An electro‐optic microwave modulator generating frequency‐swept sidebands 26–31 GHz offset from a CO2laser carrier is described. Resonant enhancement of the modulating field allows as low as 8‐mW microwave drive power. Electronic tuning of the resonances by a ferrite phase shifter inside the cavity increases the FWHM modulation bandwidth from 140 MHz (untuned) to 4 GHz.