  The properties of Josephson tunneling between a single band s-wave
superconductor and a two band $s_\pm$ superconductor are studied, in relation
to recent experiments involving iron-based superconductors. We study a single
junction and tune the order parameter (OP) phase difference across the
junction. We find a variety of behaviors which are characterized by their
energy-phase difference relation. The system is modeled on a lattice and
treated in self-consistent mean field approximation. We also study a loop
structure made with s-wave and $s_\pm$ parts with two junctions between the
parts. The phase of the order parameter is then controlled by a magnetic flux
threading the loop. Our analysis suggests four types of junction behaviors
which are characterized by the dependence of the junction energy on the phase
difference between the s-wave and the $s_\pm$ superconductors. The energy vs.
phase difference curve has either one minimum at $\Delta\phi = 0,\pi$ or
somewhere in between, or a double minimum structure. This leads to four
different behaviors in a loop structure as a function of the flux threaded
through the loop.
