On the First-order Probability Distribution of the Van der Pol Type Oscillator Output†

Applying the equivalent linearization approximation and the Fokker-Planck equation, we derive the joint first-order probability density of u(t) and $, where u(t) is the voltage on the oscillator tank circuit. This result is used to calculate the expected number of zero crossings of $ and the first-order probability density of the envelope of the oscillator output.