Dipole Antenna - Elementary Doublet

Elementary Doublet

An elementary doublet is a small length of conductor δℓ (small compared to the wavelength λ) carrying an alternating current:

Here ω = 2πf is the angular frequency (and f the frequency), and i = √−1 is the imaginary unit, so that I is a phasor.

Note that this dipole cannot be physically constructed because the current needs somewhere to come from and somewhere to go to. In reality, this small length of conductor will be just one of the multiple segments into which we must divide a real antenna, in order to calculate its properties.

In the case of the elementary doublet it is possible to find exact, closed-form expressions for its electric field, E, and its magnetic field, H. In spherical coordinates, they are

where r is the distance from the doublet to the point where the fields are evaluated, k =2π/λ is the wavenumber, and Z = √μ/ε = 1/εc = μc is the wave impedance of the surrounding medium (usually air or vacuum).

The energy associated with the term of the near field flows back and forth out and into the antenna. The exponent of e accounts for the phase dependence of the electric field on time and the distance from the dipole.

Often one is interested in the antenna's radiation pattern only in the far field, when r ≫ λ/2π. In this regime, only the 1/r term contributes, and hence

The far electric field E_θ of the electromagnetic wave is coplanar with the conductor and perpendicular with the line joining the dipole to the point where the field is evaluated. If the dipole is placed in the center of a sphere in the axis south-north, the electric field would be parallel to geographic meridians and the magnetic field of the electromagnetic wave would be parallel to geographic parallels.