Ultra-wideband transmission lines for next-generation digital systems: Modelling and analysis

The study aimed to theoretically analyse the modelling of pulse transmission in ultra-wide bandwidth media with consideration of losses, dispersion and phase shifts. A comprehensive approach was used, combining mathematical modelling and analysis of electromagnetic processes in various transmission line topologies, such as coaxial, stripline, microstrip, and structures based on metamaterials and superconductors. The study determined that the dispersion, frequency-dependent losses caused by the surface resistance, which increased proportionally to the root of the frequency, and dielectric losses with a frequency-dependent tangent caused distortion of pulses with delays of 10-100 picoseconds and phase shifts of up to 20 degrees. For pulses with a duration of 0.5 nanoseconds, the spectral width was about 2 GHz, which confirmed the dependence between the pulse duration and the frequency range. Modelling using the telegraphic equations, the Fourier transform and numerical methods such as finite difference time domain and finite element analysis quantified losses of up to 3-6 decibels per 10 cm and the critical line length, which depended on geometric inhomogeneities. The advantages of superconducting structures with losses of less than 0.01 decibels per metre up to 100 GHz and coplanar lines for transmission speeds of 25-50 Gbps were revealed. The frequency-dependent performance criteria were formulated for a reasonable choice of the line type depending on the requirements for minimising phase shifts and pulse attenuation. The practical significance of the results is determined by the possibility of their use by specialists in the design of telecommunications and sensor systems to improve the reliability and accuracy of data transmission in real-world conditions