A consequence of the projected trend in turbine-generator design towards large airgaps, airgap windings without slots, and superconducting windings, is a progressive change in the nature of the machine from ‘iron-cored’ to ‘air-cored’. A general analysis of fields and winding inductances that is applicable to all configurations is presented. The underlying unity of the various types is brought out, and particular attention is given to a comparison of the conventional design and the fully air-cored (superconducting) machine. In a companion paper the comparative design and performance analysis of air-cored and iron-cored synchronous machines is discussed.