Dielectric Resonator Antenna E field absolute open cavity 1.8 GHz

Video animation of the absolute value of the electric field at 1.8 GHz of a cylindrical DRA placed within an open metallic cavity.

Cylindrical Dielectric Resonator Antenna- Mode Methodology

Introduction

The early development of Dielectric Resonators (DRs) was exclusively focused on the design of shielded (high-Q) microwave structures, such as dielectric loaded cavity filters, resonators, etc. However, it has also been shown [B6] that DRs suspended in free space possess radiation properties, hence making them useful as antenna elements.

Antenna designers are familiar with conductive radiators, e.g. dipoles, microstrip, loop, parabolic antennas and so on. On a first view, extending your knowledge into the radiation mechanisms of isolated dielectrics, i.e. Dielectric Resonator Antennas (DRAs), seems natural, but requires an in depth understanding of terms extracted from dielectric resonators. Such terms can include: mode type, shape of electric and magnetic fields within and around the dielectric material, excitation techniques and so on. New engineers studying the theory and the principles of operation of DRAs can easily end up in confusion, since this new topic is not directly related with conductive antennas. In the topic of DRAs, distinguishing the different modes and realizing that each resonant frequency is linked with a unique radiation pattern, presents properties not found always on any other type of antennas.

Based on my experience and research, I will attempt to describe a possible methodology, which can help individuals analyse and understand easier the radiation properties of DRAs. In addition, this methodology will allow later to understand how a DRA can effectively be excited by conventional feed schemes such as, coaxial, microstrip lines and so on.

For simplicity, the analysis considers cylindrical DRAs, placed above a ground plane or suspended in free space; you can relate those two conditions using the image theory to get equivalent results. In addition, the first three modes will be analyzed, since these are the most effective for radiation (they possess low-Q factor), but similar principles can be applied for higher order modes, too.

The main idea of my methodology stems from the fact that each resonant frequency established in a DRA corresponds to a unique internal electromagnetic (EM) pattern, or mode, which in turn generates a characteristic radiation pattern. The latter, can then correctly be correlated with the radiation mechanism of an ordinary electric dipole or a magnetic dipole source (antenna). So, this creates a simplified, but logical, connection between the DRA modes and the fundamental radiation concepts of dipole antennas that leads in the understanding of the radiation properties of DRAs. This theory, which will be described in this article, is pictorially displayed in the following figure:

cyl DRA mode methodology

Above: My methodology, which links Cylindrical DRA modes with the operation of Single element Dipoles through common radiation patterns

As soon as the radiation pattern of a cylindrical DRA at a resonant frequency is identified, then the interior EM field distribution can be linked with a corresponding electric or magnetic dipole source. To bridge those two, firstly we should correctly identify the modes of the DRA. So, initially I will attempt to give a brief description of the general characteristics of the fundamental modes of a cylindrical DRA. For reference, mode nomenclature will be based on Kajfez’s discussions [F2, H1, F1]. If you already hold knowledge of this information, then you can skip the next section.

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Mode Nomeclature of Cylindrical Dielectric Resonators

[Material presented here is partially based on text found in: Ahmed A. Kishk, Yahia M. M Antar Ch. 17. ‘Dielectric Resonator Antennas’ Antenna Engineering Handbook, John Volakis, 2007. Additional sources are quoted where applicable].

The modes excited within a cylindrical DRA are classified into three distinct groups: TE, TM and HEM (hybrid) modes. On the equatorial plane, the TE and TM modes are axisymmetric, while HEM modes are azimuthally (φ) dependent [Ch.17 Kishk, Ant. Eng. Handbook]. To distinguish modes within each group, special indices are added to denote the shape of the EM field inside the resonator. For this purpose, based on mode nomenclature by Kajfez [F2, H1, F1] the modes on a cylindrical DR are indexed as follows:

 

The first index (m), denotes the number of full-period EM field variations along the azimuth direction with m = 1, 2, 3, … . For TE (transverse electric, no Ez component, i.e. Ez=0) and TM (transverse magnetic, no Hz component, i.e. Hz=0) modes m = 0, since the fields are axisymmetric – no variation takes place and the field remains constant in the azimuth direction. For HEM modes ‘m’ is a value always greater than zero.

The second index (n) implies the variation of the half wave field along the radial direction (based on the fact that the field is measured between circle’s center and the periphery), with n = 1, 2, 3, … .

Finally, the index ‘p+δ’ implies the half-wave variations along the z-axis of the cylindrical resonator, with p = 0, 1, 2, 3, … . The presence of the ‘δ’ factor indicates that the half-wave field is greater than the length (thickness, if cylinder’s axis is oriented along z-axis) of the resonator itself, with 0< δ < 1. This is because of the imperfect boundary conditions at the resonator’s dielectric-air interface. This results in some EM field escape; the standing wave interior to the resonator along z-axis is less than a half-wave and decays away from the faces. The actual value of ‘δ’ depends on several physical parameters including the value of er [Kishk, Ch. 17].

