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.

Project: Mode Analysis of Probe Fed Low Profile Enclosed Cylindrical Dielectric Resonator Antenna

open cavity dielectric resonator antenna cylindrical phd  open cavity dielectric resonator antenna cylindrical



This article analyses the theory behind the resonant and radiation characteristics of a cylindrical DRA enclosed by an open conductive cavity. The material presented in here is drawn from my research that I have undertaken, as a Ph.D student, at Essex University in UK. I will aim to present the analysis mainly in an instructive way, so to be accessible to newly engineers working in the area of antennas and electromagnetics. However, the presentation style also suits individuals whose research is exclusively devoted on these subjects. A full list of the relevant references used in this article are provided on the ‘References’ page on this website.

Structure overview

A vast amount of articles have been published in the area of DRAs since their first investigation in 1983 by Long.et al [B6]. These antennas are well known for their attractive properties over conductive type antennas, including their high radiation efficiency, low profile, ease of feeding, broadband response and so on.

In most cases, the dielectric antenna is placed over a (finite) ground plane and fed by various schemes including probe, aperture and other. The DRA geometry presented here relies on radiation from a cylindrical DRA placed inside an open conductive rectangular cavity. For simplicity, the top face of the cavity will be assumed to have been removed. Additionally, the structure is excited using probe feed located outside the dielectric resonator, a configuration that is easy to implement and modify, if needed, without drilling the dielectric antenna. Alternative excitation schemes will also be outlined. An overview of the structure to be analysed is presented below:

open cavity dielectric resonator antenna enclosed cylindrical

The cylindrical dielectric resonator (in red colour) serves as an antenna and it is inserted inside the cavity (supporters are not shown in this figure). As it can be seen, the top face of the cavity has been removed to allow radiation. The structure is fed from underneath with a probe that is attached next to the dielectric body. We will see later that the location of the DRA and the feed control the radiation characteristics of this geometry.

Enclosed DRA physical characteristics

DR dimensions (radius x thickness)

18 mm x 16 mm

DR permittivity


Cavity size interior dimensions
(width x length x height)

50 mm x 50 mm x 30 mm

Wall thickness

4 mm

Probe radius

0.5 mm


Bear in mind the illustrated orientation of xyz-coordinate system. This will remain unchanged and any graphs, plots or patterns presented in this article will be based on such orientation. An illustration of the ‘θ’ and ‘φ’ angles in relation to the coordinate axes is displayed below:

far field spherical coordinate system

The eigensolver and the transient solver

Before going into numerical details it is important to indicate the basic ground over which the problem can be developed.

Firstly, it should be understood that the structure (without the feed) possesses resonant frequencies at which unique electric (E) and magnetic (H) field configurations (also called ‘modes’, see other tutorials within this website for mode definition and their radiation properties) are established. Investigating those modes will then allow to attain an understanding in exciting the structure accordingly.In order to achieve this, we must initially list all the modes (first modes in practice) that the structure can support. Then, based on this, the mode that provides the most desired characteristics, such as the radiation, easeness of excitation, bandwidth and so on, is picked up for excitation using an appropriate feed geometry.

Hence, on first place, the above structure should be examined from the mode point of view. This can be easily done by  performing an eigenmode analysis [H1]. In brief terms, this allows to identify all the modes that can resonate within the structure and study their E and H field patterns.

Eigenmode analysis is normally applied for hightly resonant structures, such as filters, oscillators and so on. However, it is possible to extend this approach into the illustrated enclosed DRA by applying the appropriate boundary conditions. For this purpose, the 5 metallic faces of the cavity are converted into PEC walls and the top face into PMC wall. The PMC wall does not represent exactly the actual open space conditions of the top face, but it can provide reasonably accurate results on a first order analysis.

The eigensolver identifies the resonant frequencies that are possible to be excited within the structure. Among them, assuming that the appropriate mode has then been selected, it is feasible to excite the structure using the correct feed scheme and see how it could perform, as if it would be tested in a laboratory. This prediction can be performed with a computer simulation software through the, so called, transient analysis. Transient analysis shows how the fabricated structure would behave in reality, assuming of course that the software’s input parameters are as accurate as possible.

The enclosed DRA can also be excited using a disc feed, instead of a probe. The feed choice is influenced by practicallities, such as cost, ease of fabrication and performance characteristics.

