Analysis of two coupled NLTL-based oscillators
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A system of two coupled oscillators based on nonlinear transmission lines (NLTL) is proposed for pulsed-shaping applications. The maximum propagation frequency through the NLTL is calculated and optimized with a realistic numerical method. With additional design considerations, this is used to increase the waveform steepening capabilities of the NLTL and obtain an oscillator based on the shockwave concept. Coupling two of these oscillators with slightly different characteristics various pulse shapes can be achieved through composition of the individual waveforms. The coupled-system behavior is understood with the aid of a new reduced-order formulation, which takes into account the differences between the oscillator elements. The formulation is extended for stability and phase-noise analysis. It provides valuable insight into the impact of the individual oscillator characteristics on the coupled-system dominant poles and unsymmetrical stable phase-shift range. It also explains the variation of the spectral density with the phase shift, as well as the mechanisms for the phase noise corners observed when increasing the offset frequency. A more realistic analysis of the coupled system is also carried out with the conversion-matrix approach, using cyclostationary noise sources. The analysis and design techniques have been applied to several prototypes at 0.8 GHz.