Analysis of Clock-Jitter Effects in Continuous-Time $\Delta \Sigma$ Modulators Using Discrete-Time Models

This paper proposes a simple discrete-time (DT) modeling technique for the rapid, yet accurate, simulation of the effect of clock jitter on the performance of continuous-time (CT) DeltaSigma modulators. The proposed DT modeling technique is derived from the impulse-invariant transform and is applicable to arbitrary-order lowpass and bandpass CT DeltaSigma modulators, with single-bit or multibit feedback digital-to-analog converters (DACs) employing delayed return-to-zero (RZ) or non-return-to-zero (NRZ) rectangular pulses. Its accuracy is independent of both the power spectrum of the clock jitter and the loop transfer function of the DeltaSigma modulator. The proposed DT modeling technique is validated (for both independent and accumulated clock-jitter errors) against accurate simulations in SIMULINK, using behavioral blocks developed to directly simulate RZ or NRZ DACs with clock jitter. It is subsequently applied to various CT DeltaSigma modulator architectures (low- pass and bandpass, with single-bit and multibit DACs) to study the relative effectiveness of different feedback-DAC pulsing schemes (NRZ, RZ, RZ with fixed on-time, and RZ with fixed off-time) in minimizing the modulator sensitivity to clock jitter. The performance of each architecture is compared as a function of clock jitter, thereby offering a valuable reference for selecting a rectangular feedback-DAC pulse shape when designing CT DeltaSigma analog-to-digital converters.