In any case, the mode excitation is bounded by the structure’s modes. You can neither excite a mode that does not exist, nor force the generation of a mode using the wrong feed scheme. That is when eigenmore analysis comes into play, allowing later to proceed in the transient analysis. Eigenmode provides the full menu of possible modes that the structure can support, while transient analysis is influenced by the feed method (and hence less modes might be observed compared to the eigensolver analysis).

To this extend, an eigenmode analysis was performed for the cylindrical DR enclosed by PEC and PMC walls (without the feed). For comparison reasons, the analysis was also performed when the DR was isolated, that is, all walls were set to PMC. An extensive investigation of the field lines interior to the DR was then executed in order to identify the modes. The findings, for both structures, are shown in Table 1 (below).

The majority of cylindrical DRAs are operating in the fundamental modes, namely TE01, HEM11 or TE01. Among them, mode selection depends on factors including, feed scheme and radiation properties of the particular mode.

For reasons described in other sections in this website, it is easier to excite mode HEM11 in a cylindrical DRA since, this can be achieved by feeding the structure with a vertical probe feed located adjacent to the resonator’s body. Additionally, mode HEM11 possesses a low Q-factor, which is useful for radiation. For reference, a useful graph that relates the dimensions of an isolated cylindrical DRA with er=38 and that of its Q-factor, is shown below:

Q factor isolated cylindrical dielectric resonator

[Taken from book: K. M. Luk & K. W. Leung ‘Dielectric Resonator Antennas’, 2003, Chapter 4. Note: a=DR radius and ‘2h’ is DR thickness]

The radius to thickness ratio of the considered DR is: a/2h=18mm/16mm=1.125 . For this DR size, according to the above plot, the mode with the lowest Q-factor is HEM11. It has a value close to 35, which is the lowest attainable when DR is isolated, i.e. suspended in free space. Since, the DR is placed inside the enclosed cavity, more energy confinement is to be expected, which will rise the Q factor (and equivalently will reduce the bandwidth).


Transient response of the enclosed DRA fed with probe

The location of the probe feed influences mode excitation, while the probe length performs impedance matching. Based on this, an investigation of the S11 response of the structure up to 3 GHz was considered when the probe length was varying. This is shown below:

s11 oc dra probe 45 vary probe length

On the above graph, the DR was kept symmetrically within the cavity, while probe length, ‘l’, was varying from 10mm to 22mm to keep probe tip within cylinder’s upper and lower faces. It can be observed that both high-Q (sharp response) and low-Q (broadband response) modes are excited. The ripples in the response are occurring by the truncation errors due the calculation and can be smoothed out with longer simulation times. It can be seen that probe length can be adjusted to provide impedance matching for all modes across the entire frequency range.


Resonant Frequencies and mode nomenclature

We are mainly interested to investigate the low-Q modes, which radiate efficiently. Such modes occur approximately at 1.9 GHz, 2.5 GHz and 2.6 GHz as seen on the previous graph. The broadband modes are acquiring a good matching when probe length is l=22mm, in which case a more accurate response is shown below:

s11 enclosed cavity dielectric resonator antenna s11 accurate

(s=7 mm, l=22 mm, high meshing)

In the above S11 response, the resonant frequencies up to the highest low-Q mode and the field configurations interior to the resonator were studied extensively at various meridian and equatorial planes. There are two main bands where efficient radiation occurs, at 1.9 GHz and 2.5 GHz. On the first band, the bandwidth is 33MHz at 1.8968 GHz (1.7%), while on the second band is 81 MHz at 2.528 GHz (3.1%). The modes excited are HEM11 and HEM13, respectively for each band.

Similarly, a transient simulation was also performed for the structure when excited with a short probe terminated on a copper disc. A list of all observed modes for each method of analysis is provided on Table 1 and they are compared with those of the eigensolver analysis.

transient eigen solver resonant freqiencies table

Table 1

(The values of the four main modes of the isolated cylindrical DR can be cross checked with my Excel design frequency calculator! Tip: The equations of the excel file assume that the cylidrical DR is placed above a ground plane, so define thickness on the excel file as '8' mm)

The above table provides a complete characterisation of each resonant frequency for the enclosed DRA. It should be stated that in order to reach safe conclusions, a tedious investigation of the E and H fields, in X, Y and Z planes, was performed within the DR and around it.

In the eigenmode analysis, it can be observed that a given hybrid modes appears at two distinct frequencies. This is due to calculation discrepancy along x-plane and y-plane and implies the degeneracy of that mode. Note that in general all hybrid modes are degenerate. In any case, the same type of mode is implied for such frequencies shown on the table above.

