Loop gain of the common-gate Colpitts oscillator

This study presents the derivations of the voltage transfer functions of the amplifier A, the feedback network β, the loop gain T, the closed-loop gain A_f and also the characteristic equation for the common-gate (CG) Colpitts oscillator, using the small-signal model of the metal-oxide-semiconductor field-effect transistor (MOSFET) CG Colpitts oscillator. Using the characteristic equation, the expressions for the oscillation frequency of the sinusoidal output voltage and the condition for oscillation in steady state are derived. The characteristic equation is also used to obtain a plot of trajectories of the closed-loop poles of the CG Colpitts oscillator by varying the MOSFET small-signal transconductance g_m. The locations of the complex conjugate poles of closed-loop gain that depict the starting and steady-state conditions for oscillations are presented. Nyquist plots of the loop gain are given to illustrate the startup and steady-state conditions of oscillations. Simulation and experimental results to verify the theory are also given.