Simple analytical models are derived for the no-load field, the armatu
re field, the main inductance, and the torque of a permanent magnet sy
nchronous machine. The solutions are obtained by a one-dimensional car
tesian and polar as well as a two-dimensional polar coordinate treatme
nt yielding mainly closed analytical expressions. The torque is calcul
ated via Lorentz forces on the stator, or directly at the radial magne
t edges on the rotor, allowing also the determination of the non-sinus
oidal no-load held.