Representations of 3-D Scattering Matrices

1991 ◽  
Author(s):  
Jerold R. Bottiger
Keyword(s):  
Scattering Matrices

Wave-Mode Coordinates and Scattering Matrices for Wave Propagation.

1986 ◽  
Author(s):  
James H. Williams ◽  
Nagem Jr. ◽  
Yeung Raymond J. ◽  
Hubert K.
Keyword(s):  
Wave Propagation ◽  
Wave Mode ◽  
Scattering Matrices

scholarly journals Isoscattering strings of concatenating graphs and networks

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Michał Ławniczak ◽  
Adam Sawicki ◽  
Małgorzata Białous ◽  
Leszek Sirko
Keyword(s):  
Trace Function ◽  
Quantum Graphs ◽  
Mathematical Approach ◽  
Large Graphs ◽  
Graphs And Networks ◽  
Scattering Matrices ◽  
Theoretical Predictions ◽  
Infinite Strings ◽  
Microwave Networks ◽  
Insight Into

AbstractWe identify and investigate isoscattering strings of concatenating quantum graphs possessing n units and 2n infinite external leads. We give an insight into the principles of designing large graphs and networks for which the isoscattering properties are preserved for $$n \rightarrow \infty $$ n → ∞ . The theoretical predictions are confirmed experimentally using $$n=2$$ n = 2 units, four-leads microwave networks. In an experimental and mathematical approach our work goes beyond prior results by demonstrating that using a trace function one can address the unsettled until now problem of whether scattering properties of open complex graphs and networks with many external leads are uniquely connected to their shapes. The application of the trace function reduces the number of required entries to the $$2n \times 2n $$ 2 n × 2 n scattering matrices $${\hat{S}}$$ S ^ of the systems to 2n diagonal elements, while the old measures of isoscattering require all $$(2n)^2$$ ( 2 n ) 2 entries. The studied problem generalizes a famous question of Mark Kac “Can one hear the shape of a drum?”, originally posed in the case of isospectral dissipationless systems, to the case of infinite strings of open graphs and networks.

Similarity between two scattering matrices

2001 ◽  
Vol 37 (3) ◽  
pp. 193 ◽  
Author(s):  
Jian Yang ◽  
Ying-Ning Peng ◽  
Shi-Ming Lin
Keyword(s):  
Scattering Matrices

scholarly journals Method for computing waveguide scattering matrices in the vicinity of thresholds

2014 ◽  
Vol 26 (1) ◽  
pp. 91-116 ◽  
Author(s):  
B. A. Plamenevskiǐ ◽  
A. S. Poretskiǐ ◽  
O. V. Sarafanov
Keyword(s):  
Scattering Matrices

MODELING THE FREQUENCY CHARACTERISTICS OF THE QUADRATURE THREE-LOOP L-BAND WAVELENGTH BRIDGE

2021 ◽  
Author(s):  
Л.В. АЛЕКСЕЙЧИК ◽  
Н.В. АНДРИЕВСКИЙ
Keyword(s):  
Transmission Lines ◽  
Electric Circuit ◽  
Wave Resistance ◽  
Frequency Characteristics ◽  
Excitation Mode ◽  
S Matrix ◽  
Scattering Matrices ◽  
Standard Wave ◽  
Strip Lines ◽  
Algebraic Summation

