Application of autocorrelation principles to characterize line source radiation

Abstract

The problem of line source radiation is examined through the application of autocorrelation principles. These principles enable the radiation from a line source to be characterized with only knowledge of the current distribution - a priori knowledge of the antenna pattern is not required. First, the radiated power from a broadside line source radiator is examined. Exact closed-form analytical expressions for the radiated power are developed for several canonical current distributions. These expressions are validated using numerical integration of the radiated power equation. Next, the statistical concept of variance is applied to characterize the antenna pattern performance. As with the radiated power, closed-form expressions for the 'beamwidth variance' are determined through application of autocorrelation principles for several canonical current distributions, without knowledge of the antenna pattern. These results are also validated by numerically integrating the antenna pattern to calculate the variance. Finally, the methodologies developed for characterizing broadside line source radiation are extended to characterize scanning beams from line source radiators. Exact closed-form expressions for the radiated power are developed for several canonical current distributions and are validated through numerical integration of the antenna pattern. The concept of 'pattern mean' is introduced in addition to the beamwidth variance, since the mean of a scanning beam will not necessarily be along the direction of the scan angle. Exact closed-form expressions for both statistical performance measures are developed for canonical current distributions. As with the other results, numerical integration of the first and second moments of the antenna pattern are performed to validate the analytical expressions.