  We report on a theoretical analysis of the phase-shift in compact atomic
clocks working either with cold or thermal atoms. It is well known that in a
microwave cavity with electromagnetic losses, a traveling wave adds to the
standing wave of a given resonant mode. We calculate the spatial varying phase
related to this travelling wave for two geometries of interest in clock
applications, the cylindrical cavity and the spherical cavity. Due to their
motion, the atoms probe different regions of the cavity and then experience
different phases of the interrogating microwave field. We show that this
combination of atomic motion and spatial changing phase results in a
phase-shift of the clock frequency, well known in primary frequency standards,
that can affect the metrological performances also of vapor cell and compact
cold-atom clocks. In the latter case, we evaluate the phase-shift for a space
clock and a ground clock.
