  We analyze the design of a potential replacement technology for the
commercial ferrite circulators that are ubiquitous in contemporary quantum
superconducting microwave experiments. The lossless, lumped element design is
capable of being integrated on chip with other superconducting microwave
devices, thus circumventing the many performance-limiting aspects of ferrite
circulators. The design is based on the dynamic modulation of DC
superconducting microwave quantum interference devices (SQUIDs) that function
as nearly linear, tunable inductors. The connection to familiar ferrite-based
circulators is a simple frame boost in the internal dynamics' equation of
motion. In addition to the general, schematic analysis, we also give an
overview of many considerations necessary to achieve a practical design with a
tunable center frequency in the 4-8 GHz frequency band, a bandwidth of 240 MHz,
reflections at the -20 dB level, and a maximum signal power of approximately
order 100 microwave photons per inverse bandwidth.
