Abstract
A Lagrangian formulation is given for a transmission line, wherein the ‘‘equation of motion’’ for wave propagation on a lossy line (i.e., the telegrapher’s equation) is generated by an appropriate (mathematical) Lagrangian density. However, a more careful examination reveals that this Lagrangian density can also be interpreted as representing the continuum limit of a chain of lossless bandpass filter sections with variable inductance and capacitance. To provide a consistent description of the lossy line, a variational principle, based upon a modification of Hamilton’s principle, is exploited. The resulting Euler–Lagrange equation involves a (physical) Lagrangian density weighted with a time-dependent dissipation factor that explictly describes a nonisolated system losing energy to its surroundings.
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