# Enhanced phase noise modeling of fractional-N frequency synthesizers

Journal Article (Journal Article)

Mathematical models for the behavior of fractional-N phase-locked-loop frequency synthesizers (Frac-N) are presented. The models are intended for calculating rms phase error and determining spurs in the output of Frac-N. The models describe noise contributions due to the charge pump (CP), the phase frequency detector (PFD), the loop filter, the voltage control osicllator, and the delta-sigma modulator. Models are presented for the effects of static CP gain mismatch, CP dynamic mismatch and PFD reset delay mismatch. A simple analytic expression shows the level of AΔ∑ sequence noise caused by static CP current mismatch. We further show that un-equal rise time and fall time constants of the CP result in dynamic mismatch noise. Reset delay mismatch in PFD is shown to also contribute significantly to close-in phase noise. The model takes into account the reduction in CP thermal and flicker noise due to the changing duty cycle of Frac-N CP. Our model is therefore useful in characterizing the noise performance of Frac-N at the system-level, simplifying the design of fractional-N synthesizers and transmitters. Analytical and simulated results are compared and show good agreement with prior published data on Frac-N realizations. © 2005 IEEE.

### Full Text

### Duke Authors

### Cited Authors

- Arora, H; Klemmer, N; Morizio, JC; Wolf, PD

### Published Date

- January 1, 2005

### Published In

### Volume / Issue

- 52 / 2

### Start / End Page

- 379 - 395

### International Standard Serial Number (ISSN)

- 1057-7122

### Digital Object Identifier (DOI)

- 10.1109/TCSI.2004.841594

### Citation Source

- Scopus