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

PHASE OF AHARONOV-BOHM OSCILLATIONS IN CONDUCTANCE OF MESOSCOPIC SYSTEMS