wave semi-analytical solution to calculate the self and mutual impedances of two coupled spiral inductors with rectangular cross sections. In low-frequency electromagnetism, the self and mutual impedance of planar spiral inductors can be obtained based on the eddy current approximation, where the displacement current is disregarded. As the frequency increases, the size of the system can be designed to be smaller. However, the displacement current becomes more important in inductively-coupled systems. By directly deriving the Maxwells equations without the eddy current assumption, the obtained full-wave model could be applied to both homogeneous and planarly layered media for wireless power transfer systems. Compared to the traditional methods, the newly derived impedances show a considerable discrepancy at GHz frequencies for millimeter-sized inductors, indicating the significance of the displacement current if the operating frequency of wireless power transmission reaches the GHz-range.

Study of wideband patch-based Butler matrix and its high-frequency application

In this paper, a wideband Butler matrix based on the 3-dB cross-slotted patch hybrid couplers and interdigital coupled-line section is presented. After loading a tight-coupled-line section at each port of the coupler, the operating bandwidth is enhanced with one more transmission pole. The Butler matrix is first designed and implemented at 2.65 GHz, with about 36% -10dB return loss bandwidth. Amplitude imbalance of ±1dB achieves about 38% bandwidth, while the 45°±2° phase difference bandwidth is around 29.6%. In addition, its Ku-band version operating at 12.5 GHz is also designed and well investigated.

Finite Element Implementation of the Generalized-Lorenz Gauged A-

The A-Φ formulation with generalized-Lorenz gauge is free of catastrophic breakdown in low-frequency regime. In the formulation, A and Φ are completely separated and Maxwells equations are reduced into two independent equations pertinent to A and Φ. This, however, leads to more complicated equations in contrast to the traditional E formulation. The numerical dicretization of the equations is challenging, especially for the equation pertinent to A. By virtue of the differential forms theory and Whitney elements, the direct action of divergence operator on A is bypassed. Thus, the equations can be discretized compatibly using regular finite element method. The condition of the resultant matrix system is much better than that of the E formulation as frequency becomes low, and even approaches to zero. The generalized-Lorenz gauged A-Φ formulation is verified to be accurate and efficient for low-frequency circuit problems.

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In this paper, a miniaturised Butler matrix using 3-dB cross-slotted patch hybrids is presented. By asymmetrically loading the inductive cross-slotted slots on four patches, compact patch hybrid couplers can be achieved. After properly installing two quarter-wavelength short-circuited stubs as phase shifters, the overall size of the resultant Butler matrix is largely reduced. In comparison with traditional patch hybrids with half-wavelength side-length, the side-length of proposed one can be shorter than quarter-wavelength. It means that the over all circuit area achieves an area reduction of about 56%, while the comparable performance is maintained, where the -10dB return loss bandwidth is more than 14%, ±0.7 dB amplitude balance bandwidth is more than 10%, and the 45 ° ± 5 ° phase difference bandwidth is around 14%. Finally, a prototype of proposed Butler matrix is fabricated and verified experimentally.

Formulation for Low-Frequency Circuit Modeling

In this paper, a solution to the double curl equation with generalized Coulomb gauge is proposed based on the vectorial representation of the magnetic vector potential. Coulomb gauge is applied to remove the null space of the curl operator and hence the uniqueness of the solution is guaranteed. However, as the divergence operator cannot act on the curl-conforming edge basis functions directly, the magnetic vector potential is used to be represented by nodal finite elements. Inspired by the mapping of Whitney forms by mathematical operators and Hodge operators, the divergence of the magnetic vector potential, as a whole, can be approximated by scalar basis functions. Hence, the magnetic vector potential can be expanded by vector basis functions, and the original equation can be rewritten in a generalized form and solved in a more natural and accurate way.

A miniaturised Butler matrix based on patch hybrid couplers with cross slots

In this paper, a full-wave semi-analytical solution of self and mutual impedances for a coil-based system is proposed. It consists of two concentric circular coils with rectangular cross sections. Traditionally, the calculation of self and mutual impedances of these coils are based on eddy current approximation, where a simple background is assumed to achieve analytical and semi-analytical solutions. As the system operates at higher frequencies and with inhomogeneous media, the displacement current has to be taken into account. By deriving Maxwells equations without eddy current assumption, the impedances of coils immersed in the layered medium can be obtained analytically. The results show a considerable discrepancy at sub-GHz frequencies, indicating the significant effect of displacement current at higher frequencies for a coil-based wireless power transfer link.