  The latest generation of transistors are nanoscale devices whose performance
and reliability are limited by thermal noise in low-power applications.
Therefore developing efficient methods to compute the voltage and current
fluctuations in such non-linear electronic circuits is essential. Traditional
approaches commonly rely on adding Gaussian white noise to the macroscopic
dynamical circuit laws, but do not capture rare fluctuations and lead to
thermodynamic inconsistencies. A correct and thermodynamically consistent
approach can be achieved by describing single-electron transfers as Poisson
jump processes accounting for charging effects. But such descriptions can be
computationally demanding. To address this issue, we consider the macroscopic
limit which corresponds to scaling up the physical dimensions of the transistor
and resulting in an increase of the number of electrons on the conductors. In
this limit, the thermal fluctuations satisfy a Large Deviations Principle which
we show is also remarkably precise in settings involving only a few tens of
electrons, by comparing our results with Gillespie simulations and spectral
methods. Traditional approaches are recovered by resorting to an ad hoc
diffusive approximation introducing inconsistencies. To illustrate these
findings, we consider a low-power CMOS inverter, or NOT gate, which is a basic
primitive in electronic design. Voltage (resp. current) fluctuations are
obtained analytically (semi-analytically) and reveal interesting features.
