Chapter 16 - Low-noise oscillator design

Abstract

When we covered oscillators in Chapter 15 we postulated that, at power on, oscillations originate from noise perturbations inherent in the various components, that then get amplified by the gain element, resulting in a signal that builds up in amplitude and is pulled toward the oscillator design frequency by a frequency selective element (the resonator or tank circuit). Aside from the consequent, profound observation that noise is essential to initiating oscillation, this description also implies that the gain element is inherently nonlinear. The reasoning is as follows: Although the Barkhausen amplitude criterion of equation (15.2.4) implies unity loop gain in steady-state conditions, if the oscillator did have unity loop gain for all signal levels then the initial noise perturbations would never get amplified sufficiently to build up to the final signal amplitude. Notwithstanding the Barkhausen criterion, the effective loop gain must be significantly greater than unity at very low signal levels, reducing to exactly unity as the signal amplitude approaches the steady-state level. Likewise, under steady-state conditions, if the signal amplitude should drop for any reason, the higher loop gain at lower amplitudes, due to this loop gain nonlinearity, will drive the amplitude back up to a steady-state level, which is limited, at its upper bound, by the power supply voltage. In short, it is the inherent nonlinearity of the gain element (i.e., high gain at low signal levels and low gain at high signal levels) that primarily acts to maintain the oscillator output signal at a constant amplitude. This fundamental amplitude stabilization mechanism in oscillators was first described by Lord Rayleigh as early as 1896.