The cubic spline interpolation of a standing wave envelope

It is shown that exploiting the smooth behavior of the standing-wave´s envelope near maxima yields better results in impedance and return loss computations. The improvement is achieved using a very simple algorithm to locate extrema in an envelope approximated by a cubic spline and without increasing the order of the moment matrix. The method consists of interpolating the continuous standing wave envelope by a cubic spline. The fit of a spline depends on the amount of discrete data points per wavelength and on the true shape of the envelope. An increase in the number of data points, or knots, along the feedline improves the fit of a spline, but at the cost of an increase in the order of the moment matrix. The objective is to obtain a satisfactory representation of the envelope with as few discrete data points along the feedline as possible. Based on the results, it appears that, for arbitrary values on the standing wave ratio, the cubic spline interpolation of maxima is more reliable than that of minima.<>