PALS: Distributed Gradient Clocking on Chip

Johannes Bund, Matthias Fugger, Moti Medina

Research output: Contribution to journalArticlepeer-review


Consider an arbitrary network of communicating modules on a chip, each requiring a local signal telling it when to execute a computational step. There are three common solutions to generating such a local clock signal: 1) by deriving it from a single, central clock source; 2) by local, free-running oscillators; or 3) by handshaking between neighboring modules. Conceptually, each of these solutions is the result of a perceived dichotomy in which (sub)systems are either clocked or asynchronous. We present a solution and its implementation that lies between these extremes. Based on a distributed gradient clock synchronization (GCS) algorithm, we show a novel design providing modules with local clocks, the frequency bounds of which are almost as good as those of free-running oscillators, yet neighboring modules are guaranteed to have a phase offset substantially smaller than one clock cycle. Concretely, parameters obtained from a 15-nm application specific integrated circuit (ASIC) simulation running at 2 GHz yield mathematical worst-case bounds of 20 ps on the phase offset for a $32\,\, \times 32$ node grid network.

Original languageEnglish
Pages (from-to)1740-1753
Number of pages14
JournalIEEE Transactions on Very Large Scale Integration (VLSI) Systems
Issue number11
StatePublished - 1 Nov 2023

Bibliographical note

Publisher Copyright:
© 1993-2012 IEEE.


  • Globally asynchronous locally synchronous (GALS)
  • gradient clock synchronization (GCS)
  • on-chip distributed clock generation


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