Generalized Admittance Matrix Research Articles

Permittivity Spectrum of Low-Loss Liquid and Powder Geomaterials Using Multipoint Reentrant Cavities

Permittivity is a useful tool to characterize the composition and quality of many geomaterials. In general, the non-resonant permittivity measurement methods exhibit a higher degree of uncertainty than their resonant counterparts. In resonant measurements, the reduction in uncertainty comes typically with a loss in broadband. This article describes the theory, design, and application of multipoint coaxial reentrant resonant cavities applied to low-loss geomaterials at different temperatures. Specifically, a full-wave method based on circuit analysis is developed and applied for a circular corrugated waveguide. Moreover, the mode-matching method is applied to calculate the generalized admittance matrix (GAM). Two multipoint cavities and software were built and validated. The first cavity has five resonant frequencies, between 170 MHz and 2.3 GHz, and the second has four resonant frequencies, between 1.3 and 8.6 GHz. Thus, this method allows for “broadband-resonant” measurements. The permittivity values of liquid hydrocarbons, powdered kerogen, and pyrite are shown.

Modeling of Inhomogeneous and Lossy Waveguide Components by the Segmentation Technique Combined With the Calculation of Green’s Function by Ewald’s Method

This paper presents a novel algorithm for the analysis of piecewise homogeneous, possibly lossy, waveguide circuits. The algorithm is based on the segmentation technique to split the circuit into homogeneous building blocks, combined with the representation of the generalized admittance matrix (GAM) of each block by the boundary integral-resonant mode expansion (BI-RME) method. The GAMs are then recombined by a circuital cascading procedure. The core of the method is the calculation of the quasi-static Green’s function of a rectangular box, which is required to determine the terms of the BI-RME pole-expansion of the GAM. The expressions of the quasi-static Green’s function, manipulated by Ewald’s technique to improve the convergence, are fully described, and numerical considerations for their efficient and accurate calculation are provided, with a particular focus on the proper selection of the splitting parameter. To demonstrate the correctness of the given formulas, the algorithm is developed and applied in the limited case of circuits segmentable into boxed building blocks. Numerical examples demonstrate the accuracy and efficiency of the proposed technique.

Study of the multipactor phenomenon using a full-wave integral equation technique

Multipactor effect is a well-known phenomenon of RF breakdown in satellite payloads which degrades components, generates undesirable harmonics, contributes to power dissipation and increases noise in communications. Traditionally, multipactor has been investigated with the aim of obtaining the so-called multipactor threshold voltage, or to present different multipaction detection methods. However, very little attention has been focused on analysing this phenomenon using a multimodal approach. The main goal of this work is to analyse the interaction between a multipactor current and a realistic microwave cavity by means of a rigorous and accurate formulation. For the first time to the authors’ knowledge, a full-wave method based on the 3-D Boundary Integral – Resonant Mode Expansion (BI-RME) technique is proposed to model the aforementioned undesired effect. In this work, the classical formulation used in the 3-D BI-RME method is exploited to achieve a full-wave representation of the multipactor effect in terms of an equivalent multimode network expressed in the form of a generalized admittance matrix.

Enhanced Full-Wave Circuit Analysis for Modeling of a Split Cylinder Resonator

An enhanced full-wave method based on circuit analysis is presented in this paper, where the whole set of modes TEmnp and TMmnp are taken into account. The modeling of a split cylinder resonator is done with two circuit networks of one and three ports, characterized by their generalized admittance matrix, which is computed making use of the mode matching method. The improved full-wave circuit method has been applied to the accurate determination of dielectric properties of materials. The proposed method has been validated through comparisons with other published models and also with measurements.

Generalized $\pi$ Fortescue Equivalent Admittance Matrix Approach to Power Flow Solution

This paper develops a generalized admittance matrix approach in Fortescue coordinate system to solve unbalanced/unsymmetrical distribution networks including different number of phases. This generalized Fortescue π equivalent is defined in this paper for solving the heterogeneous phase, and thus Fortescue, network model. The performance of the approach is demonstrated in different model networks with number of nodes ranging between 168 and 14200. It is found that the current iteration method exploiting the decoupling in admittance matrix in Fortescue coordinate is substantially faster than the typical unbalanced three-phase solution in phase domain. The method has a significant potential for application in real time active power network management.

