A ferroresonant transformer to produce an output voltage that has a substantially constant output voltage that is substantially free of harmonics includes a ferromagnetic core with a winding part and primary and secondary windings on that part. The core also includes a flux return part. Magnetic shunts magnetically couple some of the flux from the core between the primary and secondary windings to the flux return part. The core includes a region with a reduced cross-sectional area that constitutes an air gap to form a built-in inductor. The remainder of the core works with the secondary winding and a resonating capacitor to generate a substantially harmonic-free, constant-voltage output. The transformer may have one set of primary-secondary windings if it is to operate on single-phase alternating current, or it may have multiple sets if it is to operate on multi-phase alternating current.