Telegrapher's Equations - Distributed Components

Distributed Components

The telegrapher's equations, like all other equations describing electrical phenomena, result from Maxwell's equations. In a more practical approach, one assumes that the conductors are composed of an infinite series of two-port elementary components, each representing an infinitesimally short segment of the transmission line:

• The distributed resistance of the conductors is represented by a series resistor (expressed in ohms per unit length).
• The distributed inductance (due to the magnetic field around the wires, self-inductance, etc.) is represented by a series inductor (henries per unit length).
• The capacitance between the two conductors is represented by a shunt capacitor C (farads per unit length).
• The conductance of the dielectric material separating the two conductors is represented by a shunt resistor between the signal wire and the return wire (siemens per unit length). This resistor in the model has a resistance of ohms.

The model consists of an infinite series of the infinitesimal elements shown in the figure, and that the values of the components are specified per unit length so the picture of the component can be misleading. An alternative notation is to use, and to emphasize that the values are derivatives with respect to length. These quantities can also be known as the primary line constants to distinguish from the secondary line constants derived from them, these being the characteristic impedance, the propagation constant, attenuation constant and phase constant. All these constants are constant with respect to time, voltage and current. They may be non-constant functions of frequency.