Bubble dynamics in T-bar-type circuits

A theoretical model for bubble propagation under T-bar type overlays due to an in-plane rotating field is developed. By making certain assumptions about the nature of the overlay magnetisation, it is shown that bubble driving forces can be readily calculated for a circular bubble of varying diameter moving freely in 2-dimensions. Expressions for the frictional forces acting on a bubble are derived and the resulting equations are solved to yield the bubble centre trajectory, the radius, velocity and phase variations. This analysis is applied to examine bubble propagation along a straight portion and around a corner of a T-bar circuit. Cases of successful propagation of an isolated bubble, as well as of failure to propagate, are given. Bias margins for a straight T-bar track at 100 kHz are obtained theoretically and compared with experimental results for a chip having the same parameters.