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When investigating transient and high-frequency steady-state phenomena, conductors such as a transmission line, a machine winding, and a measuring wire demonstrate a distributed-parameter nature. Well-known, lumped-parameter circuits are an approximation of a distributed-parameter circuit for describing a low-frequency, steady-state phenomenon of the conductor. That is, a current in a conductor, even a short conductor, needs time to travel from its sending end to its remote end because of its finite propagation velocity (300 m/µs in a free space). From this fact, it should be clear that a differential equation expressing the behavior of current and voltage along the conductor involves variables of distance x and time t or frequency f. Thus, it becomes a partial differential equation. However, a lumped-parameter circuit is expressed by an ordinary differential equation since no concept of the length or the traveling time exists. This is the most significant difference between the distributed-parameter circuit and the lumped-parameter circuit.
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