An Analysis of a Class of Variable-Frequency Sinusoidal Oscillators Using a Single Active Element

A class of variable-frequency sinusoidal oscillators requiring only a single active element is analyzed. The frequency of oscillation is approximately proportional (directly or inversely) to the square root of the gm of the active element. The analysis is carried out in two steps. The first step allows one to write the relation between the frequency and the circuit parameters almost by inspection, and also to determine easily an upper bound on the loading. The second step is a more detailed analysis yielding certain circuit constraints which must be met in order that the relations determined in the first step be valid. Two experimental circuits are described and compared to the theory.