  Despite the prospect of next-generation electronic technologies has spurred
the investigation of the remarkable topological magnetoelectric response, it
remains largely unexplored its potential in the application of basic electronic
devices. In this paper, we undertake this task at the theoretical level by
addressing the $\theta$-electrodynamics and examine electromagnetic properties
(e.g. tunable inductance, operating frequency range, and power consumption) of
three fundamental passive magnetic devices endowed with this effect: the
primitive transformer, the bilayer solenoid inductor, and the solenoid
actuator. We further exploit the methodology of magnetic circuits to obtain an
extended Hopkinson's law that is valid for both topological and ordinary
magnetoelectric responses (provided it is uniform in the bulk). Under low-power
conditions, we find out that the functionally passive part of the
topological-magnetoelectric transformer, solenoid inductor as well as solenoid
actuator is indistinguishable from the conventional situation up to
second-order in the magnetoelectric susceptibility; and argue that the main
benefit of using topological insulators essentially relies on a lower power
consumption. Our theoretical framework is also convenient to analyse
magnetoelectric inductors endowed with a relatively large magnetoelectric
susceptibility, they display a broad inductance tunability of over 200% up to
100 GHz in the millimeter length scale. Conversely, our treatment predicts that
the operating frequency range could be restricted below the ultra low frequency
by a significantly strong magnetoelectric response (e.g. retrieved by certain
multiferroic heterostructures).
