Analysis of ladder oscillators using the averaged potential

This paper analyzes the single‐mode and nonresonant multimode oscillations in the ladder‐type oscillator, using the averaged potential method we introduced previously. In particular, physical description of the phenomenon is presented. The averaged potential represents the time‐average of the loss in the oscillator, and the stable oscillation is produced so that its value is minimized. Based on the fact that the averaged potential is of a quadratic form when the characteristics of the active element are represented by a third‐order polynomial, an algorithm is constructed to determine all minimum points of the averaged potential. Then the condition for stable single‐ or multimode oscillation is derived as the condition for the mode configuration. By this discussion, the physical significance of the stable oscillation mode is clarified, indicating the relation between the property of an active element and the behavior of the ladder oscillator. Finally, the oscillation mode of the ladder oscillator in which active elements are fully or partially included can be described from the viewpoints of the averaged potential method. Examples are shown for the latter case where triple‐ and quadruple‐modes of oscillations can be produced.