  We present the design of a passive, on-chip microwave circulator based on a
ring of superconducting tunnel junctions. We investigate two distinct physical
realisations, based on either Josephson junctions (JJ) or quantum phase slip
elements (QPS), with microwave ports coupled either capacitively (JJ) or
inductively (QPS) to the ring structure. A constant bias applied to the center
of the ring provides the symmetry breaking (effective) magnetic field, and no
microwave or rf bias is required. We find that this design offers high
isolation even when taking into account fabrication imperfections and
environmentally induced bias perturbations and find a bandwidth in excess of
500 MHz for realistic device parameters.
