Qin S. Liu

Combined Field Integral Equation-Based Theory of Characteristic Mode

Conventional electric field integral equation-based theory is susceptible to the spurious internal resonance problem when the characteristic modes (CMs) of closed perfectly conducting objects are computed iteratively. In this paper, we present a combined field integral equation-based theory to remove the difficulty of internal resonances in CMs analysis. The electric and magnetic field integral operators are shown to share a common set of nontrivial characteristic pairs (values and modes), leading to a generalized eigenvalue problem which is immune to the internal resonance corruption. Numerical results are presented to validate the proposed formulation. This work may offer efficient solutions to CM analysis which involves electrically large closed surfaces.

Large-Scale Characteristic Mode Analysis With Fast Multipole Algorithms

Large-scale characteristic mode analysis (CMA) poses challenges in computational electromagnetics as it calls for efficient solutions of large dense generalized eigenvalue problems. In this paper, we consider two applications that involve large-scale CMA, and demonstrate that fast multipole algorithms (FMAs) can be easily incorporated into the implicitly restarted Arnoldi method (IRAM) for eigenanalysis after simple modifications. The first application performs CMA for large platforms made by closed perfectly conducting surfaces. Multilevel FMA (MLFMA) is embedded into a combined field integral equation-based theory of characteristic mode (TCM). The second application addresses multiscale modeling of small but geometrically complicated objects, which possess fine subwavelength structures. An augmented electric field integral equation-based TCM is formulated, and low-frequency (LF-)FMA is adopted to accelerate the required matrix-vector products.

An integral equation method based on vector and scalar potential formulations

In this paper, we propose a new integral equation method based on the formulations for vector potential A and scalar potential Φ. The new formulation, which is immune from low-frequency breakdown problem, is proposed for both electromagnetic scattering and circuit problems. Since both vector and scalar potentials are important for capturing the low-frequency physics, the contribution from scalar potential is solved in tandem with the vector potential equation in our new formulation. The numerical examples validate the effectiveness, stability and accuracy of the proposed formulation.

Low-frequency CMP-EFIE with perturbation method for open capacitive problems

This paper addresses the low-frequency problems for open capacitive problems in the electric field integral equation using Calderón multiplicative preconditioner (CMP-EFIE). At low frequencies, the CMP-EFIE fails to extract accurate high-order current for a capacitor problem. By representing the electric current at different frequency orders as a power series, we successfully apply the perturbation method on the CMP-EFIE for capacitive structures with open surfaces. Numerical results show that the highly accurate current for a capacitor can be obtained with fast convergence at extremely low frequencies.

Convergence of low-frequency EFIE-based systems with weighted right-hand-side effect

This paper addresses the convergence of the electric-field integral equation (EFIE)-based matrix systems with the right-hand-side effect. The role of the right-hand-side excitation in determining the convergence rate of the iterative solvers is found to be important or even crucial at low frequencies. The weighted contributions from different singular vectors are decided by not only the corresponding singular values but also the right-hand side. Based on this understanding, we investigate the low-frequency stabilized form of both EFIE and Calderón multiplicative preconditioner EFIE (CMP-EFIE) on capacitive problems. For the parallel-plate capacitor excited by the delta-gap source, the singular vectors with small singular values cannot be excited, and the charge currents on the capacitive surface dominate. Thus, the stability of the EFIE-based system can be achieved at low frequencies. Detailed spectral analysis and convergent results are carried out in order to capture the physical nature of the problems.

Implementation of a simplified form of CMP-EFIE for low-frequency capacitive problems

In this paper, a simplified form of electric field integral equation with Calderón multiplicative preconditioner (CMP-EFIE) is presented for solving capacitive problems in the low-frequency regime. The decomposed three-term CMP-EFIE, though very stable, cannot capture the current accurately for a capacitor at low frequencies. By omitting the part of the hypersingular preconditioned term, the electric currents solved from the remaining two terms are of the right frequency order for a capacitor. Hence, the resultant two-term formulation can guarantee the accuracy of results for capacitive problems, and also makes the iterative system more stable at low frequencies. Both theoretical analysis and numerical results are provided to verify the practicality of the proposed method.

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.

Theory of characteristic modes based on potential-based integral equation

The characteristic mode analysis is presented based on the potential-based integral equation, where the vector potential equation and the scalar potential are formulated separately and solved in tandem. Accordingly, the theory of the characteristic modes, originated from the electrical field integral equation (EFIE), can be analyzed for the novel potential-based integral equation system with the contributions from different components in EFIE.

Characteristic mode theory based on combined field integral equation

Characteristic mode theory is usually formulated on top of the electric field integral equation. We present in this paper a combined field integral equation based characteristic mode theory which is immune to the internal resonance corruption when the characteristic modes of closed perfectly conducting surfaces are iteratively solved for. Numerical results are presented to validate the proposed formulation. This work may offer efficient solutions to characteristic mode analysis which involves electrically large closed surfaces.

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

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.