An improved analytical method for triple stub matching (Stubs in Parallel)

In this paper we give the new improved analytical method of triple stub tuner for matching the load impedances to provide the maximum power transfer between a generator and a load. The stubs are connected in parallel with the line at the appropriate distances from the load.  The characteristic impedances of the transmission line and the stabs are different. The paper points on the determination of the length for the first stub near the load. The limit lengths for the first and the second stub are found for which the matching is possible. The length of the third stub is directly obtained from the matching conditions. Even though there is not the unique solution for the triple stub matching we also shoved the existence of unique solutions under some conditions. The special cases are also treated. The results of this method are verified by those obtained using the Smith chart and there are in exceptionally good agreement. Even though there are not many papers on this subject this work could be useful for engineers, and physicist which work in this domain.