Performance Limitation Analysis of Highly-Digital Time-Based Closed-Loop Sensor-to-Digital Converter Architectures

This brief presents the theoretical and comparative analysis of two major time-based architectures for sensor interfaces. Both use a voltage-controlled oscillator (VCO) to achieve a highly-digital scalable implementation. The first architecture is based on a phase-locked loop, while the second one is count-based. Both systems are closed loop to efficiently mitigate the VCO nonlinearity. They show inherent first-order quantization noise shaping thanks to the use of an oscillator and phase detection. The two systems having a different working principle leads to different VCO requirements in terms of gain linearity (V-to-f or V-to-T linearity). Formulas are derived to predict the maximum SQNR for both architectures. Equations for the achievable maximum SNR taking into account the VCO phase noise are also derived, since this is the limit to the SNR in practical implementations. State-variable-based simulation results are presented, confirming the theoretical analysis and emphasizing the different design trade-offs and practical considerations.