3.5: Circuit Models of Transmission Lines

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Circuit models of transmission lines are required if they are to be used in a circuit simulator. RF and microwave engineering uses two types of simulators. Spice-like simulators use lumped-element transmission line models in which an \(RLGC\) model of a short segment of line is replicated for the length of the line. If the ground plane is treated as a universal ground, then the model of a segment of length \(\Delta z\) is as shown in Figure \(\PageIndex{1}\)(a). In this segment \(r = R\Delta z\), \(l = L\Delta z\), \(g = G\Delta z\), and \(c = C\Delta z\), where \(R\), \(L\), \(G\), and \(C\) are the per unit length parameters of the line. Cascading the segments to get the length of the line yields the complete lumped-element model of the line, as shown in Figure \(\PageIndex{1}\)(b).

Figure \(\PageIndex{1}\): Lumped-element transmission line models: (a) model of a short segment (e.g. \(\lambda /20\) long); and (b) complete model of a transmission line.