Second and Third-Order Noise Shaping Digital Quantizers for Low Phase Noise and Nonlinearity-Induced Spurious Tones in Fractional- $N$ PLLs

Noise shaping digital quantizers, most commonly digital delta-sigma (ΔΣ) modulators, are used in fractional-N phase-locked loops (PLLs) to enable fractional frequency tuning. Unfortunately, their quantization noise is subjected to nonlinear distortion because of the PLL's inevitable non-ideal analog circuit behavior, which induces spurious tones in the PLL's phase error. Successive requantizers have been proposed as ΔΣ modulator replacements with the advantage that they reduce the power of these spurious tones. However, the quantization noise from previously published successive requantizers is only first-order highpass shaped, so it usually causes more PLL phase noise than that from the second-order and third-order ΔΣ modulators commonly used in PLLs. This paper presents second-order and third-order successive requantizers to address this limitation. Additionally, successive requantizer design options are presented that result in either lower-power spurious tones or lower phase noise compared to ΔΣ modulators when used in PLLs.