Delayed Feedback and Chaos on the Driven Diode-Terminated Transmission Line

Abstract

A simple model of a distributed, non-linear circuit that produces chaos at GHz frequencies is introduced and tested experimentally. The model circuit is a driven diode-terminated transmission line with the transmission line impedance mismatched to that of the source. Experiments were performed with sinusoidal driving frequencies of 10 MHz to 1.2 GHz, driving powers of -30 to +50 dBm and transmission line delay times from 3 to 20 ns. Diode reverse recovery times ranged from 4 to 100 ns. As a result of many experiments, it was found that chaotic behavior was strongly dependent on the unbiased, small-signal reactance of the system as seen by the driving source, and influenced by an applied DC voltage-bias across the diode. In the experiments that showed period-doubling and / or chaos, the reverse recovery times of the diodes were on the order of both the driving period and the delay time of the circuits. Comparisons between theory and experiment are in general agreement. Chaos produced with a driving frequency of 1.105 GHz has been observed experimentally.