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A general, analytic approach to the calculation of magnet fields in a slottless, axial-flux, permanent magnet generator is presented. The basic 'building block' is the vector potential produced by a current sheet situated between two, infinitely permeable, iron surfaces. By modelling the magnet by currents at its periphery, and integrating over the magnet thickness, the vector potential and magnetic field due to the permanent magnets can be found. In contrast the armature winding is represented by a current sheet close to the stator iron surface. Magnetic field results produced by the analytic equations have been compared with two-, and three-, dimensional finite element studies and found to produce results comparable to within 5%. In addition emf, flux and inductance measurements have been made on two generators and compared with both finite element and analytic results. The analytic model predicts the emf to within 5%. The 'end winding' inductance of a toroidal, air-gap, armature winding, is shown to contribute significantly to the overall inductance with the analytical model predicting the inductance to within 10% of the measured values.