TABLE OF CONTENTS The lossless transmission line is an important idealization for many everyday computations. Consider the arbitrary transmission line shown in Fig. 9.9 terminated in a load impedance Z L, at some point z = ? ? from the load. Since ? = j ? and ? = 0 for a lossless line, we may write Eqs. 9.27 and 9.28 as
Since the line is lossless, the propagation constant ? = j ? is imaginary and the characteristic impedance Z 0 is real. The constraint of the load impedance creates a reflected wave as before
and in terms of ? L
The average power flow into the transmission line at an arbitrary point on the line is calculated by
which can be written as
and expanded
Notice that the middle terms in the brackets sum to a purely imaginary number, [1] simplifying the calculations to
which is a constant independent of position. In particular, it is equal to the power delivered to the load. This of course follows from the lossless property of the line. Even though the power flow is constant on the line, the amplitude of the voltage and current waveforms are not constant unless ? L = 0.
When the termination is matched to the line impedance Z L = Z 0, ? L = 0 and thus the voltage along the line v(