Представлены результаты численного моделирования частотныххарактеристик квадратурного трехшлейфового моста (КШМ) L-диапазона, выполненного на основе симметричной полосковой линии с воздушным заполнением. Цель работы - установление допустимого уровня вносимых тепловых потерь полосковых линий (или других типов линий передачи), не оказывающих заметного влияния на рабочие характеристики КШМ, удовлетворяющие требуемым параметрам. Метод расчета основан на принципе декомпозиции электрической цепи КШМ на шесть симметричных 6-полюсников, три из которых соответствуют нечетной моде возбуждения КШМ, а три других - четной моде возбуждения КШМ. Алгебраическое суммирование матриц рассеяния указанных мод позволило получить частотные характеристики результирующей S-матрицы рассеяния КШМ. Нормирование S-матрицы к стандартному волновому сопротивлению 50 Ом выполнено с помощью вычисления собственных значений матриц рассеяния эквивалентных 4-полюсников КШМ. Моделирование проведено в среде LabVIEW. The paper presents the results of numerical simulation of the frequency characteristics of the L-range quadrature three-loop bridge (QLB), based on the symmetric striped line with air filling. The purpose of the study is to establish the permissible level of introduced thermal losses of strip lines (or other types of transmission lines) that do not significantly affect the performance characteristics of the QLB, satisfying the required parameters. The calculation method is based on the principle of decomposition of the QLB electric circuit into six symmetric 6-poles, three of which correspond to the odd excitation mode of the QLB, and the other three correspond to the even excitation mode of the QLB. Algebraic summation of the scattering matrices of these modes made it possible to obtain frequency characteristics of the resulting S-scattering matrix of the qLb. The normalization of the S-matrix to the standard wave resistance of 50 Ohms was carried out using the calculation of the eigenvalues of the scattering matrices of equivalent 4-poles of the QLB. The simulation was carried out in the LabVIEW environment.

scholarly journals Memory Efficient Method for Electromagnetic Multi-Region Models Using Scattering Matrices

2018 ◽  
Vol 23 (4) ◽  
pp. 71 ◽  
Author(s):  
C. Custers ◽  
J. Jansen ◽  
E. Lomonova
Keyword(s):  
Electromagnetic Field ◽  
Boundary Conditions ◽  
Efficient Method ◽  
Maximum Size ◽  
Scattering Matrix ◽  
Matrix Approach ◽  
Matrix Formulation ◽  
Scattering Matrices ◽  
Memory Efficient

This paper describes the scattering matrix approach to obtain the solution to electromagnetic field quantities in harmonic multi-layer models. Using this approach, the boundary conditions are solved in such way that the maximum size of any matrix used during the computations is independent of the number of regions defined in the problem. As a result, the method is more memory efficient than classical methods used to solve the boundary conditions. Because electromagnetic sources can be located inside the regions of a configuration, the scattering matrix formulation is developed to incorporate these sources into the solving process. The method is applied to a 3D electromagnetic configuration for verification.

scholarly journals Assessing the stochastic error of acoustic scattering matrices using linear methods

2018 ◽  
Vol 10 (4) ◽  
pp. 380-392 ◽  
Author(s):  
Luck Peerlings ◽  
Friedrich Bake ◽  
Susann Boij ◽  
Hans Bodén
Keyword(s):  
Uncertainty Analysis ◽  
Linear Method ◽  
Plane Waves ◽  
Acoustic Scattering ◽  
Higher Order ◽  
Condition Numbers ◽  
Matrix Perturbation ◽  
Stochastic Error ◽  
Scattering Matrices

To be able to compare the measured scattering matrices with model predictions, the quality of the measurements has to be known. Uncertainty analyses are invaluable to assess and improve the quality of measurement results in terms of accuracy and precision. Linear analyses are widespread, computationally fast and give information of the contribution of each error source to the overall measurement uncertainty; however, they cannot be applied in every situation. The purpose of this study is to determine if linear methods can be used to assess the quality of acoustic scattering matrices. The uncertainty in measured scattering matrices is assessed using a linear uncertainty analysis and the results are compared against Monte-Carlo simulations. It is shown that for plane waves, a linear uncertainty analysis, applied to the wave decomposition method, gives correct results when three conditions are satisfied. For higher order mode measurements, the number of conditions that have to be satisfied increases rapidly and the linear analysis becomes an unsuitable choice to determine the uncertainty on the scattering matrix coefficients. As the linear uncertainty analysis is most suitable for the plane wave range, an alternative linear method to assess the quality of the measurements is investigated. This method, based on matrix perturbation theory, gives qualitative information in the form of partial condition numbers and the implementation is straightforward. Using the alternative method, the measurements of higher order modes are analyzed and the observed difference in the measured reflection coefficients for different excitation conditions is explained by the disparity in modal amplitudes.

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