our goal was to determine first of all the characteristic impedance [Z.sub.0] and the

propagation constant of the 3-phase cable conductor modelled as a transmission line.

where [[??].sub.R] is the received signal intensity, [[??].sub.T] the transmitted signal intensity, x the distance from antennas to the point of reflection, [??] the reflection coefficient, and [??] the

propagation constant representing propagation speed and losses.

Consider a z-directed propagating wave with

propagation constant [beta] and applying the vectorial identity [nabla] x ([nabla] x A) = [nabla]([nabla] x A) -[[nabla].sup.2]A, the eigenproblem in (1a) can be written as

where [k.sub.0] is the

propagation constant in the free space, [d.sub.i] represents the spatial distance between the center of feed antenna and the ith element of RA aperture, and ([x.sub.i], [y.sub.i]) stands for the coordinates of ith element center.

This energy leakage determines the directivity of the radiated beam and is a function of the

propagation constant along the structure.

where p and [phi] are the polar coordinates, z is the coordinate along the fibre's optical axis, [k.sub.z] = [beta] + /a is the complex

propagation constant, and c is the frequency.

where [gamma] is the real

propagation constant (spectral parameter of the problem) and m is an angular integer parameter (which assumed to be known).

The

propagation constant is supposed to be a real-valued quantity.

b = [DELTA]k[L.sub.D]/2 is the normalized birefringence parameter, where [DELTA]k = [DELTA]n[k.sub.0] and [DELTA]n and [k.sub.0] are the birefringence and

propagation constant in vacuum, respectively.

Reynolds and James Rautio, "Conductor Profile Effects on the

Propagation Constant of Microstrip Transmission Lines," IEEE International Microwave Symposium, Microwave Theory & Techniques Symposium (MTTS) 2010, June 2010.

For the lossless case, where the

propagation constant [gamma] is imaginary, and assuming total reflection at the far end of the transmission line, the amplitudes of the direct and reflected waves will be equal to [U.sub.0] at all points.