Wideband generalized admittance matrix representation for the analysis and design of waveguide filters with coaxial excitation

A very efficient technique for the full‐wave analysis and design of complex passive waveguide filters, including rectangular cavities with metallic cylindrical posts and coaxial excitation, is presented. This novel technique provides the wideband generalized admittance matrix representation of the whole structure in the form of pole expansions, thus extracting the most expensive computations from the frequency loop. For this purpose, the structure is properly segmented into its key building blocks, all of them characterized in terms of wideband admittance matrices. Then, an efficient iterative algorithm for combining these matrices, and finally providing the wideband generalized admittance matrix of the complete structure, is followed. In order to validate the accuracy and efficiency of this full‐wave modal technique, four different waveguide filters have been considered. In particular, the design of a compact four‐pole in‐line filter with tuning screws and of an evanescent‐mode filter, both operating in the X‐band and including a standard (vertical) coaxial excitation, are first presented. Finally, two C‐band six‐resonator comb‐line filters, one of them with a cross‐coupling configuration, and both excited with a collinear end‐launcher transition based on a disc‐ended coaxial, are also designed. Numerical data from a commercial software, as well as measurements of a manufactured prototype, are included for verification purposes.

Full-Wave Analysis of Dielectric-Loaded Cylindrical Waveguides and Cavities Using a New Four-Port Ring Network

In this paper, a full-wave method for the electromagnetic analysis of dielectric-loaded cylindrical and coaxial waveguides and cavities is developed. For this purpose, a new four-port ring network is proposed, and the mode-matching method is applied to calculate the generalized admittance matrix of this new structure. A number of analyses on dielectric-loaded waveguide structures and cavities have been conducted in order to validate and to assess the accuracy of the new approach. The results have been compared with theoretical values, numerical modeling from the literature, and data from commercial electromagnetic simulators. The method has been also applied to the accurate determination of dielectric properties, and we provide an example of these measurements as another way to validate this new method.

Generalized admittance matrix models of OTRAs and COAs

This paper proposes new admittance matrix models to approach the behavior of fully-differential Operational Transresistance Amplifiers (OTRAs) and Current Operational Amplifiers (COAs). The infinity-variables method is used in order to derive the new generalized models. As a consequence, standard nodal analysis being improved to compute fully-symbolic small-signal characteristics of fully-differential analog circuits.

Closed-Form Expressions for the Equivalent Circuit Model of Square-Waveguide T-Junctions and Its Application in Ortho-Mode Transducer Design

In this paper, closed-form expressions for the equivalent circuit model of square-waveguide T-junctions are presented. The square-waveguide T-junction is first modeled as a generalized admittance matrix and then reduced to a general five-port network. It is theoretically seen that the general five-port network can be simplified as a combination of a two-port subnetwork and a three-port subnetwork through the mode-matching analysis. Accurate closed-form expressions are derived with proper approximations to calculated the admittance parameters of these two subnetworks. A short-circuited branch ortho-mode transducer is then designed in a circuit simulator using the proposed equivalent circuit model. Measured results exhibit an excellent agreement with those from circuit simulation.

Closed-form expressions for the equivalent circuit model of H-plane waveguide T-junctions

In this study, the authors present simple and accurate closed-form expressions for the equivalent circuit model of H-plane waveguide T-junctions with a side arm of arbitrary size. The effect of higher-order modes is included through the generalised admittance matrix with proper approximation and simplification. Calculated results agree very well with those from the full-wave mode-matching analysis over the entire single-mode operating band and these expressions exhibit significant improvements compared with those available in the literature. Based on these closed-form expressions, the design of an H-plane diplexer in the circuit level is considered and the initial value of the diplexer can be quickly obtained by circuit optimisation. Results from this circuit model are compared with those from the full-wave simulation and the comparison shows that this circuit model is very suitable for the initial design of diplexers.

