Abstract
Coordinate transformation (CT) theory has shown great potentials in manipulating both time-varying and static fields for different physics ranging from electromagnetism and acoustics to electrostatic and thermal science. Nevertheless, as inhomogeneous and anisotropic materials are required to be realized for the implementation of CT-based devices, the applicability of this method is restricted due to difficulties in the fabrication process. In this paper, based on transformation electrostatic (TE) methodology, the design principle of an arbitrary shape dc electric concentrator is established which yields the enhancement of static electric fields in a predefined region with only one homogeneous conductivity, named as dc null medium (DNM). It is shown that one constant DNM is sufficient for localizing steady electric current in any arbitrary shape region, which in turn obviates the tedious mathematical calculations that conventional methods suffer from. In other words, the same DNM can be used for different concentrators regardless of their cross-section geometries, which makes the presented approach suitable for scenarios where reconfigurability is of utmost importance. Several numerical simulations are performed in order to demonstrate the capability of the proposed dc electric concentrator in localizing steady electric fields into the desired region. Moreover, by utilizing the analogy between electrically conducting materials and resistor networks, the attained DNM is realized with low-cost resistors and then exploited for fabricating a square shape dc electric concentrator on a printed circuit board (PCB). It is demonstrated that the measurement results agree well with the theoretical predictions and numerical simulations, which corroborate the effectiveness of the propounded method. The presented idea of this paper could find applications in scenarios where highly confined electric fields/currents are of critical importance such as electronic skin devices and electrical impedance tomography.