Miniaturizing patch antenna by adding a shorting pin near the feed probe $a folded monopole equivalent

Miniaturizing patch antenna by a shorting pin near the feed probe has been successful in hardware experiments. The physics behind such success is that the feed probe with the shorting pin is equivalent to a folded dipole antenna. The paper looks at the equivalence of the folded monopole antenna (half of a folded dipole). The equivalence makes it possible to use the Smith chart to: (1) aid the selection of the feed and pin dimensions; (2) provide the limit of possible miniaturization.