1,720,969 research outputs found
DUAL FORMULATIONS FOR ERROR ESTIMATION IN NONUNIFORM TRANSMISSION LINES
No full textA time domain discrete model for non uniform transmission lines, based on a complementary formulation of the transmission line equations, is considered. By recasting the line equations in terms of flux and charge, one has to discretise alternatively only one of the two equations, the other being exactly verified. This approach has been widely used in electromagnetics to evaluate discretization error. With reference to simple examples, we show how the error estimation can be used for a selective meshing of the line, leading to much better approximation with the same computational effort
A new technique for simulating nonlinear loaded lossy lines
No full textA numerical model for simulating linear lossy transmission lines ended with nonlinear resistors is described. It based on two complementary formulations of the telegrapher's equations and uses the Galerkin method. The proposed approach appears computationally less cumbersome than that based on the time-domain convolution method, especially when the analysis of multiconductor transmission lines is considered. Particular attention is paid to the uniqueness of the solution and to the convergence of the numerical approximation, Complementary formulations provide a powerfull tool to study the convergence
Bifurcations and chaos in transmission lines
No full textIn this article we present some examples of bifurcations and chaotic phenomena theoretically observed in a simple electromagnetic system. The system consists of a linear lossless, or Heaviside distorsionless, transmission line connected to a Linear resistor at one end (active branch) and to a nonlinear resistor at the other end (passive branch). The time dynamics of the backward voltage wave evaluated across the nonlinear resistor are described by a one-dimensional non linear mapping. A uniqueness theorem and the discussion of a problem with more than one solution complete the paper
Coupling of A Nonlinear Diffusive Electromagnetic System To A Linear Electric-circuit
No full textA composite electromagnetic system including a non-hysteretic ferromagnetic conducting body and a linear resonant circuit fed by a sinusoidal voltage source is studied. The diffusion of the magnetic field in the iron core "inductor" is described by means of a finite dimensional nonlinear dynamic system obtained by applying the Galerkin method. These equations are coupled with the circuit ones. This physical system might exhibit different nonlinear phenomena: multiple periodic oscillations and even apparently completely disordered aperiodic "chaotic" motions. In this paper multiple harmonic and subharmonic oscillations are investigated by computer-aided analysis using a static method
DUAL FORMULATIONS FOR ERROR ESTIMATION IN NONUNIFORM TRANSMISSION LINES
No full textA time domain discrete model for non uniform transmission lines, based on a complementary formulation of the transmission line equations, is considered. By recasting the line equations in terms of flux and charge, one has to discretise alternatively only one of the two equations, the other being exactly verified. This approach has been widely used in electromagnetics to evaluate discretization error. With reference to simple examples, we show how the error estimation can be used for a selective meshing of the line, leading to much better approximation with the same computational effort
Chaotic Dynamics In An Infinite-dimensional Electromagnetic System
No full textThe paper deals with bifurcation and chaos phenomena theoretically observed in a simple electromagnetic system consisting of a linear, distortionless transmission line connected to an active linear resistor (R < 0) at one end and to a pn-junction diode at the other end. The active resistor gives rise to the stretching phenomena and the diode the back folding one; the combination of these two mechanisms may lead to chaotic dynamics. The Poincare map of the ''backward voltage wave'' at pn-junction diode is obtained by solving a one dimensional nonlinear implicit difference equation. For R < -R(c) (R(c) is the characteristic ''impedance'' of the line) the mapping is unimodal and the dynamics follow the Feigenbaum route to chaos [1]. The nonlinear implicit difference equation is solved numerically. Spatiotemporal chaos is observed in the voltage and current waves. By replacing the pn-junction diode with a twin-pn junction diode circuit, the hopping mechanism is also met
EFFICIENT TIME-DOMAIN SIMULATION OF LOSSY MULTICONDUCTOR LINES WITH NON-LINEAR LOADS
No full textThe convolution method is applied to analyse lossy multiconductor lines with non-linear loads. The line is described as a time-domain m-port, through the input and transfer impulse responses. A new method is used to evaluate analytically the principal parts of these responses, i.e., the parts containing all the irregular terms, such as Dirac pulses. Once the irregular parts are known, the regular remainders are easily calculated by numerical inversion. The convolution integrals have been evaluated using two different methods, one based on crude trapezoidal rule and the other based on a fast recursive algorithm. The latter is obtained by an exponential fitting of the regular parts of the impulse responses. A comparison between the computation times of these two methods is presente
A didactic electronic set-up for introducing to complex networks of chaotic oscillators
No full textThe paper describes a portable didactic experiment, realizing a complex network of Chua's circuits, along with its use for introducing collective dynamics in networks of nonlinear oscillators to students. The equipment enables the full configurability of the node's parameters and the network structure (topology and link impedances). An 8 nodes portable version is realized as a demonstrator, however the corresponding laboratory experiment is designed to be easily scalable to a high number of nodes. The network's control and the data acquisition are automated thanks to a USB interface board and a LabVIEW control interface. The experiment allows the student to perform some direct real time analysis of a set of networked (coupled) Chua's circuits, with the goal to give immediate impact to the discovery of collective behaviors. In particular, the proposed experiences range from the characterization of the complex dynamics of the isolated nodes to the complete synchronization, as well as the emergence of clustering and waves. It is adopted within some course on Advanced Circuit Theory at the Master Degree level
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