Noise response of non-linear oscillators
Yusuf Bozkurt Ozal · Spiral (Imperial College London) · 1968
The main effect of noise on the performance of a non-linear oscillator may be characterised in two ways: a) by a broadening in the output spectrum, or b) by an uncertainty in the oscillator frequency (i.e. as measured by zero counting method).There are many methods for analysing this problem.In this work a new method using generalised definitions of amplitude and phase is presented.The contents of the chapters are as follows: Chapter 1.An introduction to the problem of noise in non-linear oscillators is made.After describing main sources and effects of noise, a brief account of existing methods is given.Method of the work is introduced and compared with other approaches.Finally, a statement of originality is made.Chapter 2. Normalized equations are derived from physical circuits.Various solutions of the noiseless oscillator equation are presented.Chapter 3. The potential function are developed and their relationship to amplitude and phase demonstrated.A generalisation of phase and amplitude is 'made.Chapter 4. Analysis of the noise is made by transforming the oscillator equation into the curvilinear co-ordinates formed by the equipotentials of the potential functions.Chapter 5. Discussion of the results and suggestions for future work are made.