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Invisibility cloaking devices constitute a unique and potentially disruptive technology, but only if they can work over broad bandwidths for electrically-large objects. So far, the only known scheme that allows for broadband scattering cancellation from an electrically-large object is based on an active implementation where electric and magnetic sources are deployed over a surface surrounding the object, but whose 'switching on' and other characteristics need to be known (determined) a priori, before the incident wave hits the surface. However, until now, the performance (and potentially surprising) characteristics of these devices have not been thoroughly analysed computationally, ideally directly in the time domain, owing mainly to numerical accuracy issues and the computational overhead associated with simulations of electrically-large objects. Here, on the basis of a finite-difference time-domain (FDTD) method that is combined with a perfect (for FDTD's discretized space) implementation of the total-field/scattered-field (TFSF) interface, we present detailed, time- and frequency-domain analyses of the performance and characteristics of active cloaking devices. The proposed technique guarantees the isolation between scattered- and total-field regions at the numerical noise level (around -300 dB), thereby also allowing for accurate evaluations of the scattering levels from imperfect (non-ideal) active cloaks. Our results reveal several key features, not pointed out previously, such as the suppression of scattering at certain frequencies even for imperfect (time-delayed) sources on the surface of the active cloak, the broadband suppression of back-scattering even for imperfect sources and insufficiently long predetermination times, but also the sensitivity of the scheme on the accurate switching on of the active sources and on the predetermination times if broadband scattering suppression from all angles is required for the electrically-large object. © 2021 Optical Society of America.