Effects of Inductor Parasitics on Loop Gain in Single‐Ended Common‐Drain Colpitts Oscillator

ABSTRACT Derivation of the characteristic equation (CE) of a single‐ended common‐drain (CD) Colpitts oscillator with inductor parasitics is presented using a small signal model. The inductor of the LC resonant circuit is modeled with parasitic equivalent series resistance (ESR) and parasitic equivalent parallel capacitance (EPC). By applying the characteristic equation, expressions for the oscillation frequency of the sinusoidal output as well as the loop gain condition for steady‐state oscillation are derived. It is presented that, while both parasitic quantities are present in the expressions for oscillation frequency and steady‐state oscillation condition, with reasonable approximations it is inferred that their influence is selective. Namely, it is shown that the parasitic ESR, in spite of its small value, in particular cases may have significant influence on the condition for steady‐state oscillation. On the other hand, the parasitic EPC can influence the oscillation frequency when its value is of comparable orders with the capacitance of the LC resonant circuit. In addition, the voltage transfer functions of the amplifier stage, feedback network, and the loop gain with non‐zero quantities for inductor parasitics are also presented. All derivations apply for CD amplifier with constant current bias, self bias, or combination bias topology.