For simplicity, factors ‘δ’ and p=0 within the third index ‘p+δ’ are sometimes omitted, since they are implied by default. For example, speaking about mode HEM11 means the same as if you imply mode HEM110+δ (m=1, n=1, p=0) or HEM11δ or HEM110. Similarly, mode TM011 is the same as if you imply mode TM011+δ (m=0, n=1, p=1) and so on.

Isolated Dielectric Resonator Image Theory

Above: Equivalent principle of a DR above a ground plane (left)and in free space (right)

Simulated E and H field plots of the first six modes of an isolated cylindrical DR with thickness (2H) of 4.6mm, radius (a) of 5.25mm and dielectric constant (er) of 38 are shown on my tutorial section of ‘isolated DR’. From those plots you can study the relation between the mode nomenclature and the variation of EM, as described above.

A tip about the distribution of the interior fields of the resonator for TE0n and TM0n modes: The Eφ field for TE modes and the Hφ field for TM modes, posses a rotational symmetry in the equatorial plane (constant z-plane). Also, for TE modes Ez = 0 and for TM modes Hz = 0. This is a helpful way to quickly identify a TE or a TM mode. Obviously, by observing this symmetry in the equatorial plane you can also exclude a mode from being an HEM mode or otherwise.

Based on these descriptions, as an example, the internal E and H field distributions of the first three modes of an isolated cylindrical DR are shown below:

HEM11_E HEM11_H

HEM11 (E) left, and (H) right

TE01_E TE01_H

TE01 (E) left, and (H) right

 

TM01_E TM01_H

TM01 (E) left, and (H) right

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Simplified approach of electric and magnetic field distribution within a dielectric resonator

The mode nomenclature of the previous section established the basis of indexing the modes of isolated cylindrical DRs. An excellent field analysis of the fundamental modes in isolated cylindrical DRs is given by Kajfez [F2, H1, F1] and by Kishk [Luk, chapter 4, ‘Dielectric Resonator Antennas’], which I will try to outline below for the interested reader of this website.

Mode TM01:

Since m=0, n=1 (and p=0), for TM mode there is a circulation of a constant Ηφ field in the xy-plane (equatorial plane).

The ideal far field pattern of TM01 mode for a DR placed above a ground plane is shown below:

far field TM01 mode dielectric resonator electric dipole

Drawing by [Kishk]

You can notice straight away that this far field pattern is identical with that generated by a vertical quarter wavelength electric dipole placed above a perfect ground plane. Indeed, the E and H field distributions inside the DR responsible for such radiation pattern (due to TM01 mode) are the same with the E and H near fields (see image below) of a vertical quarter wavelength electric dipole above a ground plane.

So, we can conclude that the radiation mechanism of a DRA operating in mode TM01 is due to a vertical electric dipole source. This brings us back to my methodology which connects the principle of mode excitation of DR antenna modes with those of a dipole source (antenna).

electric dipole free space E H fields

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Mode TE01:

Since m=0, n=1 (and p=0), for TE mode there is a circulation of a constant Eφ field in the xy-plane (equatorial plane).

The ideal far field pattern for mode TE01 is displayed below:

TE 01 far field pattern ideal dielectric resonator

Drawing by [Kishk]

Notice the orientation of z-axis. The mechanism responsible for such radiation pattern is due to a magnetic dipole oriented along the z-axis and in the middle of the isolated cylindrical DR. In reality it is not possible to generate a magnetic dipole inside the DR; instead a slot located above a ground plane has to be considered. For this to happen, the isolated DR has to be split into half and lay horizontally on the ground plane.

magnetic dipole free space

half split cyl DRA HEM11 mode

You should bear in mind that the thickness of the half split DR remains unaltered, i.e. thickness = 2H. This is because the magnetic dipole is not affected from the presence of the metallic ground plane and requires no modification.

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Mode HEM11:

The ideal far field pattern of HEM11 mode for a cylindrical DRA above a ground plane is shown below:

far field pattern cylindrical DRA HEM11 mode

Drawing by [Kishk]

Since, this is a hybrid mode you do not expect to observe any rotational symmetry. The exact identification of hybrid modes is generally not straightforward, even studying carefully the mode nomenclature. The electric and magnetic fields inside the DR need to be analyzed at various planes to extract a safe conclusion for the order of a hybrid mode.

The shape of the far field pattern shown above represents that of a horizontal magnetic dipole source. In contrast with mode TE01, to allow the generation of mode HEM11 the DR have to remain above a ground plane (thickness = H) with a flat face tangent to the metallic plate and the magnetic dipole source (slot) oriented along the y-axis to create the far field pattern  shown previously, as shown below:

cyl DRA HEM11 mode slot

Conclusions

The radiation patterns of TE01, TM01 and HEM11 modes of an isolated dielectric resonator antenna have been briefed. By matching their radiation patterns with those of either an electric or a magnetic dipoles, it is possible to identify the distribution of the electric and magnetic field inside the dielectric resonator. This methodology allows us to understand in a clear and ease manner the radiation properties of cylindrical DRAs.

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