  Motivated by a recent experiment we analyze in detail the phase of
Aharonov-Bohm oscillations across a 1D ring with a stub coupled to one of its
arms, in the presence of a magnetic flux. We demonstrate that there are two
kinds of conductance extremas. One class of them are fixed at particular flux
values and can only change abruptly from a maxima to a minima as incident
energy is varied. We show a different mechanism for such abrupt phase change in
conductance oscillation. We demonstrate that these extremas can exhibit
$``$phase locking". However, the second kind of extremas can shift continuously
as the incident energy is varied.
