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

Frequency modulation in ring VCOs is investigated. Primarily, the linearity of conversion from input voltage to output frequency is considered. Bulk-voltage control of the threshold voltage of the VCO transistors is found to be a very promising approach for applications in frequency ΔΣ converters. Different approaches apply in presence of high supply voltages, when transistors work in strong inversion, compared to low supply voltages, when transistors are in weak inversion. In strong inversion, second-order effects controlled by the supply voltage linearize the VCO modulation, while in weak inversion an improved linearity can be obtained using soft rails, at the expense of a reduced sensitivity.