This paper presents a switched self-biasing and a tail current-shaping technique to suppress the 1/f noise from a tail current source in differential cross-coupled inductance-capacitance (LC) voltage-controlled oscillators (VCOs). The proposed LC VCO has an amplitude control characteristic due to the creation of negative feedback for the oscillation waveform amplitude. It is fabricated using a 0.13 ${mu}m$ CMOS process. The measured phase noise is -117 dBc/Hz at a 1 MHz offset from a 4.85 GHz carrier frequency, while it draws 6.5 mA from a 0.6 V supply voltage. For frequency tuning, process variation, and temperature change, the amplitude change rate of the oscillation waveform in the proposed VCO is 2.1 to 3.2 times smaller than that of an existing VCO with a fixed bias. The measured amplitude change rate of the oscillation waveform for frequency tuning from 4.55 GHz to 5.04 GHz is 131 pV/Hz.