Study of chaos in the buck converter

A DC-DC buck converter controlled by naturally-sampled, constant-frequency pulsewidth modulation in continuous conduction mode gives rise to a great variety of behavior, depending on the values of the parameters of the circuit. We analyze the one-periodic and two-periodic orbits which cross the voltage ramp once per cycle, and we study their stability by computing the characteristic multipliers associated with each one. Subharmonics, bifurcations, and the presence of a strange attractor are also studied. A plot of the number of crossings in the ramp is drawn. This becomes a helpful tool for investigating the evolution of the trajectories when they are close to the attractor. When analytic computations are impossible, we resort to numerical algorithms to simulate the orbits.