From Cauer synthesis to Legendre polynomials — The case of the lossless transmission line

Fabien Soulier (1) , Nicolas Dollinger (2) , Patrick Lagonotte (1)

1 LET - Laboratoire d'études thermiques
2 PSA - PSA Peugeot - Citroën

In this article, we study a simple Time Delay System (tds), the short-circuited lossless transmission line. By realizing the Cauer synthesis of the input impedance, we can put in evidence a special expression of the impulse response of this system. Furthermore, we illustrate on this example a particular link between the Cauer synthesis of infinite order systems and the Legendre polynomials.

Mots clés: transmission line; partial differential equations; circuit models; networks; impulse response; polynomial transform

Domaines: Energie électrique; Sciences de l'ingénieur [physics]

Fabien Soulier, Nicolas Dollinger, Patrick Lagonotte. From Cauer synthesis to Legendre polynomials — The case of the lossless transmission line. 4th IFAC Workshop on Time Delay Systems (TDS 2003), International Federation of Automatic Control (IFAC), Sep 2003, Rocquencourt, France. pp.391-396, ⟨10.1016/S1474-6670(17)33358-X⟩. ⟨hal-02087528⟩