Bifurcations and Averaging in a Series Array of Tunnel Diodes

We investigate nonlinear electrical conduction properties of a series array of tunnel diodes using both numerical simulation and experimental measurement. Tunnel diodes are negative differential resistance (NDR) circuit elements and, in a series configuration, they provide a useful model system for nonlinear transport in more complex electronic structures such as semiconductor superlattices [1]. Measurements reveal high-frequency (of order 1 GHz), small-amplitude oscillations in the current when the diodes are voltage-biased in the NDR region. For a system of $N$ diodes, these fast oscillations are associated with Hopf bifurcations in a $3N$-dimensional nonlinear circuit model that includes intrinsic reactances for each diode. A nonlinear averaging method is applied to the full model, allowing the elimination of fast time scale behavior, and results in a reduced dynamical system of dimension $N$. Simulations of the reduced model are found to accurately describe the experimental circuit behavior on time scales that are much greater than the oscillatory time scale. [1] H. Xu and S. W. Teitsworth, Phys. Rev. B {\bf 76}, 235302 (2007).