A novel technique for the direct determination of multimode equivalent circuit models for substrate integrated waveguide discontinuities

A novel technique is presented for the automatic, self-consistent and direct determination of wide-band lumped-element equivalent circuit models of substrate integrated waveguide discontinuities. This technique is based on the full-wave analysis of substrate integrated waveguide components by using the Boundary Integral-Resonant Mode Expansion method, which provides a generalized admittance matrix of the components in the form of a pole expansion in the frequency domain. This expression of the admittance matrix permits to directly identify the topology of a multimodal equivalent circuit and the values of its lumped elements, thus avoiding any initial guess or fitting procedure. The basic theory of the full-wave analysis method and the procedure for determining the equivalent circuit model are reported. The features of the proposed technique are detailed through the modeling of an iris-like discontinuity. Moreover, this technique is validated by modeling substrate integrated waveguide filters, whose frequency response is compared with numerical and experimental results. The proposed method can be adopted to obtain libraries of parametric models of substrate integrated waveguide discontinuities, which can be included in computer aided design tools. The multimodal parametric model of an iris-like discontinuity is presented and discussed. © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2009.

Full-wave modeling and optimization of Bøifot junction ortho-mode transducers

The full-wave design of broadband ortho-mode transducers based on the Bøifot junction has two main aspects: an efficient analysis method and a design process divided into tasks with relatively low computational effort. In the analysis part, a rigorous mode-matching technique has been developed to obtain the generalized admittance matrix of the Bøifot junction. The other elements of the device are also analyzed by mode-matching. With respect to the design, the proposed procedure starts with the optimization of the individual building blocks of the device. Their interaction is also taken into account in a systematic process. The analysis and design methods have been validated with other numerical methods and an experimental prototype. © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2008.

Fast S-domain modeling of rectangular waveguides with radially symmetric metal insets

This paper describes the application of the boundary integral-resonant-mode expansion (BI-RME) method to the modeling of rectangular waveguides with metal insets. It extends to more complicated radially symmetric insets, a method recently introduced by the authors, for the simple case of a cylindric post. In this extension, a self-consistent new theory is presented, which fully exploits the peculiarities of the considered class of structures, thus straightforwardly leading to the system equations. The efficiency of the BI-RME method, already demonstrated in the wide-band modeling of arbitrarily shaped waveguide components, is further enhanced in the particular application considered in this paper because the currents on the waveguide walls are not involved in the calculation. For this reason, the method-of-moments discretization of the field equations leads to a mathematical model of order much smaller than in the general BI-RME approach and in other boundary integral methods. Due to the state-space formulation of this model, a wide-band representation of the generalized admittance matrix of the structure is easily found in the form of a pole expansion in the S-domain by the calculation of a reasonably small number of eigensolutions of a matrix eigenvalue problem. The method is very fast and reliable, and permits the realization of a very efficient software, well suited for inclusion in computer-aided design tools for microwave circuit design. Some examples show the efficiency of the method, including the application to multiple and slanting insets and to the modeling of an evanescent-mode filter.

The computation of the input impedance of a biconical antenna by means of a method of segmentation based on 3D finite elements

AbstractThe analysis of structures with complex geometries leads to the use of three‐dimensional numerical methods. Such devices can be unmanageable unless a segmentation technique is applied. In this work, a hybrid 3D finite‐element‐mode matching method, based on the generalized admittance matrix (GAM) is applied to the computation of the input impedance of a biconical antenna fed by a cylindrical cavity loaded with resonant slots and matched by a coupling network composed of three multi‐ridge circular irises and sections of circular waveguides. The structure is segmented into regions which are analysed separately and, by means of linking the partial matrices calculated, the generalized scattering matrix (GSM) is obtained. In order to validate the method, numerical results and measurements are compared. Copyright © 2003 John Wiley & Sons, Ltd.

A rigorous and efficient full-wave analysis of uniform bends in rectangular waveguide under arbitrary incidence

In this paper, a rigorous full-wave analysis of uniform bends in rectangular waveguides is performed. An accurate and efficient method-of-moments solution combined with the generalized-admittance-matrix (GAM) formulation is proposed in order to achieve a full-wave characterization of the analyzed structures. This full-wave modal solution turns out to be necessary for modeling complex microwave devices involving an arbitrary number of discontinuities between curved and straight waveguides, where all the modes of the involved guides are excited. The key feature of the presented method lies in the GAM representation of single and cascaded curved E- and H-plane uniform bends, which allows the construction of accurate models of the investigated discontinuities. To validate the theory, the convergence of the method is discussed and comparisons between our simulations and theoretical and experimental data are presented. The excellent behavior of our results, together with the computational efficiency of the proposed method, proves that the developed computer-aided-design tool can be successfully used in the design of complex microwave subsystems involving curved waveguides.

