TABLE OF CONTENTS We can account for loss in a transmission line by working directly with Eqs. (9.27) and (9.28). In particular, all the calculation of the previous section can be redone to yield similar expressions.
Taking the ratio of voltage to current on the transmission line, we have the general expression
Using the definition of the reflection position, ?( z ), we have
which can be written explicitly in terms of the load impedance
It s easy to show that the above equation degenerates to Eq. (9.5) under the lossless case.
Calculate the input impedance of a short-circuited transmission line of length ? at low frequency. Assume the line is very short, e.g. ? ? ? 0.
From Eq. (9.6), substituting Z L = 0, we have
Recalling the definition of ? and Z 0, we have
where R T is the resistance of the line and L T is the inductance of the line. Thus a shorted short transmission line behaves like a lumped inductor.
In general, a lossy transmission line introduces distortion due to dispersion. Dispersion occurs when the propagation speed and attenuation is frequency dependent. If a group of frequencies are excited along the line, they travel along the line with different velocity and experience different attenuation. Thus, if an arbitrary waveform (say a pulse) is excited on the line, after significant propagation it will arrive with a completely...
