{'fraction_non_alphanumeric': 0.018743109151047408, 'fraction_numerical': 0.002205071664829107, 'mean_word_length': 5.485714285714286, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Oscillator Modeling and Phase Noise

Oscillator Modeling and Phase Noise by Brian Nguyen Limketkai Doctor of Philosophy in Engineering-Electrical Engineering and Computer Sciences University of California, Berkeley Professor Robert W. Brodersen, Chair Using a dynamical systems perspective, we develop a method to calculate phase noise in oscillators based on a particle diffusion model. Starting from the basic nonlinear equations of motion, a phase diffusion equation is formulated by viewing the system in state space. The resulting phase diffusion solution is then found approximately by using multiple scale perturbation theory to get closed-form analytical expressions. In this way, the effects of the nonlinearities on the phase diffusion become evident. Similar techniques are then also applied to finding the locking bandwidth of a 2:1 injection-locked frequency divider. Robert W. Brodersen, Chair