A new complementary Colpitts (C-Colpitts) oscillator topology is introduced and the oscillation mechanism as a one-port model is analyzed. Based on the one-port analysis and the existing phase-noise model, the phase-noise equation of the proposed C-Colpitts oscillator is derived as the function of the oscillation frequency, Q factor of tank circuit, and bias current. The phase-noise equation provides the design guideline to optimize the phase noise of the proposed Colpitts oscillator, of which the property is proven with simulation and measurement results. The proposed Colpitts voltage-controlled oscillators are fabricated using 0.35-mum CMOS technology for 2-, 5-, 6-, and 10-GHz bands. Measurement shows that the phase noise is -118.1 dBc at 1-MHz offset from 6-GHz oscillation while dissipating 4.6 mA of current from a 2.0-V supply.