@MastersThesis{Greco:2013:AnMoLi,
author = "Greco, Ana Fl{\'a}via Guedes",
title = "An{\'a}lise e modelagem de linhas de transmiss{\~a}o n{\~a}o
lineares com elementos concentrados nas configura{\c{c}}{\~o}es
LC e CL",
school = "Instituto Nacional de Pesquisas Espaciais (INPE)",
year = "2013",
address = "S{\~a}o Jos{\'e} dos Campos",
month = "2013-11-27",
keywords = "linhas de transmiss{\~a}o n{\~a}o lineares, solu{\c{c}}{\~a}o
num{\'e}rica de equa{\c{c}}{\~o}es diferenciais n{\~a}o
lineares, modelagem e simula{\c{c}}{\~a}o, gera{\c{c}}{\~a}o
de RF, gera{\c{c}}{\~a}o de s{\'o}litons claros e escuros,
nonlinear transmission lines, numerical solution of nonlinear
differential equations, modeling and simulation, RF generation by
nonlinear transmission lines, generation of bright and dark
solitons.",
abstract = "Em uma formula{\c{c}}{\~a}o geral descrita por um sistema de
equa{\c{c}}{\~o}es diferenciais ordin{\'a}rias no
dom{\'{\i}}nio do tempo, o presente trabalho de
disserta{\c{c}}{\~a}o investiga os fen{\^o}menos de
propaga{\c{c}}{\~a}o em linhas de transmiss{\~a}o lineares e
n{\~a}o lineares constitu{\'{\i}}das de c{\'e}lulas LC e CL.
Foram desenvolvidas e em seguida comparadas duas
formula{\c{c}}{\~o}es matem{\'a}ticas, importantes do ponto de
vista conceitual, mas pouco discutidas na literatura. Para a
primeira formula{\c{c}}{\~a}o tem-se como vari{\'a}veis de
estado a corrente de malha que circula em cada se{\c{c}}{\~a}o,
e a correspondente carga armazenada em cada capacitor. Para a
outra formula{\c{c}}{\~a}o consideram-se a corrente no indutor
de cada se{\c{c}}{\~a}o e a tens{\~a}o nos capacitores. De
import{\^a}ncia sob o aspecto num{\'e}rico e uma vez que existem
poucos estudos sobre tais formula{\c{c}}{\~o}es, foram adotadas
estas vari{\'a}veis de maneira que as equa{\c{c}}{\~o}es
diferenciais sejam todas de primeira ordem. A
formula{\c{c}}{\~a}o desenvolvida foi escrita para que a cada
elemento discreto em uma se{\c{c}}{\~a}o particular i possam ser
atribu{\'{\i}}dos valores arbitr{\'a}rios L\$_{i}\$ e
C\$_{i}\$. Al{\'e}m disso, a formula{\c{c}}{\~a}o permite a
an{\'a}lise no regime transit{\'o}rio das linhas sendo excitadas
por um pulso de forma arbitr{\'a}ria. No regime linear, foram
examinadas as caracter{\'{\i}}sticas de propaga{\c{c}}{\~a}o
em linhas peri{\'o}dicas, nas quais c{\'e}lulas unit{\'a}rias
id{\^e}nticas repetem-se periodicamente, e tamb{\'e}m linhas
duplamente peri{\'o}dicas, onde cada se{\c{c}}{\~a}o
{\'{\i}}mpar comp{\~o}e-se de um par de elementos L\$_{1}\$ e
C\$_{1}\$, enquanto as se{\c{c}}{\~o}es pares incluem um
indutor L\$_{2}\$ e um capacitor C\$_{2}\$. Na
atribui{\c{c}}{\~a}o dos valores dos elementos do circuito dois
casos foram considerados. Para linhas peri{\'o}dicas destaca-se a
interpreta{\c{c}}{\~a}o de velocidades de fase positiva e
negativa associadas respectivamente {\`a}s topologias LC e CL,
considerando um sinal senoidal. J{\'a} para linhas duplamente
peri{\'o}dicas destaca-se o car{\'a}ter de filtragem espacial,
uma vez que as linhas assim sintetizadas com elementos
concentrados exibiram forte dispers{\~a}o espacial em que cada
n{\'o} da linha apresenta um espectro distinto de
frequ{\^e}ncia. No regime n{\~a}o linear, foram investigados
alguns fen{\^o}menos associados {\`a} linha LC tais como
gera{\c{c}}{\~a}o de RF, gera{\c{c}}{\~a}o de s{\'o}litons, e
redu{\c{c}}{\~a}o dos tempos de subida e de descida de pulsos
que se propagam ao longo da linha. E para linhas CL foram
investigados a forma{\c{c}}{\~a}o de s{\'o}litons claros e
escuros (que constituem caracter{\'{\i}}sticas {\'u}nicas das
linhas CL) e tamb{\'e}m a gera{\c{c}}{\~a}o de
sub-harm{\^o}nicas e compress{\~a}o de pulsos considerando
pulsos senoidais e de RF. ABSTRACT: In a general formulation
described by a system of ordinary differential equations in the
time domain, this dissertation investigates the propagation
phenomena in linear and nonlinear transmission lines consisting of
LC and LC cells. Important from conceptual point of view but
little discussed in the literature, two mathematical formulations
were developed and then compared. For the first formulation the
state variables were assigned as the mesh current flowing in each
section and the corresponding charge stored in each capacitor. For
the second formulation the inductor current of each section and
the voltage across the capacitors were the state variables
considered. Of importance from the numerical standpoint and since
there are few studies on such formulations, these variables were
adopted so that the differential equations are all first order.
The developed formulation was written so that to each discrete
element in a particular section i values arbitrary L\$_{i}\$ and
C\$_{i}\$ could be assigned. Furthermore, the formulation allows
the analysis of transmission lines being excited by a pulse of
arbitrary shape. In the linear regime, we examined the propagation
characteristics of periodic lines in which the unit cells repeat
themselves periodically, and also doubly periodic lines, where
each odd-numbered section consists of one pair of elements
L\$_{1}\$ and C\$_{1}\$, while the even sections include an
inductor L\$_{2}\$ and a capacitor C\$_{2}\$. In assigning the
values of the circuit elements two cases were considered. For
periodic lines the interpretation of positive and negative phase
velocities, respectively associated to LC and LC topologies, were
highlighted upon considering sinusoidal signals. As for doubly
periodic lines spatial filtering properties were emphasized, since
such lines with lumped elements exhibited strong spatial
dispersion in which each node of the line has a distinct frequency
spectrum. In the nonlinear regime, we investigated some phenomena
associated with the LC line such as RF generation, generation of
solitons, and reduction of the rise and fall times of trapezoidal
pulses propagating along the line. Concerning CL lines we examined
the formation of bright and dark solitons (the latter is a
distinguished feature of CL lines) and also sub-harmonic
generation and pulse compression by considering sinusoidal,
Gaussian, and RF pulses.",
committee = "Ricci, Mario Cesar (presidente) and Castro, Joaquim Jos{\'e}
Barroso de (orientador) and Rossi, Jos{\'e} Osvaldo (orientador)
and Coutinho, Olympio Lucchini",
englishtitle = "Modeling and analysis of nonlinear transmission lines with lumped
elements in LC and CL configurations",
language = "pt",
pages = "144",
ibi = "8JMKD3MGP7W/3FDFFC5",
url = "http://urlib.net/ibi/8JMKD3MGP7W/3FDFFC5",
targetfile = "publicacao.pdf",
urlaccessdate = "16 jun. 2024"
}