Application of the Green's Function to Calculating the Impedance of a Uniform Current Density between Two Multilayered Media

The equivalent impedance of a system consisting of a uniform current density placed between two multilayered planar media is derived by using the Green's function. The impedance is posed in terms of a semi-analytical expression in which the different physical and geometric parameters of the system are taken into account. Both media consist of several layers of homogeneous materials which are characterized by means of their physical properties. This system is the basis of many practical applications, such as non-destructive sensing devices, induction heating or electromagnetic field shielding. Considering these applications, the magnetoquasistatic (MQS) regime is adopted in this analysis. The analysis also shows that the impedance comprises two contributions: the first one is dependent of the sources of the fields; the second one is defined by the effect of the media. According to this analysis, a Green's function solution is obtained for each contribution and the total impedance is obtained by adding the two solutions. The convolution of the Green's function solutions with the current density is required to obtain the equivalent impedance of the system; in this case such convolution is reduced to a product in a transformed version of the problem. Taking advantage of the axial symmetry of the problem, a spectral transform like the Hankel Transform is used. Some experimental results are provided in order to verify the developed impedance expression. These results show the dependence of the complex impedance with respect to the frequency, which is measured by means of conventional impedance analyzers.