  In this paper, we study the effect of small Brownian noise on a switching
dynamical system which models a first-order DC/DC buck converter. The state
vector of this system comprises a continuous component whose dynamics switch,
based on the ON/OFF configuration of the circuit, between two ordinary
differential equations (ODE), and a discrete component which keeps track of the
ON/OFF configurations. Assuming that the parameters and initial conditions of
the unperturbed system have been tuned to yield a stable periodic orbit, we
study the stochastic dynamics of this system when the forcing input in the ON
state is subject to small white noise fluctuations of size $\varepsilon$,
$0<\varepsilon \ll 1$. For the ensuing stochastic system whose dynamics switch
at random times between a small noise stochastic differential equation (SDE)
and an ODE, we prove a functional law of large numbers which states that in the
limit of vanishing noise, the stochastic system converges to the underlying
deterministic one on time horizons of order $\mathscr{O}(1/\varepsilon^\nu)$,
$0 \le \nu < 2/3$.
