Characterization of a Long Lossless Line

For a lossless line, the line resistance is assumed to be zero. The characteristic impedance then becomes a pure real number and it is often referred to as the surge impedance . The propagation constant becomes a pure imaginary number. Defining the propagation constant as γ = jβ and replacing l by x we can rewrite (2.41) and (2.42) as

	(2.52)
	(2.53)

The term surge impedance loading or SIL is often used to indicate the nominal capacity of the line. The surge impedance is the ratio of voltage and current at any point along an infinitely long line. The term SIL or natural power is a measure of power delivered by a transmission line when terminated by surge impedance and is given by

(2.54)

where V₀ is the rated voltage of the line.

At SIL Z_C = V_R / I_R and hence from equations (2.52) and (2.53) we get

	(2.55)
	(2.56)

This implies that as the distance x changes, the magnitudes of the voltage and current in the above equations do not change. The voltage then has a flat profile all along the line. Also as Z_C is real, V and I are in phase with each other all through out the line. The phase angle difference between the sending end voltage and the receiving end voltage is then θ = β l. This is shown in Fig. 2.7.

Fig. 2.7 Voltage-current relationship in naturally loaded line.