Conditions for the physical realizability of a typical component z(y)-matrix of a matching quadrupole of a general form in a concentrated elemental basis

When solving problems of broadband matching, very often there is a need for a certain form of the amplitude-frequency characteristic. In connection with this, the problem comes up of synthesizing broadband matching devices that simultaneously have correcting properties, i.e. having a given frequency dependence of the power conversion coefficient in the operating frequency band. The use of broadband reactive matching - correcting circuits in most practical cases is difficult because of the reflected power. This leads to the problem of the synthesis of broadband matching-correcting circuits with arbitrary immittances of the signal source and load in an elemental basis of a general form, containing along with reactive and active elements, which has not been adequately solved. Therefore, it becomes necessary to find the conditions for the physical realizability of a typical component of the immitance matrix of a two-port network of general form containing poles in the left half-plane of complex frequencies. In this paper the necessary and sufficient conditions are defined for the physical realizability of the immitance matrix of a typical component of a subclass of two-terminal networks of general form in a lumped elemental electric basis, when the poles of the Eigen functions in the Foster representation can be in the left half-plane of complex frequencies, excluding the imaginary and real axes. This allows to synthesis of broadband dissipative matching, matching-correcting circuits and matched attenuators in an elemental basis of a general form with arbitrary immitances of the signal source and load from a single point of view.

Necessary conditions of physical realizability of the bifocal lens collimator

The conditions of physical realizability of one of the varieties of aplanitic lens collimators, a bifocal lens collimator, which has two points of perfect focus and do not lie on the main optical axis, are considered. Based on the relationship of the parameters specified during the design of the bifocal lens collimator (aperture size, thickness, focal length, distance from the main optical axis to the focal point, tilt of the phase front in the aperture), conditions that are necessary for the synthesis of a physically feasible collimator are formulated. The solution of this problem is based on the properties of an ellipse of equal edges and the geometry of a bifocal lens collimator. The graphic dependencies of the obtained expressions are given and analyzed. Based on this analysis, the mutual dependence of the parameters specified at the beginning of the calculation of the lens surface is determined. Systems of inequalities that establish the conditions for the realizability of a bifocal lens collimator are written. A number of restrictions on the initial parameters of the bifocal lens collimator are recorded. The fulfillment of the inequalities obtained in the article is a necessary condition for the physical realizability of the bifocal lens collimator.

Influence of voltage reserve on the parameters of parallel power active compensators in mining

The static and dynamic reserve of voltage in input of voltage autonomous inverter being a component of parallel power active compensator on the physical realizability of inactive current components with the determined response, pulsations amplitude and commutation frequency of invertor switches was considered. Invariance of closed system of automated power quality regulation with relay control to the parametric and external disturbances is provided by the dynamic voltage reserve calculated from the obtained expressions. Special attention is given to the possibility of using this system in mining. Proposed approaches also can be used in the training of engineers in the electrical and mining industries.

Physically Realizable Parallel Decompositions of Experimentally Determined Mueller Matrices

Parallel decompositions have proved to be powerful tools for the analysis and interpretation of the physical information provided by Mueller matrices experimentally obtained. In this work, the procedure for the so-called arbitrary decomposition of Mueller matrices is validated through its application to a set of representative experimentally determined Mueller matrices. The covariance and passivity criteria required for the physical realizability of the Mueller matrices involved in the parallel decompositions are integrated in the procedure, which ensures the physical consistency of the results presented.

Dynamics and Entropy Analysis for a New 4-D Hyperchaotic System with Coexisting Hidden Attractors

This paper presents a new no-equilibrium 4-D hyperchaotic multistable system with coexisting hidden attractors. One prominent feature is that by varying the system parameter or initial value, the system can generate several nonlinear complex attractors: periodic, quasiperiodic, multiple topology chaotic, and hyperchaotic. The dynamics and complexity of the proposed system were investigated through Lyapunov exponents (LEs), a bifurcation diagram, a Poincaré map, and spectral entropy (SE). The simulation and calculation results show that the proposed multistable system has very rich and complex hidden dynamic characteristics. Additionally, the circuit of the chaotic system is designed to verify the physical realizability of the system. This study provides new insights into uncovering the dynamic characteristics of the coexisting hidden attractors system and provides a new choice for nonlinear control or chaotic secure communication technology.