||Voltage-controlled oscillators (VCO) are one of the most essential building blocks in phase-locked loops and frequency synthesizers, which are required in all data communication and telecommunication systems for generating highly accurate timing reference sources. However, existing VCOs need a supply voltage larger than the devices' threshold voltage. Therefore, a new VCO design is needed for achieving high performance in terms of low supply voltage, low phase noise, and low power consumption. The new VCO employs an on-chip transformer as feedback, where the primary coil is used as the inductive load and the secondary coil as the source degeneration. By magnetic coupling between the two coils, a positive feedback is obtained. The breakthrough of the new design enables the VCO to have more voltage headroom and to operate at a supply voltage much lower than the devices' threshold voltage, which is still not achievable with existing technologies. In addition, with the invention, the VCO can ensure the same phase shift for the voltages at the drain of the source, which in turn results in pulse shaping of the drain current and minimizing the overall phase noise. A prototype VCO using the invention has successfully operated at a supply voltage as low as 0.35V in a standard CMOS process even with the devices!\ threshold voltage being kept at around 0.65V. Another prototype VCO optimized for low power, low phase noise, and high frequency has also been designed and fabricated. Simulation shows that this VCO achieves a comparable phase noise while consuming only 1 mW, which is much lower than what is achievable with existing design techniques.