Oscillator with Distributed Nonlinear Structure on a Segment of Lossy Transmission Line

Abstract

We consider a model of self-oscillator with distributed amplifying structure realized on a segment of lossy transmission line. The distributed structure of tunnel diode type generates nonlinearity of polynomial type in the hyperbolic transmission line system. The transmission line is terminated by nonlinear reactive elements at both ends. This means that using Kirchhoff’s law we obtain nonlinear boundary conditions. Then a mixed problem for lossy transmission line system is formulated. We give a new approach to present the mixed problem in a suitable operator form and using fixed point method we prove existence-uniqueness of a solution. To apply the theorem proved one has to check just several inequalities. We demonstrate conditions obtained on a numerical example.