Using Chaos to Broaden the Capture Range of the Phase-Locked Loop

Phase-locked loops (PLLs) are a common and useful family of circuits; their function is to hunt for and synchronize to an external sine wave signal. Every radio contains a PLL that helps it "lock on" to the closest station. The range over which the circuit can accomplish this task, called the capture range, is an important design parameter - consider, for instance, the button on your car radio that shifts its range from "city" (a narrow band that lets the circuit capture one radio station from all of the closely spaced stations in an urban area) to "country" (a wide band that gives the circuit more leeway in which to hunt).

Chaos can be used to broaden the capture range, improving the design of the circuit. Specifically, we judiciously drive the loop into a specific chaotic regime, using the denseness of the system's chaotic attractor to establish the control-theoretic property known as reachability for the loop's locked state, thereby expanding the capture range out to the original lock range limits.


  • Doug Straub, a Ph.D. student in Electrical and Computer Engineering, verified this idea experimentally as his final project in CSCI 6446.
  • Prof. Liz Bradley, project leader.