scholarly journals Modal waves in multiconductor transmission lines by using fundamental matrix response

2020 ◽  
Vol 42 ◽  
pp. e38
Author(s):  
Julio Cesar Ruiz Claeyssen ◽  
Daniela De Rosso Tolfo ◽  
Rosemaira Dalcin Copetti
Keyword(s):  
Differential Equation ◽  
Transmission Line ◽  
Transmission Lines ◽  
Fundamental Matrix ◽  
Propagation Constant ◽  
Matrix Differential Equation ◽  
Reflection And Transmission ◽  
Admittance Matrix ◽  
Multiconductor Transmission Line ◽  
Matrix Differential

The differential equations that model voltage and current for a multiconductor transmission line are written in matrix form. Supposing a time exponential solution through of the modal analysis the modal waves are obtained and solution of a ordinary matrix differential equation, thus determining the amplitude for voltage and current. The modal waves are given in terms of the fundamental matrix solution associated to the ordinary matrix differential equation. The decomposition of the modal waves in forward and backward propagators are used for determine the reflection and transmission matrices for junction in transmission lines. Circulant symmetric transmission lines are discussed, case in that the values for the self-impedance are the same as well as the mutual-impedance values and the same considerations to the admittance matrix. In particular, for these transmission lines are characterized the propagation constants and is observed that the number of multiconductors has effects only on a specific propagation constant. Numerical example of one multiconductor transmission line is presented allowing to observe important aspects of the methodology developed.

scholarly journals ON CONDITIONING FOR A GENERAL SYSTEM OF FOUR POINT BOUNDARY VALUE PROBLEMS

1996 ◽  
Vol 27 (3) ◽  
pp. 219-225
Author(s):  
M. S. N. MURTY
Keyword(s):  
Differential Equation ◽  
Fundamental Matrix ◽  
Close Relationships ◽  
General System ◽  
Point Boundary ◽  
Matrix Differential Equation ◽  
Growth Behaviour ◽  
First Order ◽  
Matrix Differential ◽  
The Stability

In this paper we investigate the close relationships between the stability constants and the growth behaviour of the fundamental matrix to the general FPBVP'S associated with the general first order matrix differential equation.

Transmission Line

2020 ◽  
pp. 43-71
Keyword(s):  
Transmission Line ◽  
Transmission Lines ◽  
Magnetic Energy ◽  
Propagation Constant ◽  
Characteristic Impedance ◽  
Electric Energy ◽  
Electromagnetic Energy ◽  
The Other ◽  
Electrical Characteristics ◽  
Lumped Elements

A transmission line (TL) is simply a medium that is capable of guiding or propagating electromagnetic energy. The transmission line stores the electric (E) and magnetic (M) energies and distributes them in space by alternating them between the two forms. This means that at any point along a TL, energy is stored in a mixture of E and M forms and, for an alternating signal at any point on the TL, converted from one form to the other as time progresses. Transmission line is usually modelled using lumped elements (i.e., inductors for magnetic energy, capacitors for electric energy, and resistors for modelling losses). The electrical characteristics of a TL such as the propagation constant, the attenuation constant, the characteristic impedance, and the distributed circuit parameters can only be determined from the knowledge of the fields surrounding the transmission line. This chapter gives a brief overview of various transmission lines, with more detailed discussions on the microstrip and the SIW.

Output Control by Linear Time-Varying Systems using Parametric Identification Methods

2020 ◽  
Vol 21 (7) ◽  
pp. 387-393
Author(s):  
V. Q. Dat ◽  
A. A. Bobtsov
Keyword(s):  
Differential Equation ◽  
Initial Conditions ◽  
Control Object ◽  
The State ◽  
Time Varying ◽  
State Variables ◽  
Matrix Differential Equation ◽  
Matrix Differential ◽  
Uniform Observability ◽  
Riccati Matrix

In this paper the problem of control for time-varying linear systems by the output (i.e. without measuring the vector of state variables or derivatives of the output signal) was considered. For the control design, the well-known online procedure for solving the Riccati matrix differential equation is chosen. This procedure involves the synthesis of linear static feedbacks on state variables in the case of known parameters of the plant. If state variables are not measured, then for the observer design using the matrix Riccati differential equation, using the dual scheme, which provides for the transposition of the state matrix and the replacement of the input matrix by the output matrix. It is well known that an observer of state variables built on the basis of a solution of the Riccati matrix differential equation ensures the exponential stability of a closed loop system in the case of uniform observability. Despite the fact that this type of observer can be classified as universal, its have a number of significant drawbacks. The main problem of such observers is the need for accurate knowledge of the parameters and the requirement for uniform observability, which in practice cannot always be realized. Thus, the problem of the new methods design for constructing observers of state variables of linear non-stationary systems is still relevant. Some time ago, a number of methods for the adaptive observers design of state variables for nonlinear systems were proposed. The main idea of the synthesis of observers was based on the transformation of the original dynamic system to a linear regression model containing unknown parameters, which in turn were functions of the initial conditions of the state variables of the control object. This approach in the English language literature is called PEBO. This paper, based on the PEBO method, proposes a new approach for the observers design of state for non-stationary systems. This approach provides the possibility of obtaining monotonic convergence estimates with transient time tuning.

scholarly journals A Simple Distributed RGC Model of MOSFET for Pre-Pinch Off Region

1988 ◽  
Vol 13 (1) ◽  
pp. 55-65 ◽  
Author(s):  
Umesh Kumar ◽  
Arun Mirchandani
Keyword(s):  
Differential Equation ◽  
Transmission Line ◽  
Transmission Lines ◽  
Computer Aided Design ◽  
Small Signal ◽  
Line Model ◽  
Single Section ◽  
Computer Aided ◽  
Aided Design ◽  
And Behavior

The differential equation describing the small signal behavior of a MOSFET channel is derived. Based on the analogy of the channel to distributed transmission lines, which has been very well established in literature, an entirely new RGC line model of MOSFET is presented. The element values of the line are determined by equivalence to a general distributed transmission line and subsequently the model is lumped into a single section in two possible Π and T representations. The postulated model considerably simplifies the study of the properties and behavior of MOSFET structures and can be suitably utilized in analysis and Computer Aided Design.

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