Impedance responses and size-dependent resonances in topolectrical circuits via the method of images (original) (raw)
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A non-Hermitian system is characterized by the violation of energy conservation. As a result of unbalanced gain or loss in the forward and backward directions due to non-reciprocal couplings, the eigenmodes of such systems exhibit extreme localization, also known as non-Hermitian skin effect (NHSE). This work explores unconventional scenarios where the interplay of multiple asymmetric couplings can cause the NHSE to vanish, with the admittance spectra taking identical dispersion under open boundary conditions (OBC) and periodic boundary conditions (PBC). This is unlike known non-Hermitian models where the NHSE vanishes only when the non-Hermiticity is turned off. We derive general conditions for the NHSE, with the overall eigenmode localization determined by the geometric mean of the cumulative contributions of all asymmetric coupling segments. In the limit of large unit cells, our results provide a route towards the NHSE caused by asymmetric hopping textures, rather than single asy...
2009 Mediterrannean Microwave Symposium (MMS), 2009
an efficient computation technique is developed for analysis anisotropic multilayered microwave circuits constituted of several conducting strips/slots which are located on several interfaces of dielectric layers. Used technique is based on extension of spectral domain approach. The numerical solutions obtained by this technique are discussed and compared with the published data. The technique is believed useful in the determination of dispersion characteristics of those circuits such as effective dielectric constant, phase velocity and normalized wavelength. Authorized licensed use limited to: University of Ottawa. Downloaded on November 19, 2008 at 08:59 from IEEE Xplore. Restrictions apply.
Characteristic of the equivalent impedance for an m×n RLC network with an arbitrary boundary
Frontiers of Information Technology & Electronic Engineering
Considerable progress has been made recently in the development of techniques to determine exactly two-point resistances in networks of various topologies. In particular, a general resistance formula of a non-regular m×n resistor network with an arbitrary boundary is determined by the recursion-transform (RT) method. However, research on the complex impedance network is more difficult than that on the resistor network, and it is a problem worthy of study since the equivalent impedance has many different properties from equivalent resistance. In this study, the equivalent impedance of a non-regular m×n RLC network with an arbitrary boundary is studied based on the resistance formula, and the oscillation characteristics and resonance properties of the equivalent impedance are discovered. In the RLC network, it is found that our formula leads to the occurrence of resonances at the boundary condition holding a series of specific values with an external alternating current source. This curious result suggests the possibility of practical applications of our formula to resonant circuits.
Improvements of Spectral Domain Analysis Techniques for Arbitrary Planar Circuits
20th European Microwave Conference, 1990, 1990
Spectral domain analysis techniques using roof-top functions as expansion functions for the surface current density have proofed to lead to a flexible tool for the calculation of arbitrarily shaped planar microwave structures. Several improvements of this method e.g. the introduction of new integration paths and analytic integration of a separated part of the dyadic function which reduce the computation time and which for the first time introduce losses (without using perturbation techniques) into the spectral domain analysis will be described. Furthermore the influence of surface waves and radiation is considered so that the transmission properties of planar microwave components can be described more realistically.
International Journal of RF and Microwave Computer-Aided Engineering, 1998
In this paper we propose an efficient technique for computation of the capacitance matrix of a set of infinitely thin conductor patches embedded in a multilayered medium. The patches present a manhattan-type shape, i.e., they can be subdivided into a ( ) finite number of rectangular regions. The generalized biconjugate gradient method GBGM in conjunction with FFT algorithms, is adapted to solve the convolution integral equation governing the free-charge density distribution on the conductors. Important computational improvements are achieved by including asymptotic extraction techniques in the determination of the space domain periodic Green's functions. The analysis is also applied to the quasistatic modelling of some microstrip discontinuities.
IEEE Transactions on Antennas and Propagation, 2000
This work presents an equivalent circuit to model the transmission/reflection of a plane wave that impinges obliquely on a periodic arrangement of metallic rectangular dipoles embedded between two dielectric slabs. The equivalent circuit takes advantage of the periodicity of the structure to reformulate the original problem as a certain equivalent waveguide scattering problem. Equivalent transmission lines are used to simulate the wave propagation whereas equivalent lumped circuit elements account for presence of the metallic patches. The obtaining of the circuit parameters is carried out via a systematic procedure, which provides a robust strategy that gives rise to surprisingly accurate results even for rather complex situations. The proposed equivalent circuit model simplifies considerably the original complex electromagnetic problem and provides a valuable physical insight into the parameters that are relevant in the phenomenon as well as an in-depth understanding of the operation principles of the periodic surface. Thus, the reported reduced-order model of the corresponding scattering problem can be a very convenient and helpful tool for the analysis and/or design of many practical devices.
