Magnetic decoupling principle when applied to electrical machines states that if two windings are configured for different number of pole pairs, they would not interact with each other magnetically even though they share a common magnetic core. This principle forms the basis for developing special machines where two or more machines can be integrated with the same magnetic circuit. This paper deals with formulating the mathematical analysis that determines the validity of this principle during practical conditions (i.e. non-sinusoidal winding distribution, flux saturation, etc.). Extensive Finite Element Method (FEM) simulation results from the Ansys Maxwell-2D software platform closely obey the conclusions derived from the mathematical analysis. As an example, new brushless and magnetless synchronous machines (SMs) have been developed by using this principle. It is designed by embedding an induction machine (IM) with a SM. Experimental investigations conducted on the laboratory prototype support the mathematical analysis dealt with in th