Loop Gain of the Common-Drain Colpitts Oscillator

This paper presents the derivations of the voltage transfer functions of the amplifier A, the feedback network β, and the loop gain T of the common-drain (CD) Colpitts oscillator, using the small-signal model of the CD Colpitts oscillator. The derivation of the characteristic equation of the CD Colpitts oscillator is presented. Using the characteristic equation, the equation for the oscillation frequency of the sinusoidal output voltage and the condition for steady-state oscillation are derived. The characteristic equation is used to obtain a plot of trajectories of the poles of the CD Colpitts oscillator by varying the MOSFET small-signal transconductance gm. The locations of the complex conjugate poles depicting starting and steady-state conditions for oscillations are also presented. Keywords—Band-pass feedback networks, Colpitts oscillator, common-drain amplifier, location of poles, loop gain, oscillation conditions, positive feedback, resonant oscillators, tuned oscillators, voltage-controlled oscillators (VCO).