**Significance Statement**

Nonlinear wave attributes in transmission lines periodically loaded with tunnel diodes have attracted numerous research attention in the fields of science and engineering. A tunnel diode simulates the nerve axon; therefore, it is applied in physiology to characterize electrical pulses that propagate across a nerve axon. Above all, a tunnel diode line has recently been investigated in the field of high-speed electronics. Each tunnel diode is linked by a series conductor in a bid to achieve high frequency.

Setting the required biasing voltage as well as current for the line produces a steep gradient pulse by the loaded tunnel diodes. A number of schemes employing the tunnel diode lines to produce short electrical pulses have been investigated recently. It has been observed that a voltage edge turns around halfway on a tunnel line with a suitable boundary condition. The edge oscillation has been identified to be a limit cycle that indicates a number of synchronization mechanisms.

Professor Koichi Narahara at Kanagawa Institute of technology in Japan investigated the external synchronization of the oscillating edge on a tunnel diode line implementing numerical along with experimental approaches. He made prediction by phase-evolution equation and validated then by the experimental observations, and this made it natural to consider two edges of oscillations that were mutually synchronized. He considered point-coupled tunnel diodes lines. The research work is now published in * Communications in Nonlinear Science and Numerical Simulation*.

He used current-voltage relationship of the tunnel diode for the calculations. There were two characteristic voltages: valley and peak voltages. The tunnel diodes exhibited negative differential resistance at voltages located between the peak and valley voltages. Any form of tunnel diode such as resonant and Esaki, could be used as a platform to come up with edge oscillation.

The edge was attenuated gradually due to leakage and losses, and it nearly disappeared. At this point, a stable travelling front developed and started propagating back to the near end. When the voltage end returned to the input end, it was reflected again and propagated from the input end. The voltage edge repeated the same process, therefore, oscillating on the line. This edge oscillation had unique attributes including, voltage controlled oscillation frequency and spatial extendedness.

The velocity of the edge did not depend significantly on the input DC voltage. In addition, the edge propagated further, therefore, increasing the turnaround time for greater DC voltages, and for this reason, the frequency of the oscillation decreased when the DC voltage increased.

Professor Koichi Narahara observed that the out-of-phase mutual synchronization reduced the phase noise of an edge oscillation. Initially, an edge oscillation had the unique attribute that the oscillation frequency varied based on the input voltage. Therefore, the synchronized edge oscillations led to a low phase noise voltage controlled oscillator. This phase reduction scheme may function as a better tool to identify coupling structure of tunnel diode lines.

### **Reference**

Koichi Narahara. **Mutual synchronization of oscillating pulse edges in point-coupled transmission lines with regularly spaced tunnel diodes.** Commun Nonlinear Sci Numer Simulat, volume 42 (2017), pages 236–246.