Linearity of bulk-controlled inverter ring VCO in weak and strong inversion

In this paper linearity of frequency modulation in voltage controlled inverter ring oscillators for non feedback sigma delta converter applications is studied. The linearity is studied through theoretical models of the oscillator operating at supply voltages above and below the threshold voltage of a transistor, bringing the transistors in respectively strong and weak inversion. The theoretical results are tested with more advanced models through spectreRF simulations. A soft rail approach implemented to improve linearity in weak inversion is proposed and demonstrated. The influence from voltage noise, process variations and temperature variations have also been simulated to indicate the advantages of having the soft rail bias transistor in the VCO.