A 0.0019-mm² <i>LC</i>-Ring Oscillator With an Ultra-Compact Transformer Achieving 175.2 dBc/Hz FoM@1MHz and 202.4 dBc/Hz FoMA

This brief describes an area-efficient LC-ring oscillator featuring an ultra-compact transformer resonator. The series inverters could be equivalent to the negative resistors providing gain compensation. The involved inverters and switched-capacitor banks are fully integrated underneath the transformer resonator. Thus, with a comparable area of the typical ring oscillators, our oscillator shows significantly improved phase noise (PN) and figure-of-merit (FoM). Besides, we implemented the stacked-coupling and distributed-coupling transformer-based LC-ring oscillators for the PN and FoM comparison. The stacked-coupling LC-ring oscillator can lower the PN with the same frequency and power budget. Fabricated in 40-nm CMOS, our stacked-coupling LC-ring oscillator scores a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathrm { PN}}_{\unicode {0x0040}1{\mathrm { MHz}}}$ </tex-math></inline-formula> of -110.4 dBc/Hz across the frequency tuning range from 3.7 to 5.1 GHz with an active area of 0.0019 mm2, corresponding to a superior FoM (FoMA)<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${}_{\text {@1MHz}}$ </tex-math></inline-formula> of 175.2 dBc/Hz (202.4 dBc/Hz) that is 4.2 dB (6 dB) higher than the distributed-coupling LC-ring oscillator.