  We explore the 1/4 BPS configurations of the supersymmetric gauge theories on
$R^{1+3} \times S^1$. The BPS bound for energy and the BPS equations are
obtained and the characteristics of the BPS solutions are studied. These BPS
configurations describe electrically charged calorons, which are constituted of
dyons and carry linear momentum along the compact direction. We carry out
various approaches to the single caloron case in the theory of SU(2) gauge
group.
