Period-doubling analysis and chaos detection using commercial harmonic balance simulators

Two of the most common phenomena leading to chaos are the period-doubling c ascade and the formation of transverse homoclinic orbits. In this paper, a bifurcation analysis technique is presented for the prediction of both phen omena in microwave circuits, The fact that the technique is based on the us e of commercial harmonic balance software constitutes a major advantage for the circuit designer. The accuracy of the method relies on the capability to detect and calculate the successive period doublings, which, in period-d oubling cascades, provides a good estimation of the parameter values for th e onset of chaos. Another important aspect of the new method is the equilib rium point determination, necessary for the prediction of the homoclinic ch aos. The accuracy in the calculation of the limit cycle, taking into accoun t the most influential period doublings, ensures a good estimation of the p arameter values for the formation of possible homoclinic orbits. In order t o validate the method, it is initially applied to an RL-diode circuit, with a period-doubling route to chaos, A practical microwave frequency doubler is then analyzed, determining its parameter ranges for stable operation. Ex cellent results are obtained in comparison with the time-domain simulations . As an example of the method's capabilities for the prediction of homoclin ic chaos, the bifurcation loci of Chua's circuit, with a cubic nonlinearity , are obtained and they agree closely with time-domain simulations.