New infinitesimal method for the calculation of self and mutual inductances of arbitrary AC windings

The paper describes a new universal infinitesimal method, which enables the calculation of self and mutual inductances of arbitrary AC windings. The method is based on the notion of the local angular density of conductors n(α) = dN(α)/dα. It will be proved the proportionality B(α)≈ ∫n(α)dα for the magnetic flux density in the air gap. The function n(α) can be arbitrary, i.e. of continual or impulse character. Spatial functions n(α), B(α) may be evolved into Fourier series. The first harmonic components of these functions serve to the electromagnetic design of the induction or synchronous motor. Higher harmonic components serve to the calculation of the differential leakages.