A Compact 0.2–0.3-V Inverse-Class-F23 Oscillator for Low 1/f 3 Noise Over Wide Tuning Range

We introduce a new mode of oscillation in an LC -tank: an inverse class-F ₂₃ . In contrast to the conventional class-F oscillators, in which a high value of the real impedance (i.e., resistance) is presented to the third (in class-F ₃ ) or/and to the second (in class-F ₂ /class-F ₂₃ ) oscillator harmonics via an auxiliary resonance, here low resistive impedances (resembling a non-ideal short) are presented at both the second and third harmonics. This is made possible by tight magnetic coupling in the differential and common modes, respectively, afforded by a new compact 2:3 transformer. Being largely free from the harmonics in the voltage waveform and their possible deleterious phase shift effects on the flicker noise up-conversion, the phase noise performance in the flicker and thermal regions is further improved by narrowing the conduction angle. The 2:3 step-up transformer also provides a high passive gain to help with the startup in face of low supply. The switched-capacitor banks and cross-coupled transistor pair are carefully integrated under the transformer with a special arrangement of native (high-resistivity) substrate layer to mitigate their effect on the oscillation while reducing the area by 30%. The proposed digitally controlled oscillator (DCO) is implemented in 28-nm CMOS and achieves −95 dBc/Hz and −118 dBc/Hz at 100 kHz and 1 MHz offsets, respectively, while operating at a 0.3 V supply. The measured $1/f^{3}$ corner stays within 60 to 100 kHz over the 35% tuning range (TR) (from 2.02 to 2.87 GHz). This results in a figure-of-merit (FoM) with normalized TR (FoM _T ) of −196 and −199 dB at 100 kHz and 1 MHz offsets, respectively, is a record in the space of ≤0.5 V and ≤1 mW.