Nonlinear Waves in Transmission Lines Periodically Loaded with Tunneling Diodes

Abstract

We review the properties of nonlinear waves on the electrical transmission lines periodically loaded with tunneling diodes (TDs) termed—TD lines.In general, the transmission equation of a linear dispersive line allows both sinusoidal and exponential solutions. However, exponential solutions are usually discarded because they diverge at infinity, and therefore, do not satisfy any physically meaningful boundary conditions. In a TD line, once the input pulse crosses the peak voltage of the loaded TDs, the exponential wave develops atsmaller voltagesthan the peak, and the ordinary sinusoidal wave is coupled to it atgreater voltages. The sinusoidal part can continuously unite with the leading exponential wave, so that the exponential wave can be formed along the dispersive line without violating physical boundary conditions. By developing exponential waves, a TD line exhibits technologically useful properties that result in the generation and management of short pulses.When an impulse is input to a TD line, the resulting exponential wave is much steeper than the input; therefore, the input pulse experiences significant shortening. Moreover, when a rising step pulse, whose bottom and top voltage levels lie in the voltage ranges below and above the peak voltage is input, the pulse edge oscillates on the line. This chapter discusses nonlinear wave propagation on TD lines in detail. We first define TD lines and describes their circuit configuration and principle of operation. We employ an idealized model of a TD line, which makes a comprehensive description of the operating principles possible. It also gives us design criteria for a short-pulse generator or oscillator using TD lines. We then examine the validity of the analytically obtained design criteria through numerical integration of the transmission equations of a TD line. We alsocharacterize the line using full-wave calculations for monolithically integrated lines. Next, severalexperimental results are described, which are obtained by the time-domain measurements using TD lines breadboarded with Esaki diodes. Finally, we describe the potential of TD lines for the management of short pulses.