A Theory of Mutual Coupling Between Two Collinear Wire Antennas

The impedances of two collinear wire antennas are studied using classic operations, transforms, and concepts—namely, Fourier transforms, Hilbert transforms, convolution, and correlation—in the spatial domain. In particular, the Hilbert transform is justified as a valid spatial domain operator for determining the port reactances from the port resistances by appealing to boundedness and analyticity. As thoroughly studied in the previous papers, the port resistances are obtained from the radiation resistances in the context of energy conservation under the assumption of lossless media. Provided that the current distributions of the wires are known, closed-form impedance results can be obtained whether the current distributions are the same or different. Various examples are presented to justify the theory presented herein, and numerical data are provided to validate the equations. Furthermore, an interpretation is provided that states that the self- or mutual impedance is a measure of the auto- or cross correlation between the current distributions, in juxtaposition to the reaction or induced EMF interpretation.