Mutual synchronization of oscillating pulse edges in point-coupled transmission lines with regularly spaced tunnel diodes

Abstract In this paper, we investigate the mutual synchronization of oscillating pulse edges developed in point-coupled transmission lines periodically loaded with tunnel diodes (TDs). When supplied with an appropriate voltage at the end of a TD line, a pulse edge exhibits a spatially extended limit-cycle oscillation on the line. In this study, the properties of this mutual synchronization of edge oscillation established in two coupled TD lines are discussed. We examine the mutual synchronization using phase sensitivity calculated by applying phase-reduction scheme to the transmission equation of a TD line. The phase difference between the synchronized edges and oscillation frequency is calculated depending on the coupling cell. We then validate the reduced model via time-domain calculations of edge oscillations.

[1]  Yoshiki Kuramoto,et al.  Chemical Oscillations, Waves, and Turbulence , 1984, Springer Series in Synergetics.

[2]  K. Narahara.  Electromagnetic continuous-wave generation using switch lines , 2006 .

[3]  I. Richer.  The Switch-Line: A Simple Lumped Transmission Line that can Support Unattenuated Propagation , 1966 .

[4]  D. Jäger,et al.  Development of Short Electrical Pulses in a Schottky Line Periodically Loaded with Resonant Tunneling Diodes , 2012 .

[5]  Alwyn C. Scott,et al.  Neuroscience: A Mathematical Primer , 2002 .

[6]  Koichi Narahara,et al.  Experimental characterization of short-pulse generation using switch lines , 2008, IEICE Electron. Express.

[7]  K. Miyakawa,et al.  External synchronization of oscillating pulse edge on a transmission line with regularly spaced tunnel diodes. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  M. Reddy,et al.  A traveling-wave resonant tunnel diode pulse generator , 1994, IEEE Microwave and Guided Wave Letters.

[9]  Alwyn C. Scott,et al.  Active and nonlinear wave propagation in electronics , 1970 .

[10]  Eugene M. Izhikevich,et al.  Phase Equations for Relaxation Oscillators , 2000, SIAM J. Appl. Math..

[11]  S. Yoshizawa,et al.  An Active Pulse Transmission Line Simulating Nerve Axon , 1962, Proceedings of the IRE.

[12]  A. Balanov,et al.  Synchronization: From Simple to Complex , 2008 .

[13]  A. Demir,et al.  Phase noise in oscillators: a unifying theory and numerical methods for characterization , 2000 .