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The influence of the machine topology and dq-axis cross-coupling on the rotor position estimation error in an extended back-EMF based sensorless brushless AC drive is investigated by both finite element analysis and experimentally on four brushless AC machines having different rotor topologies, viz. interior circumferentially magnetized, interior radially magnetized, surface-mounted, and inset magnets. The d- and q- axis apparent self- and mutual-inductances, Ld, Lq, Ldq and Lqd, are predicted by finite element analysis for various d- and q-axis currents. The error in the estimated rotor position of the four machines is investigated and compared when (a) the influence of magnetic saturation is neglected, (b) only the influence of the dq-axis current on Lq is considered, but dq-axis cross-coupling magnetic saturation is neglected, and (c) the influence of dq-axis cross-coupling magnetic saturation is taken into account. It is shown that the error is more strongly influenced by the q-axis current/permeance than the dq-axis current/permeance, since the dq-axis current does not distort the symmetrical field distribution about the q-axis, and that dq-axis cross-coupling magnetic saturation can significantly affect the accuracy of the rotor position estimation. However, by introducing an apparent mutual winding inductance in the extended back-EMF based sensorless method, the error in all four machines under consideration is reduced significantly, to a similar level to that which results with surface-mounted magnet machines.