Soliton Generation and Pulse Optimization using Nonlinear Transmission Lines

Nonlinear Transmission Lines (NLTLs) have gained significant interest due to their ability to generate ultra-short, high-power RF pulses, which are valuable in applications such as ultrawideband radar, space vehicles, and battlefield communication disruption. The waveforms generated by NLTLs offer frequency diversity not typically observed in High-Power Microwave (HPM) sources based on electron beams. Nonlinearity in lumped element transmission lines is usually introduced using voltage-dependent capacitors due to their simplicity and widespread availability. The periodic structure of these lines introduces dispersion, which broadens pulses. In contrast, nonlinearity causes higher-amplitude regions to propagate faster. The interaction of these effects results in the formation of stable, self-localized waveforms known as solitons.
Soliton propagation in NLTLs can be described by the Korteweg-de Vries (KdV) equation. In this thesis, the Bäcklund Transformation (BT) method has been used to derive both single and two-soliton solutions of the KdV equation. This method links two different partial differential equations (PDEs) and their solutions to produce solutions for nonlinear PDEs. The two-soliton solution is obtained from the single soliton solution using a nonlinear superposition principle known as Bianchi’s Permutability Theorem (BPT). Although the KdV model is suitable for NLTLs where the capacitance-voltage relationship follows that of a reverse-biased p-n junction, it cannot generally represent arbitrary nonlinear capacitance characteristics.
To address this limitation, a Finite Difference Time Domain (FDTD) method has been developed to numerically solve the NLTL equation for soliton propagation. To demonstrate the pulse sharpening and RF generation capability of a varactor-loaded NLTL, a 12-section lumped element circuit has been designed and simulated using LTspice and verified with the calculated result. In airborne radar systems, operational constraints such as range, accuracy, data rate, environment, and target type require flexible waveform design, including variation in pulse widths and pulse
repetition frequencies. A gradient descent optimization technique has been employed to generate pulses with varying amplitudes and frequencies by optimizing the NLTL parameters. This work provides a theoretical analysis and numerical simulation to study soliton propagation in NLTLs and demonstrates the generation of tunable RF pulses through optimized circuit design.