Log periodic circuit analysis

The paper deals with the analysis of a class of log-periodic circuits. Closed form expressions are developed for the Foster type LP networks with or without losses. It is proved that the locus of the input impedance of these networks on a reflection coefficient chart, e.g., on the Smith chart, is a circle for networks of order one. It is shown that for a network of a general order the plot is not necessarily a circle. The input impedance of a log periodically loaded transmission line is studied. It is found that for certain conditions the reflection coefficient plot is very close to a circle but in general it generates closed curves of various shapes.