Synthesis Method for Filtering Antennas Based on Multiple Radiation Port Topology

In this paper a new approach to the synthesis of coupling matrices for microwave filters is presented. The new approach represents an advance on existing direct and optimization methods for coupling matrix synthesis in that it will exhaustively discover all possible coupling matrix solutions for a network if more than one exists. This enables a selection to be made of the set of coupling values, resonator frequency offsets, parasitic coupling tolerance etc that will be suited to the technology it is intended to realize the microwave filter with. To demonstrate the use of the method, the case of the recently - introduced 'extended box ' coupling matrix configuration is taken. The extended box is a new class of filter configuration adapted to the synthesis of asymmetric filtering characteristics of any degree. For this configuration the number of solutions to the coupling matrix synthesis problem appears to be high and offers therefore some flexibility that can be used during the design phase. We illustrate this by carrying out the synthesis process of two asymmetric filters of 8 th and 10 th degree. In the first example a ranking criterion is defined in anticipation of a dual mode realization and allows the selection of a best coupling matrix out of 16 possible ones. For the 10 th degree filter a new technique of approximate synthesis is presented yielding some simplifications of the practical realization of the filter as well as of its computer aided tuning phase.

Coupling matrices are often used to design modern microwave filters. They are useful, as they can directly relate the coupling strengths of a set of coupled resonators to the filter response. However, given a physical filter geometry it can be difficult to find the exact terms of the coupling matrix from traditional measurements.In this paper, a technique is introduced to extract the coupling matrix from a fullwave field simulation of a filter structure. This extraction technique incorporates direct method for determining the loss in the filter. Both the loss in the resonators and the loss in the coupling terms are extracted directly from the full-wave simulation. The extraction technique presented here is based on the ability to probe the individual resonators of a filter in a full-wave simulation. This probing is accomplished by careful placement of lumped ports in each of the filter's resonators. The result of a simulation with such probes will be an admittance matrix relating the coupling of each resonator to every other resonator, and to both the input and output of the filter. The coupling matrix of the filter can then be directly extracted from this admittance matrix. This technique is similar to one demonstrated by Xinshe Yin (Xinshe Yin, Symposium Digest (MTT) 2012). However, the technique presented by Yin does not account for either loss in the resonators or the couplings between the resonators. The technique presented here includes both loss mechanisms. Results will be shown comparing the scattering parameters extracted from the coupling matrices of both techniques (with and without loss) to the scattering parameters obtained directly through full-wave simulations and measurements. The structure that will be used for this demonstration is a tunable near-field filter with six resonators used to isolate two antennas from each other. In this structure, the antennas (which are stacked patch antennas) are also modeled as resonators in the filter structure. Since they are designed to radiate, modeling their “loss” is essential to create a good model of the system. The coupling matrix extracted using the method presented here matches the full-wave simulation (which has been shown to match the measured response) quite well. This coupling matrix will make it possible to modify the design of these near-field filters to give better filter responses.

In this paper a new approach to the synthesis of coupling matrices for microwave filters is presented. The new approach represents an advance on existing direct and optimization methods for coupling matrix synthesis in that it will exhaustively discover all possible coupling matrix solutions for a network if more than one exists. This enables a selection to be made of the set of coupling values, resonator frequency offsets, parasitic coupling tolerance etc that will be best suited to the technology it is intended to realize the microwave filter with. To demonstrate the use of the method, the case of the recently – introduced ‘extended box’ (EB) coupling matrix configuration is taken. The EB represents a new class of filter configuration featuring a number of important advantages, one of which is the existence of multiple coupling matrix solutions for each prototype filtering function, eg 16 for 8th degree cases. This case is taken as an example to demonstrate the use of the synthesis method – yielding one solution suitable for dual-mode realization and one where some couplings are small enough to neglec

A braided subfactor determines a coupling matrix Z which commutes with the S- and T-matrices arising from the braiding. Such a coupling matrix is not necessarily of "type I", i.e. in general it does not have a block-diagonal structure which can be reinterpreted as the diagonal coupling matrix with respect to a suitable extension. We show that there are always two intermediate subfactors which correspond to left and right maximal extensions and which determine "parent" coupling matrices Z^\pm of type I. Moreover it is shown that if the intermediate subfactors coincide, so that Z^+=Z^-, then Z is related to Z^+ by an automorphism of the extended fusion rules. The intertwining relations of chiral branching coefficients between original and extended S- and T-matrices are also clarified. None of our results depends on non-degeneracy of the braiding, i.e. the S- and T-matrices need not be modular. Examples from SO(n) current algebra models illustrate that the parents can be different, Z^+\neq Z^-, and that Z need not be related to a type I invariant by such an automorphism.

