Low phase-noise oscillator design using large signal transfer function and complex quality factor

In this study we use large signal closed loop transfer function and complex quality factor to design a low phase noise feedback oscillator. The method offers two major advantages. First it evaluates the closed loop transfer function, which inherently takes into account the impedance mismatch between the elements of the loop and the nonlinear behavior of the active device. These factors affect the loaded quality factor of the frequency stabilization element, as well as the location of frequency at which minimum phase noise is obtained. Secondly the method uses complex quality factor to estimate the frequency of best phase noise performance. Unlike the conventional quality factor which only uses the derivative of phase response, complex quality factor takes into account both amplitude and phase variations and provide better insight for low noise design. It has been shown experimentally that complex quality factor changes significantly for saturated loop. By using complex quality factor of saturated loop, phase noise performance can be more accurately predicted compared to the methods which do not take saturation effects into account.