Capacitively isolated current-loaded or current-driven charge pump circuits and related methods transfer electrical energy from a primary side to a secondary side over a capacitive isolation boundary, using a controlled current source to charge isolation capacitors with constant current, as opposed to current impulses, while maintaining output voltage within tolerance. The charge pump circuits provide DC-to-DC converters that can be used in isolated power supplies, particularly in low-power applications and in such devices as sensor transmitters that have separate electrical ground planes. The devices and methods transfer electrical energy over an isolated capacitive barrier in a manner that is efficient, inexpensive, and reduces electromagnetic interference (EMI).