In this paper, novel approaches to synthesize admittance function polynomials and canonical <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> +2 coupling matrices for narrowband lossy filters are presented. The methods are simpler and more general than the ones found in the literature. The polynomial synthesis approach is fully analytical and also very useful for lossless polynomial synthesis with simpler derivations. The coupling matrix synthesis method is based on a lossy transversal network model, which can also accommodate direct source to load coupling. Unlike the lossless transversal coupling matrix, the lossy coupling matrix model requires the assumption of complex <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</i> -inverters and additional resistive elements in the network. The complex <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</i> -inverter circuit model is defined and explained in detail in this paper. The lossy transversal <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> +2 matrix can be systematically rotated to obtain a number of practical realizations. Parallel-coupled pairs and folded lossy configurations are shown as examples. Moreover, the synthesis of novel networks with different return-loss levels at source and load is presented. A performance comparison with a predistorted filter is also included in this paper.

A hybrid optimisation algorithm that synthesises coupling matrices for cross-coupled microwave filters is presented. A binary encoded genetic algorithm is combined at regular intervals with a sequential quadratic programming local search method to form a hybrid, exploiting the speed of the local search, while maintaining diversity with the genetic algorithm. The genetic algorithm uses the stochastic uniform selection technique and a multiple point crossover operator. A compact, efficient cost function requiring only the determinant and a cofactor of the coupling matrix is used as the basis of the optimisation algorithm. Optimisation algorithms simplify the process of synthesising coupling matrices, compared with analytical synthesis. However, algorithms that use only local search methods cannot be guaranteed to find a global minimum. This hybrid method aims to extend the range of coupling matrices that can be synthesised by optimisation, while maintaining the speed of search. A coupling matrix for a tenth order coupling matrix for a dual band symmetric filter and a seventh order asymmetric filter are synthesised to verify the method.

The Plate Boundary Observatory, the geodetic component of the EarthScope program, includes 74 borehole strainmeters installed in the western United States and on Vancouver Island, Canada. In this study, we calibrate 45 of the instruments by comparing the observed M2 and O1 Earth tides with those predicted using Earth tide models. For each strainmeter, we invert for a coupling matrix that relates the gauge measurements to the regional strain field assuming only that the measured strains are linear combinations of the regional areal and shear strains. We compare these matrices to those found when constraints are imposed which require the coupling coefficients to lie within expected ranges for this strainmeter design. Similar unconstrained and constrained coupling matrices suggest the instrument is functioning as expected as no other coupling matrix can be found that better reduces the misfit between observed and predicted tides when the inversion is unconstrained. Differences imply a coupling matrix with coefficients outside typical ranges gives a better fit between the observed and predicted tides. We find that 22 of the strainmeters examined have coupling matrices for which there is little difference between the constrained and unconstrained inversions. If we allow a greater divergence in the shear coupling coefficients and consider the possibility that one gauge may not function as expected, the discrepancies between the unconstrained and constrained coupling matrices are resolved for a subset of the remaining strainmeters. Our results also indicate that most of the strainmeters are less sensitive to areal strain than expected from theory.

A hybrid optimization method that synthesizes coupling matrices for cross-coupled microwave filters is presented. This method consists of a general solvopt algorithm and fmincon algorithm, respectively. To avoid divergence from the coupling matrix, two cost functions are built, where the first one is constructed from the eigenvalues of the coupling matrix and its principal sub- matrices, while another one is dependent on the determinant of the coupling matrix and one of its cofactors. The values of non-zero elements of the coupling matrix serve as the independent variables to minimize the cost functions by using solvopt and fmincon. Although the stochastic initial values are not sufficiently close to the global optimum, the hybrid optimization procedure is still robust to find multiple coupling matrices to overcome the initial problem. It is significant that the suitable coupling matrix can be chosen from the multiple solutions to meet the given requirements in practice. For demonstrating the proposed hybrid optimization algorithm, some extraordinary prototype topologies are provided which validate the efficiency of the proposed synthesis procedure.

