Mode analysis of a multimode ladder oscillator

An arbitrary number of van der Pol oscillators mutually coupled by inductances or capacitances (i.e., a low-pass and a high-pass ladder oscillator) is investigated using the equivalent linearization technique of Kryloff and Bogoliuboff. The network is almost linear and is described by a nonlinear vector differential equation. The active element is assumed to be a cubic nonlinear shunt conductance. It is demonstrated that 1) nonresonant simultaneous double-mode oscillation can be stably excited in a ladder oscillator in which both end cells are opened, 2) but it is not excited in a ladder oscillator in which both end cells are grounded, 3) and more than three modes can not be excited in any ladder oscillator. Experiments confirm that nonresonant simultaneous double-mode oscillation can be excited stably in a ladder oscillator in which both end cells are opened. The experimental amplitudes and oscillating frequencies agree well with theoretical values.