The cochlear outer hair cell motility must be based on a tonic change in the membrane voltage: Implications for the cochlear amplifier

It has been widely assumed that the function of the OHC is to increase the sensitivity and frequency selectivity of the cochlea via a phasic OHC voltage, which controls the soma length. This action is called the cochlear amplifier. According to this view the length of the OHC is assumed to follow the stimulus to the upper frequency limit of hearing, in a phasic manner (cycle by cycle), adding power at the signal frequency. We propose an alternative view that the OHC controls the dynamic range in a parametric, or tonic manner, via the cells axial stiffness. In this case the change in gain seen by the IHC does not require a phasic response at high frequencies. The OHC could mediate a fast acting gain control, via impedance changes, that follows the OHC membrane tonic voltage envelope. Given a level-dependent change in dynamic range (i.e., dynamic range compression), the tuning and sensitivity would necessarily change. Our analysis and conclusions are based upon a re-interpretation of existing mammalian outer hair cell (OHC) studies using a generalized admittance matrix formulation of the OHC, that relates the plasma membrane voltage and current to the soma axial force and velocity.

Frequency/time‐domain modelling of 3D waveguide structures by a BI‐RME approach

AbstractThis paper presents a full wave method for the determination of the mathematical model of a 3D waveguide structure in the form of the pole expansion in the s‐plane of its generalized admittance matrix. The method is based on a boundary integral‐resonant mode expansion approach. By the introduction of appropriate state‐variables, the method leads to the pole expansion by solving a linear generalized eigenvalue problem, like in the well‐known techniques used up to now in frequency/time domain modelling based on finite difference or finite element methods. With respect to these methods we have the advantage of a significant reduction in both memory allocation and computing time. Two examples show the accuracy of the results and the efficiency of the method. Copyright © 2002 John Wiley & Sons, Ltd.

Multiport analysis of arbitrary circular-rod insets in rectangular waveguide by the generalized admittance matrix

An original generalized-admittance-matrix (GAM) approach for the analysis of multiport junctions in rectangular waveguide having an arbitrary circular-rod inset is presented in this paper. The method is based on an efficient computation of the GAM for the blocks that compose the structure. The efficiency is due to the fact that, for each block, the full three-dimensional GAM is obtained by solving a set of uncoupled two-dimensional problems. The accuracy and efficiency of the method developed have been assessed by comparing the results obtained with some measured data and with data obtained by the finite-element method.

SFELP-an efficient methodology for microwave circuit analysis

A hybrid method based on the segmentation technique, the finite-element method, and a matrix Lanczos-Pade algorithm (SFELP) for the analysis of microwave circuits is introduced in this paper. This method computes symmetric matrix-Pade approximations of a matrix transfer function for any number of inputs and outputs via a Lanczos-type process (SyMPVL) for obtaining the generalized admittance matrix of a microwave circuit on a wide band of frequencies. The formulation that provides the three-dimensional finite-element/segmentation method is suitable for applying the symmetric Pade via Lanczos algorithm, except for the frequency dependence of the matrix of excitation vectors. In this paper, this problem is analytically overcome for the case in which excitation vectors correspond to modes of homogeneous waveguides or transmission lines. The accuracy and efficiency of the proposed method are shown by means of different examples.

Analysis of passive microwave circuits by using a hybrid 2-D and 3-D finite-element mode-matching method

A method of analysis of passive microwave circuits based on the segmentation concept is introduced. Complex three-dimensional (3-D) structures are divided into regions delimited by arbitrarily shaped waveguide ports, in which a modal expansion of the field is made. Waveguides can also be filled with inhomogeneous and/or anisotropic media. The regions are analyzed by the mode-matching method (MM) combined with either a two-dimensional (2-D) finite-element method (2-D FEM/MM) or a 3-D FEM (3-D FEM/MM). Open regions are dealt with using the perfectly matched layer. The result of the 3-D FEM analysis is a multimode multiport generalized admittance matrix, from which a generalized scattering matrix is computed. Finally, the method is applied to the analysis of a coax-to-waveguide transition and of a pair of unshielded microstrip lines coupled through an aperture in the common ground plane.