Smart Grids (SGs) can be successfully supported by Wireless Sensor Networks (WSNs), especially through these consisting of intelligent sensors, which are able to efficiently process the still growing amount of data. We propose a contribution to the development of such intelligent sensors, which in an advanced version can be equipped with embedded low-power artificial neural networks (ANNs), supporting the analysis and the classification of collected data. This approach allows to reduce the energy consumed by particular sensors during the communication with other nodes of a larger WSN. This in turn, facilitates the maintenance of a net of such sensors, which is a paramount feature in case of their application in SG devices distributed over a large area. In this work, we focus on a novel, energy-efficient neighborhood mechanism (NM) with the neighborhood function (NF). This mechanism belongs to main components of self learning ANNs. We propose a realization of this component as a specialized chip in the CMOS technology and its optimization in terms of the circuit complexity and the consumed energy. The circuit was realized as a prototype chip in the CMOS 130 nm technology, and verified by means of transistor level simulations and measurements.