  Artificially created media allow employing material parameters as additional
valuable degrees of freedom in tailoring electromagnetic scattering. In
particular, metamaterials with either negative permeability or permittivity
allow creating deeply subwavelength resonant structures with relatively high
scattering crosssections. However, the equivalence principle allows replacing
volumetric structures with properly designed curved impedance surfaces,
ensuring the same electromagnetic properties. Here, we examine this statement
from a practical standpoint, considering two structures, having a dipolar
electric resonance at the same frequency. The first realization is based on
arrays of inductively loaded electric dipoles printed on stacked circuit boards
(a volumetric metamaterial), while the second structure utilizes a 4-wire
spiral on a spherical surface (surface impedance realization). An intermediate
conclusion is that the surface implementation tends to outperform the
volumetric counterparts in the scenario when a single resonance is involved.
However, in the case where multiple resonances are overlapping and lossy
materials are involved, volumetric realization can have an advantage. The
discussed structures are of significant importance to the field of electrically
small antennas, superdirective antennas, and superscatterers, which find use in
wireless communications and radar applications, to name just a few.
