Title :
Chaos in mutually coupled phase-locked loops
Author :
Endo, Tetsuro ; Chua, Leon O.
Author_Institution :
Dept. of Electr. Eng., Nat. Defense Acad., Yokosuka, Japan
Abstract :
It is shown both by experiment and by computer simulation that two mutually coupled phase-locked loops (PLLs) can become chaotic when the two PLLs are operating in a marginal out-of-lock condition (that is, they are out of lock but very close to lock-in). The system is described by a fourth-order nonlinear autonomous equation. The power spectrum of the out-of-lock solution (close to lock-in) is observed to be a continuous broad band similar to that of a random signal. The largest Lyapunov exponent is found to be positive. This chaotic regime is observed over a large area of typical damping coefficients used in practical coupled PLL systems
Keywords :
chaos; circuit analysis computing; nonlinear network analysis; phase-locked loops; Lyapunov exponent; chaos; chaotic regime; computer simulation; continuous broad band; coupled PLL systems; damping coefficients; fourth-order nonlinear autonomous equation; marginal out-of-lock condition; mutually coupled; phase-locked loops; power spectrum; Chaos; Chaotic communication; Communication systems; Computer simulation; Equations; Filters; Frequency synchronization; Mutual coupling; Phase locked loops; Voltage-controlled oscillators;
Conference_Titel :
Circuits and Systems, 1990., IEEE International Symposium on
Conference_Location :
New Orleans, LA
DOI :
10.1109/ISCAS.1990.112056
