A high voltage power supply for use in small diameter spaces such as in oil well logging devices includes an AC voltage source which provides an AC voltage to a voltage multiplier circuit that converts the AC voltage to a high DC voltage. A parallel or combination parallel-series multiplication circuit is used, rather than a series multiplication circuit, to reduce the reverse voltage across each semiconductor rectifier in the multiplication circuit. A plurality of parallel capacitors is constructed using an elongate common capacitor electrode with individual capacitors formed from individual capacitor electrodes spaced along and separated from the common electrode by a layer of dielectric material. The layer of dielectric material can be tapered along the common electrode, and additional dielectric material can be positioned between edges of adjacent individual electrodes. A high voltage end individual electrode can be made wider to increase its capacitance.