A radio frequency (RF) transmitter, comprising a Tesla transformer and an LC oscillator, said Tesla transformer comprising inner and outer conductors (10, 20), said inner conductor (20) comprising a generally tubular magnetic core (22) carrying a conductive member (22a) on its outer surface and said outer conductor (10) comprising a generally tubular magnetic core (13) carrying a conductive member (12) on its inner surface, said LC oscillator including a secondary winding module (40) comprising a generally tubular body (41) carrying a conductive coil (42) on its outer surface, said inner conductor (20), outer conductor (10) and secondary winding module (40) being arranged in a substantially concentric nested configuration such that said inner conductor (20) is located within said secondary winding module (40) and said secondary winding module (40) is located within said outer conductor (10), wherein a first portion (45) of relatively high permittivity dielectric material is provided between said conductive member (22a) of said inner conductor (20) and said conductive coil (42) and a second portion (33) of relatively high permittivity dielectric material is provided between said conductive coil (42) and said conductive member (12) of said outer conductor (10).