  We present a general framework for the computation of structure-agnostic
bounds on the performance of passive cloaks over a nonzero bandwidth. We apply
this framework in 2D to the canonical scenario of cloaking a circular object.
We find that perfect cloaking using a finite-sized isotropic cloak is
impossible over any bandwidth, with the bounds scaling linearly with the
bandwidth before saturating due to the finite size of the cloak and the
presence of material loss. The bounds also exhibit linear scaling with material
loss in the cloak and linear scaling with the inverse of the radial thickness
of the design region before saturation due to finite-size effects or the
presence of material loss. The formulation could readily find applications in
the development of cloaking devices, setting expectations and benchmarks for
optimal performance.
