Spurious Tone Mitigation in Fractional-N Phase-Locked Loops
Fractional-N phase-locked loops (PLLs) are widely used to synthesize local oscillator signals for modulation and demodulation in communication systems. Their phase error inevitably consists of both a periodic component made up of spurious tones and a random component called phase noise. Spurious tones are particularly harmful to the performance of typical communication systems, so most communication standards stipulate stringent limits on their maximum power in relevant frequency bands.
High-performance PLLs generally contain noise-shaping coarse quantizers to control their output frequency. Such quantizers are a fundamental source of spurious tones in the PLL’s phase error. This is because spurious tones are inevitably induced when the quantizer’s quantization noise is subjected to nonlinear distortion from analog circuit imperfections. This dissertation presents a rigorous analysis of this effect and a way to mitigate it through the use of a class of digital quantizers with first and higher-order highpass shaped quantization noise which are optimized for spurious tone and phase noise mitigation.
The first chapter of this dissertation presents a mathematical analysis of spurious tone generation via nonlinear distortion of quantization noise. It proves that subjecting the quantization noise running sum of a digital quantizer to a nonlinearity of a certain order will inevitably induce spurious tones, and shows the relation between such nonlinearity order and the range of values the quantization noise running sum takes. The results are general and apply to any digital quantizer.
The second chapter of this dissertation presents a class of digital quantizers with optimal immunity to nonlinearity-induced spurious tones and with first-order highpass shaped quantization noise. It presents design solutions for digital quantizers with quantization noise that can be subjected to nonlinear distortion of a given order without inducing spurious tones, and relies on the results from the first chapter to prove that the presented solutions are optimal in terms of spurious tone generation.
The third chapter of this dissertation presents digital quantizers with second and third-order highpass shaped quantization noise which can be optimized for either spurious tone or phase noise mitigation. These quantizers can replace the often-used delta-sigma modulators in high-performance PLLs to either improve spurious-tone performance at the expense of slightly higher PLL phase noise or lower PLL phase noise.
The fourth chapter of this dissertation present an integrated circuit PLL which implements the second and third-order digital quantizers presented in the third chapter. It demonstrates record-setting spurious tone performance due to the use of these digital quantizers and to a new linearity-enhancement PLL timing scheme.