A 50μW Ring-Type Complementary Inverse-Class-D Oscillator with 191.4dBc/Hz FoM and 205.6dBc/Hz FoMA

There are long-standing trade-offs between the ring [1, 2] and LC-tank [4–5] oscillators in terms of power consumption (PDC), area, phase noise (PN) and sensitivity to supply perturbations. A recent work to merge the two—a ring of series-LC tanks [3, 7]—has attained considerably improved PN and supply pushing insensitivity, while occupying comparable system area to the conventional inverter-based ring-oscillators (RO); however, it still burns several milliwatt with limited FoM. In this paper, we greatly reduce $\mathrm{PDC}_{\mathrm{D}}$ in LC-assisted tiny ring-type VCOs into as low as $50 \mu \mathrm{W}$, while demonstrating high FoM approaching that of LC-VCOs by means of a highly efficient complementary class-$\mathrm{D}^{-1}$ topology. To shrink consumed $\mathrm{PDC}_{\mathrm{DC}}$, transformer-based resonant tanks are employed to replace the series-LC tanks used in [3, 7], as proposed in Fig.1(b-c). They are capable of generating a 180° or 0° phase shift by configuring the transformer as inverting or non-inverting, respectively, thus reducing the number of stages required to start the oscillation to two or ultimately one (‘degenerated’ case). The normally expected start-up circuit [3] can also be averted as the dc feedback is avoided thanks to the transformer’s isolation. A $2 \times$ to $4 \times$ reduction in power can be readily expected. Furthermore, the resulting “single-stage RO” in Fig.1(c) is configured into a complementary class-$\mathrm{D}^{-1}$ switching operation, which not only obtains high energy efficiency due to non-overlapping voltage and current waveforms, but also minimizes the drain parasitic discharge power loss as the transistor’s CDS capacitance is absorbed into the parallel resonant tank.