Closed-loop nonlinear modeling of wideband ΣΔ fractional-N frequency synthesizers

Hiva Hedayati, Bertan Bakkaloglu, Waleed Khalil

Research output: Contribution to journalArticlepeer-review

52 Scopus citations


Wideband low-noise ΣΔ fractional-N synthesizers pose several design challenges due to the nonlinear time-varying nature of synthesizer building blocks such as phase frequency detectors (PFDs), charge pump, and frequency dividers. Loop nonlinearities can increase close-in phase noise and enhance spurious tones due to intermodulation of high-frequency quantization noise and tonal content; therefore, an accurate simulation model is critical for successful implementation of loop parameters and bandwidth widening techniques. In this paper a closed-loop non-linear simulation model for fractional-N synthesizers is presented. Inherent nonuniform sampling of the PFD is modeled through an event-driven dual-iteration-based technique. The proposed technique generates a vector of piecewise linear time-voltage pairs, denning the voltage-controlled oscillator (VCO) control voltage. This method also lends itself to modeling of cyclostationary thermal and nicker noise generated by time-varying charge-pump current pulses. A flexible third-order ΣΔ modulated RF synthesizer core with integrated loop filter and LC-tank VCO is designed and fabricated in 0.13-μm CMOS process in order to validate the technique experimentally. The proposed modeling technique was able to predict in-band spur power levels with 1.8-dB accuracy, and spur frequency offsets with lower than 400-Hz accuracy with several programmable nonidealities enabled.

Original languageEnglish (US)
Article number1705684
Pages (from-to)3654-3663
Number of pages10
JournalIEEE Transactions on Microwave Theory and Techniques
Issue number10
StatePublished - Oct 2006


  • Fractional-N frequency synthesizers
  • Phase noise
  • Phase-locked loops (PLLs)
  • Quantization noise
  • Sigma-delta modulation
  • Spurs

ASJC Scopus subject areas

  • Radiation
  • Condensed Matter Physics
  • Electrical and Electronic Engineering


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