RMS frequency error performance and spurious signals in two-point modulators due to path imbalances

Abstract

In this study the authors introduce an analysis of rms frequency error performance and spurious signals generated by two-point modulators. The analysis is not limited to a constant delay and magnitude imbalance between modulation paths but allows frequency-dependent group delay and amplitude variations as well. Moreover, a discrete time phase frequency detector model is incorporated in Laplace domain analysis that takes into account the sampling nature of a phase-locked loop (PLL). Using the spectrum of pulse width modulated charge pump pulses, the spurious signals at the output of the PLL are evaluated. The proposed formulae are tested on a practical setup and quite accurate results are obtained.