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.