Analytical modeling of electrical solitons in a nonlinear transmission line using Schamel-Korteweg deVries equation

Nonlinear transmission lines (NLTLs) provide an effective means of experimental investigation of nonlinear dispersive media paving the way for accurate modeling of electrical solitons. In this work, an appropriate analytical model is proposed to analyze and predict electrical solitons in an NLTL. The model is based on a new form of nonlinearity which utilizes fractional powers to render an accurate representation of the Capacitance-Voltage (C-V) curve, even for relatively higher voltages. A complete analytical procedure is adopted to obtain the soliton solution in an NLTL. Nonlinear analysis results in a Schamel type Korteweg deVries (S-KdV) equation, instead of a conventional KdV equation. An extended version of the Tanh method is employed to find the solution of S-KdV which yields narrower solitons of Sech⁴ shape. The proposed model is validated experimentally by using a specially designed NLTL (100 sections) comprising of linear inductors and nonlinear capacitances. Square pulses with a repetition rate of 100 kHz are used to generate the solitons. The comparative analysis shows excellent profile matching between theoretically predicted and experimentally obtained solitons. Furthermore, in consistence with the prediction of the proposed model, the product of the Amplitude and fourth power of the Width (A × W⁴) is found to be constant in experimental results. This model proposed in the present work can be of help in understanding and predicting the behavior of electrical solitons in NLTLs.