Method for Analysis of Transmission Lines Terminated by Nonlinear Loads
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| Title: | Method for Analysis of Transmission Lines Terminated by Nonlinear Loads |
|---|---|
| Description: | It is known that transmission lines model various guiding structures such as power lines, wires, cables, printed circuit board traces, buses for carrying digital data in electronic circuits, and microwave circuits and so on. The transmission line theory has received renewed attention because of`important applications in the area of high-speed VLSI interconnect, while it has retained its significance in the area of power transmission. The behavior of the transmission lines is described by transmission line equations. From a mathematical point of view they represent a hyperbolic system of first order partial differential equations. The transmission lines are terminated by various configurations of linear or nonlinear loads. The Kirchoff's laws regulate the behavior of these lumped circuits and define boundary conditions. Adding appropriate initial conditions, we can formulate a mixed problem for the transmission line system with unknown functions of the voltage and current of the line. The main purpose of the present book is to propose a method for solving the mixed problem for transmission line systems reducing it to a neutral equation (or system) on the boundary. Arising nonlinearities in the neutral systems are caused by nonlinear characteristics of the RGCL-loads. In view of the applications we consider mainly periodic and oscillatory problems for lossless transmission lines. We point out, however, that here we propose an extended procedure for reducing the mixed problem for lossless and lossy transmission lines. We introduce also an extension of Heaviside condition and this way we can consider the case of time-varying specific parameters-per-unit length resistance, conductance, inductance and capacitance. We find a solution of the obtained neutral equations by discovering operators whose fixed points in suitable function spaces are periodic or oscillatory solutions of the formulating problems. Using fixed point theorems for contractive mappings in uniform and metric spaces (proved by the author in the previous papers) we prove existence-uniqueness results for periodic and oscillatory problems. We obtain also successive approximations of the solution with respect to a suitable family of pseudo-metrics and give an estimate of the rate of convergence. Although the question of finding the initial approximation is not trivial. We show that one can begin with a simple harmonic initial approximation. The rate of convergence depends on the parameters of the transmission lines and characteristics of the nonlinear RCL-loads. Our conditions are applicable even in some cases to non-uniform transmission lines. Numerical examples demonstrate the applicability of the main results to design of circuits. It is easy to verify a system of inequalities between basic parameters without examining the proofs of the theorems. |
| Authors: | Angelov, Vasil Georgiev |
| Resource Type: | eBook. |
| Subjects: | Telecommunication lines--Mathematical models, Electric lines--Testing, Electric lines--Mathematical models, Telecommunication lines--Testing |
| Categories: | TECHNOLOGY & ENGINEERING / Mechanical |
| Database: | eBook Collection (EBSCOhost) |
| FullText | Links: – Type: ebook-pdf Text: Availability: 0 |
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| Header | DbId: nlebk DbLabel: eBook Collection (EBSCOhost) An: 665646 RelevancyScore: 1051 AccessLevel: 6 PubType: eBook PubTypeId: ebook PreciseRelevancyScore: 1050.81640625 |
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| Items | – Name: Title Label: Title Group: Ti Data: Method for Analysis of Transmission Lines Terminated by Nonlinear Loads – Name: Abstract Label: Description Group: Ab Data: It is known that transmission lines model various guiding structures such as power lines, wires, cables, printed circuit board traces, buses for carrying digital data in electronic circuits, and microwave circuits and so on. The transmission line theory has received renewed attention because of`important applications in the area of high-speed VLSI interconnect, while it has retained its significance in the area of power transmission. The behavior of the transmission lines is described by transmission line equations. From a mathematical point of view they represent a hyperbolic system of first order partial differential equations. The transmission lines are terminated by various configurations of linear or nonlinear loads. The Kirchoff's laws regulate the behavior of these lumped circuits and define boundary conditions. Adding appropriate initial conditions, we can formulate a mixed problem for the transmission line system with unknown functions of the voltage and current of the line. The main purpose of the present book is to propose a method for solving the mixed problem for transmission line systems reducing it to a neutral equation (or system) on the boundary. Arising nonlinearities in the neutral systems are caused by nonlinear characteristics of the RGCL-loads. In view of the applications we consider mainly periodic and oscillatory problems for lossless transmission lines. We point out, however, that here we propose an extended procedure for reducing the mixed problem for lossless and lossy transmission lines. We introduce also an extension of Heaviside condition and this way we can consider the case of time-varying specific parameters-per-unit length resistance, conductance, inductance and capacitance. We find a solution of the obtained neutral equations by discovering operators whose fixed points in suitable function spaces are periodic or oscillatory solutions of the formulating problems. Using fixed point theorems for contractive mappings in uniform and metric spaces (proved by the author in the previous papers) we prove existence-uniqueness results for periodic and oscillatory problems. We obtain also successive approximations of the solution with respect to a suitable family of pseudo-metrics and give an estimate of the rate of convergence. Although the question of finding the initial approximation is not trivial. We show that one can begin with a simple harmonic initial approximation. The rate of convergence depends on the parameters of the transmission lines and characteristics of the nonlinear RCL-loads. Our conditions are applicable even in some cases to non-uniform transmission lines. Numerical examples demonstrate the applicability of the main results to design of circuits. It is easy to verify a system of inequalities between basic parameters without examining the proofs of the theorems. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Angelov%2C+Vasil+Georgiev%22">Angelov, Vasil Georgiev</searchLink> – Name: TypePub Label: Resource Type Group: TypPub Data: eBook. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Telecommunication+lines--Mathematical+models%22">Telecommunication lines--Mathematical models</searchLink><br /><searchLink fieldCode="DE" term="%22Electric+lines--Testing%22">Electric lines--Testing</searchLink><br /><searchLink fieldCode="DE" term="%22Electric+lines--Mathematical+models%22">Electric lines--Mathematical models</searchLink><br /><searchLink fieldCode="DE" term="%22Telecommunication+lines--Testing%22">Telecommunication lines--Testing</searchLink> – Name: SubjectBISAC Label: Categories Group: Su Data: <searchLink fieldCode="ZK" term="%22TECHNOLOGY+%26+ENGINEERING+%2F+Mechanical%22">TECHNOLOGY & ENGINEERING / Mechanical</searchLink> |
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| RecordInfo | BibRecord: BibEntity: Classifications: – Code: 621.3192 Scheme: ddc Type: prePub Languages: – Code: eng Text: English Subjects: – SubjectFull: Telecommunication lines--Mathematical models Type: general – SubjectFull: Electric lines--Testing Type: general – SubjectFull: Electric lines--Mathematical models Type: general – SubjectFull: Telecommunication lines--Testing Type: general Titles: – TitleFull: Method for Analysis of Transmission Lines Terminated by Nonlinear Loads Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Angelov, Vasil Georgiev – PersonEntity: Name: NameFull: Angelov, Vasil Georgiev IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2013 – D: 04 M: 02 Type: profile Y: 2014 Identifiers: – Type: isbn-print Value: 9781626189096 – Type: isbn-electronic Value: 9781628080070 Titles: – TitleFull: Method for Analysis of Transmission Lines Terminated by Nonlinear Loads Type: main |
| ResultId | 1 |
