A transmission element for a downhole tool comprising an annular housing and an annular ferrite channel within the annular housing. An annular nonlinear coil may be disposed within the annular ferrite channel, and the nonlinear coil may be connected to a cable running within the downhole tool. The housing may be an annular groove or recess within the tool, an annular metal trough, or an annular polymeric block. The polymeric block may comprise a composite of a polymer and a volume of ferrite elements comprising Fe and Mn. The annular nonlinear coil may comprise a wave, a helix, a twisted pair of wires, a transformer comprising a coil and a metal core, or a combination thereof. The polymeric block may comprise and bumper on its periphery and a void opening within the block proximate the bumper. The ferrite channel and the coil may be molded within the polymeric block.

First and second wires form a wire assembly by being wound around a winding core portion together. The wire assembly includes a twisted wire portion, an inner layer portion, an outer layer portion, a plurality of outward transition portions, and an inward transition portion. The outer layer portion includes a first outer layer portion which is connected to one of the outward transition portions extending from an intermediate position of the inner layer portion and connected to the inward transition portion. The inward transition portion extends to an intermediate position of the inner layer portion.

A winding core includes, for example, four planes, that is, a top surface, a bottom surface, a first side surface, and a second side surface around its central axis. A first wire and a second wire are wound around the winding core in the same direction and have a twisted section. In the twisted section in a plurality of turns at the top surface, bottom surface, first side surface, and second side surface, both the first wire and the second wire are in close contact with each of the ridges between the top surface, bottom surface, first side surface, and second side surface.

A magnetic module includes: a magnetic core; and plural enameled wires wound on the magnetic core, the enameled wire being wound on the magnetic core to form a primary coil and a secondary coil, the primary coil including a first group of enameled wires and a second group of enameled wires, the secondary coil including a third group of enameled wires and a fourth group of enameled wires, wherein the parts of the first group of enameled wires and the fourth group of enameled wires wound around the magnetic core are twisted together to form a first stranded wire, the parts of the second group of enameled wires and the third group of enameled wires wound around the magnetic core are twisted together to form a second stranded wire, and the first stranded wire and the second stranded wire are twisted together to form a total stranded wire.

An inductor structure includes a first inductor and a second inductor. A first portion of the first inductor is disposed on a first layer and a second portion of the first inductor is disposed on a second layer. A first portion of the second inductor is disposed on the first layer and a second portion of the second inductor is disposed on the second layer. The first portion of the first inductor and the second portion of the second inductor at least partially overlap. The second portion of the first inductor and the first portion of the second inductor at least partially overlap.