Single- and Double-Stub Impedance Matching

Single- and double-stub impedance matching on transmission-line feeders are described. Formulae determining the position and the length of a single matching stub for any load impedance or any observed standing-wave voltage distribution are derived, neglecting losses in the matching sections. Conditions for minimum length of stub and minimum distance between load and stub are specified. For the double-stub arrangement, expressions for the lengths of and distance between stubs are derived for any possible combination of load and distance between stubs. A double-stub tuner with any fixed distance between stubs cannot match all loads to the feeder, and the limits are specified. The optimum location on the feeder of the double-stub tuner is discussed. A graphical method employing a circle diagram for computing the lengths and position of the stubs is explained. The graphical determination of the stub lengths of the double-stub tuner is facilitated by auxiliary circular loci which also indicate the range of admittances over which an impedance match may be effected.