Mutual Synchronization of Spatially Distributed 24 GHz Oscillators up to Distances of 500 m

Research output: Contribution to journalResearch articleContributedpeer-review



This brief studies how mutual synchronization of oscillators can be achieved for cross-coupling time delays much larger than the period of the oscillations. Using the closed loop transfer function for a system of two mutually delay-coupled phase-locked loops (PLLs) and applying the Nyquist stability criterion, the critical time delay for which stable in- and anti-phase synchronized states become unstable is calculated. The analysis reveals the range of feed-forward loop gains for a given time delay value so that stable in- or anti-phase synchronized states can exist. These theoretical predictions are then verified by measurements with PLLs operating at 24GHz and for cross-coupling time delays ranging from the nano- to the microseconds domain. Such delays are equivalent to coupling at distances of up to 500m. The experimental results show a good agreement with the theoretical predictions. Hence, this brief shows how to setup a network of mutually delay-coupled PLLs and achieve stable synchronized states for a given time delay.


Original languageEnglish
Article number9
Pages (from-to)3689-3693
Number of pages5
JournalIEEE Transactions on Circuits and Systems II: Express Briefs
Issue number9
Publication statusPublished - 20 May 2022

External IDs

Scopus 85130483889
Mendeley eb0f62c5-7e88-377d-bc57-81c70727cb5a
dblp journals/tcasII/HoyerWPWJE22
unpaywall 10.1109/tcsii.2022.3176827
WOS 000848263100017
ORCID /0000-0001-6778-7846/work/142240141
ORCID /0000-0002-6200-4707/work/145698424


Research priority areas of TU Dresden

ASJC Scopus subject areas


  • Synchronization, couplings, delay coupling, delay effects, delays, frequency synchronization, oscillator, phase locked loops, Delay effects, Frequency measurement, Phase locked loops, Voltage-controlled oscillators, Stability criteria, Delays