Exploring the phase diagrams of multidimensional Kuramoto models

Chebyshev-type diplexers designed using coupling matrix method

In this article, we investigate the optimal control of network-coupled subsystems with coupled dynamics and costs. The dynamics coupling may be represented by the adjacency matrix, the Laplacian matrix, or any other symmetric matrix corresponding to an underlying weighted undirected graph. Cost couplings are represented by two coupling matrices which have the same eigenvectors as the coupling matrix in the dynamics. We use the spectral decomposition of these three coupling matrices to decompose the overall system into <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$({L+1})$</tex-math></inline-formula> systems with decoupled dynamics and cost, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L$</tex-math></inline-formula> is the number of linearly independent eigendirections associated with nonzero eigenvalue triples of the three coupling matrices. Furthermore, the optimal control input at each subsystem can be computed by solving <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$({L_\text{dist}+1})$</tex-math></inline-formula> decoupled Riccati equations, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_\text{dist}\,(L_\text{dist}\leq L)$</tex-math></inline-formula> is the number of distinct nonzero eigenvalue triples of the three coupling matrices. A salient feature of the result is that, given the spectral decompositions of the couplings, the solution complexity does not directly depend on the number of subsystems. Therefore, the proposed solution framework provides a scalable method for synthesizing and implementing optimal control laws for large-scale network-coupled subsystems.

The development of integrated energy system in rural areas has great prospects. In response to problems such as redundancy and poor flexibility of traditional integrated energy system, integrated demand response and biogas energy will be introduced to maintain the balance of supply and demand in multiple forms of energy together with energy hub. Establish an energy hub coupling matrix model to study the differences in the form of the coupling matrices for typical villages with different characteristics under different input data. A computerized model of energy hub coupling incidence matrix is proposed. The coupling incidence matrix is quickly formed under various boundary conditions, and then the corresponding coupling matrix is generated, thereby improving the efficiency of calculation and analysis of IES planning and operation. Establish an optimal configuration model of the rural integrated energy system that takes into account the coupling matrix, integrated demand response, biogas and other resources. With the goal of the lowest total cost, make decisions on the configuration plans of the corresponding resources to obtain the optimal configuration scheme. In the case study, multiple sets of initial conditions were set, and the most corresponding optimal configuration schemes were obtained respectively, which verified the effectiveness of the method.

A complex coupling matrix has been extensively used in lossy filters and negative group delay devices. For the realization, conventional technique decomposes the complex coupling matrix into lossy resonators and complex inverters. Since the complex inverter does not follow the passivity in some cases, the resultant realization may be globally passive but locally active. This paper proposes a new decomposition technique to ensure the passivity everywhere. It decomposes the complex coupling matrix into a resistive connection matrix and a conventional real coupling matrix, which are both passively realizable. This technique provides a passive realization of the complex coupling matrix. Furthermore, a loss equalization technique is also proposed, to further achieve a uniform quality factor (Q) distribution among all the lossy resonators. Several illustrative examples and an experimental validation are finally provided.

A simulation method is proposed which approximates the atmospheric beam path as an extremely large aperture hollow waveguide containing a numerically sufficient subset of linearly polarized lossless propagation modes. The proposed method is shown to agree numerically with the standard angular spectrum of plane waves method in a single transverse dimension simulation and is readily expandable into two transverse dimensions but currently limited by available hardware. The method is expanded to involve coupling matrices describing the transition through each phase screen and the intermediate free-space portions. The coupling matrices are combined into a single multimode coupling matrix describing the propagation for one instance of atmosphere. The proposed matrix method has potential to evaluate multiple input beams simultaneously or condense high turbulence simulations requiring many phase screens. The input beam can be constructed by multiplying the decomposition of the desired output profile with the pseudo-inverse of the coupling matrix; however, the matrix cannot be realized in experiment. Therefore, the opportunity for beam shaping to compensate optical turbulence is evaluated by principal component analysis of the compound coupling matrix. It is shown that an average of the lowest order eigenmode across multiple simulations produces a super-Gaussian-like beam with improved power delivery and stability. The implication for optical countermeasure beam control is the potential to create any desired beam shape at the target plane.

The equations of motion for pressure and displacement fields in a waveguide have been used to derive an energy-conserving, one-way coupled mode propagation model. This model has three important properties: First, since it is based on the equations of motion, rather than the wave equation, instead of two coupling matrices, it only contains one coupling matrix. Second, the resulting coupling matrix is anti-symmetric, which implies that the energy among modes is conserved. Third, the coupling matrix can be computed using the local modes and their depth derivatives. The model has been applied to two range-dependent cases: Propagation in a wedge, where range dependence is due to variations in water depth and propagation through internal waves, where range dependence is due to variations in water sound speed. In both cases the solutions are compared with those obtained from the parabolic equation (PE) method.