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This brief identifies the cause of frequency-dependent distortion in ring oscillator voltage-controlled oscillator (VCO) analog-to-digital converters (ADCs). First, a VCO model is presented which takes into account the capacitance at the VCO terminals. This allows the most common drive configurations to be analyzed to determine the origin of the frequency-dependent distortion and the vulnerability of the different drive configurations. A conclusion is that voltage control is relatively robust against this effect. Based on the preceding analysis, a novel foreground calibration procedure is developed. The effectiveness of the proposed calibration method is demonstrated for a manufactured open-loop VCO ADC in 28nm CMOS and compared to results obtained using a prior art calibration method and results without calibration. For a    $\mathbf {750 mV_{pp}} 26.5$    MHz signal, the proposed calibration procedure leads to an improvement in THD of 20 dB and 47 dB compared to results using prior art calibration and no calibration respectively.

Origin of Frequency-Dependent Distortion and Calibration for Ring Oscillator VCO ADCs