Inevitability of phase-locking in a charge pump phase lock loop using deductive verification

Hafiz Ul Asad, Kevin D. Jones

Research output: Chapter in Book/Report/Conference proceedingConference proceedings published in a bookpeer-review

Abstract

Phase-locking in a charge pump (CP) phase lock loop (PLL) is said to be inevitable if all possible states of the CP PLL eventually converge to the equilibrium, where the input and output phases are in lock and the node voltages vanish. We verify this property for a CP PLL using deductive verification. We split this complex property into two sub-properties defined in two disjoint subsets of the state space. We deductively verify the first property using multiple Lyapunov certificates for hybrid systems, and use the Escape certificate for the verification of the second property. Construction of deductive certificates involves positivity check of polynomial inequalities (which is an NP-Hard problem), so we use the sound but incomplete Sum of Squares (SOS) relaxation algorithm to provide a numerical solution.

Original languageEnglish
Title of host publicationGLSVLSI 2015 - 25th 2015 Great Lakes Symposium on VLSI
PublisherAssociation for Computing Machinery (ACM)
Pages295-300
Number of pages6
ISBN (Electronic)9781450334747
DOIs
Publication statusPublished - 20 May 2015
Event25th Great Lakes Symposium on VLSI, GLSVLSI 2015 - Pittsburgh, United States
Duration: 20 May 201522 May 2015

Publication series

NameProceedings of the ACM Great Lakes Symposium on VLSI, GLSVLSI
Volume20-22-May-2015

Conference

Conference25th Great Lakes Symposium on VLSI, GLSVLSI 2015
Country/TerritoryUnited States
CityPittsburgh
Period20/05/1522/05/15

ASJC Scopus subject areas

  • General Engineering

Keywords

  • AMS circuits
  • Deductive verification
  • Escape certificate
  • Lyapunov certificate
  • SOS programming

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