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3D Si integration seems a right way to go and compete with Moore's law (more than Moore versus more Moore). However, it is still a long way to go. A crippling problem, not really considered currently, concerns the noise propagation, especially when complex 3D interconnects, in the radiofrequency range and at a nano-scale, is embedded into the substrate. First of all, from any source, we calculate the spreading impedance. Compact Green kernel, over or into a multi-layered substrate, is derived by solving Poisson's equation analytically. The Discrete Cosine Transform and its variations are used for rapid evaluation. Using this technique, the substrate coupling and loss in IC's can be analyzed. We implement our algorithm in MATLAB. Thus, it permits to extract 3D impedances between any two embedded contacts, real or virtual. A third point is we can calculate from any contact source in the bulk where appear some current fluctuations, some voltage fluctuations at any other embedded contacts, and get transfer impedances, a key item for noise propagation calculations; we think that is the very originality of this paper. We investigate our models on 052 Glo. Adv. Res. J. Eng. Technol. Innov. both analytical and numerical methods, like finite elements-based simulations. This extended model enables one to extract substrate impedance, parasitic elements and noises between any two points embedded into the substrate. They are fully compatible with SPICE-like solvers and should allow an investigation in depth of the impact of buried contacts on circuit performance. Concerning noise calculations, we introduce the Impedance Field Method; it describes the response of local noise sources to target points, both points being anywhere into the bulk, and possibly to terminals. Some physical noise models, GR-like, are introduced. The implementation of noise analysis into our simulator is begun and first results of the calculation into the substrate are shown.
IEEE Transactions on Microwave Theory and Techniques, 2008
In this paper, a practical implementation of the spatial images technique for the analysis of shielded multilayered printed circuits inside convex cavities is proposed. A new method is introduced in order to automatically locate the images surrounding the structure in order to impose the appropriate boundary conditions for the potentials. The boundary conditions are imposed at discrete points along the cavity wall and, therefore, the technique proposed is an approximation to the exact cavity modeling. Furthermore, for the analysis of electrically long cavities, the use of several rings of images surrounding the entire cavity at different heights is employed. Using the special features of the formulation, a new method of moments implementation combined with the spatial images technique is proposed in order to efficiently analyze practical multilayered printed filters, considerably reducing the computational cost. Several examples with CPU time comparisons are provided, demonstrating the accuracy and efficiency of the new technique. A novel transversal filter in a trapezium-shaped cavity is designed, manufactured, and tested for the first time using the spatial images technique.
Type-II corner modes in topolectrical circuits
Physical Review B
We study the rich properties of a topolectrical (TE) circuit array consisting of lossless basic electrical components, such as capacitors and inductors, which can be designed to exhibit higher-order topological phases (HOTP). The HOTP of the circuit exhibits the characteristics of higher-order topology, i.e., unconventional bulk-boundary correspondence with strongly localized corner modes, and higher winding numbers. More interestingly, a type-II corner mode emerges in the presence of long-range interaction, which is realized in the TE circuit by the introduction of next-nearest neighbor (NNN) coupling capacitances. Unlike the usual (i.e., "type-I") corner modes that are localized at a particular sublattice node due to the chiral symmetry, the type-II corner modes possess a spatial extent with an exponential decay length. We analytically derive this decay length as a function of the circuit parameters. The NNN coupling is also associated with the tilt parameter in the admittance spectrum of the circuit. The admittance spectrum is reminiscent of that of Dirac fermions. Changing the tilt parameter can lead to a transition from the type-I to the overtilted type-II Dirac dispersion. This overtilting results in a hybridization of the bulk and corner modes in which the distinct corner modes disappear. Furthermore, the type-I and type-II corner modes can be distinguished by their impedance readout. By virtue of their flexibility, the TE circuits provide an ideal platform to demonstrate unusual features of HOTPs arising from long-range interactions, and to engineer different types of robust topological corner modes.