This work analytically establishes a multi-variable energy function for a three-phase grid-following inverter leveraging a unified equivalent-circuit model for its physical- and control-layer subsystems. This is a significant contribution to the prior art in which analytical approaches to large-signal stability for inverters have largely been attempted with simplified models. Central to our effort is to cast physical- and control-layer dynamics of each dynamical subsystem as an equivalent circuit consisting of familiar circuit elements adopting a positive-sequence modeling framework. An energy function for the inverter is then constructively synthesized by summing the energy functions across the various subsystems that are readily derived from circuit-theoretic principles. Numerical simulations are presented to validate the equivalent-circuit model of the inverter as well as the efficacy of the synthesized energy function in characterizing large-signal stability following a disturbance.