Efficient time-domain analysis of highly dispersive linear and non-linear metamaterial waveguide and antenna structures operated in the impulse-regime

A numerical method is proposed for the analysis of highly dispersive linear and non-linear metamaterial structures. Firstly, pulse propagation along non-linear composite right/left-handed (CRLH) transmission line (TL) is studied. The dispersive CRLH line is loaded with hyper-abrupt diodes to achieve non-linearity. The characteristic impedance and propagation constant of each unit-cell of the CRLH TL is varied at each time-step, and the non-uniform line is then analysed. A novel interpolation scheme, based on the smooth behaviour of the propagation constant with small variations of the shunt capacitor is proposed. Numerical results show that high accuracy and up to 80% reduction of the computational cost is achieved. A general example which combines dispersion and non-linearity is presented, validated and discussed. Secondly, the impulse-regime radiation of a leaky-wave antenna is analysed and used to describe a real-time spectrogram analyser (RTSA). A new calibration method for the system, which takes into account the directivity variation of the antenna with frequency, is proposed. This method provides an extremely fast and accurate tool to characterise the behaviour of leaky-wave-based RTSA systems.