Approximation of a long line by a ladder system
Abstract
A system of ordinary equations, with a corresponding ladder system ascribed to it, was obtained from a partial equation describing the voltage distribution along a long line during the discretization of the spatial variable. A method of solution of the ladder system is given for an arbitrary method of discretization of the spatial variable. A criterion for the selection of the discretization points is proposed, ensuring minimization of the fixed error at the final control instant. An example of an exponentially convergent line is presented. Various ladder systems, approximating to the Thomson cable, are also compared.
- Publication:
-
NASA STI/Recon Technical Report N
- Pub Date:
- September 1978
- Bibcode:
- 1978STIN...7918175M
- Keywords:
-
- Approximation;
- Differential Equations;
- Electric Potential;
- Transmission Lines;
- Analysis (Mathematics);
- Convergence;
- Electrical Engineering;
- Electronics and Electrical Engineering