New Soliton Solution of a Varactor-Loaded Nonlinear Transmission Line

The nonlinearity of a nonlinear transmission line (NLTL) may have a variety of forms. The Korteweg-de Vries (KdV) equation is the governing equation of a highly specific category of NLTLs having a C-V characteristic as C(V) = C
₀
(1-bV), but works as an approximate model in a general NLTL having any other kinds of nonlinearities. Here, the soliton response of a varactor-loaded NLTL is studied analytically. The presented analysis gives the exact nonlinear partial differential equation (PDE) governing these networks. It is shown that the obtained PDE, being different from the KdV equation, has soliton solutions showing the well-known properties of the KdV solitons. These obtained solitons have shown velocities proportional to their amplitudes, but in a different way compared to the KdV and generalized KdV solitons. The simulation and experimental results confirm that the presented analysis gives more accurate results compared to those of a KdV approximation of these networks. The comparison with the data obtained from the reported experimental studies of other researchers in this field reinforces these analytical results. The presented analysis is useful in more concretely modeling of the soliton wave propagation on NLTLs.