A highly efficient time-domain simulation method for circuits characterized by carrier-modulated signals is presented. It leverages a new formulation of dynamic phasors. It significantly reduces the computational burden by achieving up to two orders of magnitude improvement in simulation speed compared to conventional formulations, while preserving numerical accuracy. It is well suited for simulating electrical power grids characterized by very fast, localized disturbances that require electromagnetic simulations (e.g., faults), as well as by slow electromechanical dynamic responses, such as those following fault clearing. To demonstrate its ability to simulate complex multi-scale dynamics with drastically reduced CPU time, the method is validated using a set of benchmark grids of increasing complexity, the final one being a transmission system with several distribution feeders, each including a multitude of inverter-based resources (IBRs). The sheer number of IBRs and control logic are such that an accurate assessment of overall grid dynamics and stability requires a detailed modeling of both transmission networks and active distribution feeders. These power grids can easily yield models with hundreds of thousands of equations, whose simulation would be prohibitive unless advanced solutions such as the one presented here are adopted.