Ultra Wide Band Antennas

Appendix A

Reciprocity of the Antennas in Reception and Transmission Modes

It is proposed to prove here in a very general way the reciprocity property of the antennas¹ functioning in transmission or reception. This important property will take the form of a relationship between the ATF in transmission and reception (equation [3.24]).

For this we will follow the approach of Deschamps in [DES 66]. First of all let us consider the electromagnetic field in one point of space as a 6-dimensional vector:

[A.1]

In a source-free region of a linear medium, isotropic but not necessarily homogeneous, this vector verifies the following Maxwell’s equation, merging the two principal equations curl E + jωμ H = 0 and curl H − jωε E= 0:

[A.2]

From two solutions F_I and F_II of [A.2], corresponding to various configurations of the sources, we can form the cross product:

[A.3]

which is a three-dimensional vector, bilinear in F_α. The cross flux of F_I and F_II is defined as the flux of the vector F_I ×F_II through an oriented surface S² and denoted as:

[A.4]

The cross flux verifies the following properties: ...