The internally stored electric energy (

Because of their increasing importance electrically small antennas have often been discussed in the literature. An overview can be found in

Many techniques have been suggested and investigated for reducing the

The role of the

In this paper we further investigate the aforementioned example of a disk-loaded monopole antenna

The paper is organized as follows: We first derive an expression for the real part of the permeability of the dispersive shell leading to an equivalence of stored electric and magnetic energies. Next we apply the Kramers-Kronig transform to obtain the corresponding imaginary part of the permeability. We also check the consistency of the method, i.e., if the repeated application of the Kramers-Kronig transforms delivers the correct (initial) values of the real part of the permeability. Finally we numerically investigate the effect of shielding the disk monopole antenna by the designed magnetic dispersive material on the antenna's performance by applying a commercial frequency-domain solver.

Assume a disk monopole antenna as shown in Fig.

Cross sectional view of a disk monopole antenna

To reduce the electric energy below the cap the antenna is often equipped with a shorting post (SP) as shown in Fig.

Real

We introduce a cylindrical coordinate system

Since the permeable shielding material is dispersive, Eq. (

The total stored electric energy is calculated as

Input impedance of the open disk monopole (no shielding) (green curves) and of the shielded disk monopole antenna (red curves). Geometry of the antenna: ^{©} frequency-domain solver.

Input return loss of the open disk monopole (no shielding) (blue curve) and of the shielded disk monopole antenna (red curve). The other data can be found in Fig.

Antenna gain of the open disk monopole (no shielding) (blue curve) and of the shielded disk monopole antenna (red curve). The other data can be found in Fig.

Electric field distribution

Electric energy density

In a magnetically dispersive material the magnetic flux density

Both types of the disk monopole antennas in Fig.

As proven in

We have introduced a systematic method showing that the numerical evaluation of the Kramers-Kronig transformations can be used to design wide-band antennas consisting of dispersive material. In the future the method will also be applied to other antenna geometries and to a material with a negative value of the real part of the permeability and/or permittivity (metamaterial) to eventually avoid the high dispersion losses and the corresponding reduced gain.

The data are available from the authors upon request.

The theoretical work was done by LK and MB. The numerical evaluation was performend by MB.

The authors declare that they have no conflict of interest.

This article is part of the special issue “Kleinheubacher Berichte 2018”. It is a result of the Kleinheubacher Tagung 2018, Miltenberg, Germany, 24–26 September 2018.

This research has been supported by the Deutscher
Akademischer Austauschdienst (DAAD) and the Egyptian Ministry
of Higher Education and Scientific Research within the

This paper was edited by Thomas Eibert and reviewed by Hans-Jürgen Steiner and three anonymous referees.