In the transient analysis, modes described as ‘Not excited’ are simply not visible for the reasons described previously. On the other hand, for the eigenmode solver, modes that are not supported by the structure are described as ‘Not present’.

Interestingly, TE02 is not present, unless if the cylindrical DR is kept isolated. Mode TE02 has azimuth symmetry, with the Eφ field lines circulating around the z-axis. According to the boundary conditions, the conductive cavity walls are tending to short circuit the Eφ field lines since they are tangential to the wall, hence suppressing mode TE02.

Logically, someone may ask: In the eigensolver with PEC and PMC walls, why does not mode TE01 vanish for the same reason? This is because, the Eφ-field lines for mode TE01 are strong around the resonator and the surrounding PEC walls cannot eliminate them completely. On the other hand, the Eφ-field lines for mode TE02 are weaker around the resonator and the PEC wall deteriorates them significantly to the point of extinction.

From the S11 response it can be observed that the first radiating mode, HEM11, is coupled well with the feed. This comes in agreement with the predictions that mode HEM11 field configuration is supported by the orientation of the coupling mechanism, i.e. vertical electric probe placed on the cylinder’s periphery (mode HEM11 radiates like a horizontal magnetic dipole).

An interesting scenario is noticed in the next radiating mode: HEM13. It appears both at 2.5067 GHz and 2.5933 GHz. This dual phenomenon might be supported by the location of the probe feed towards the corner of the cavity; mode HEM13 has been excited in a degenerate fashion.

(((((((((HEM11 Hz equations??????))))))))))

Finally, it should be stated that the orientation of the probe feed reassembles that of a vertical electric dipole. This does not favour the generation of the azimuthally symmetrical modes, such as TE0n. For this reason this type of mode cannot be observed in the transient response.


Field Configurations in the transient solver

For the interested reader, the field configurations for each mode  up to the second radiating mode for the enclosed DRA, are shown below. As mentioned previously, mode HEM13 occurs both at 2.5067 GHz and 2.5933 GHz, so only one of those field configurations is presented.

  • HEM11 H-field
  • HEM12 E-field
  • TM01 H-field
  • HEM21 H-field
  • HEM22 E-field
  • HEM13 H-field


HEM11 H field


HEM12 E-field


TM01 H-field


HEM21 H-field


HEM22 E-field


HEM13 H-field


Far field patterns

The gain of the 2 radiating modes is shown below.

far field pattern dielectric resonator antenna

Both, modes HEM11 and HEM13, radiate like a horizontal magnetic dipole above a ground plane; this justifies their similarity in the far field pattern. However, the finite size of the cavity results in some back lobe radiation taking place as seen from the plots. We can observe that the main lobes of modes HEM11 and HEM13, radiate towards the +z-axis and attain a gain of 4.8 dB and 5.9 dB respectively. Had both modes being investigated at a cutting plane φ=90, an identical far field pattern would appear due to the symmetry of the structure.

The polarisation of the far field for each mode can be examined by studying the axial ratio plots at various cutting planes. This is shown on the figure below.

axial ration dielectric resonator antenna

Both modes exhibit an almost linear polarisation in the upper z-plane. The plot above is shown for the φ=90 cutting plane, but the axial ratio for both modes remains identical on the φ=0 plane, due to the symmetry of the structure. The value of the axial ratio for each mode is at least 20db with a maximum value of 40dB above the antenna, i.e. θ=0 (higher values of axial ratio indicate a more linear polarisation, while values close to 0 dB indicate a more circular polarisation. Higher values of axial ratio are also an indication of polarisation purity, i.e. only one mode is excited at a particular frequency). We will see later, that it is possible to excite two orthogonal modes and achieve a circular polarisation.


Further analysis: Investigation of DR location within the cavity

So far, the dielectric cylinder has been symmetrically located within the rectangular cavity, i.e. 7mm spacing from all cavity faces. It would be interesting to investigate how the location of the DR affects the resonant modes. Specifically, a parametric analysis was performed to study how the S11 response was affected by the DR axial movement (i.e. along the z-axis) while keeping the probe length fixed. The results are shown on the next figure for mode HEM11:


On the above investigation, the length of the probe was kept fixed at 22mm during the DR movement. The distance of the DR from the bottom of the cavity, assigned with letter ‘s’, has been varying from 6 mm to 14 mm (the original distance was 7mm). Between those two limits, the resonant frequency of the first radiating mode, HEM11, shifted from 1.91 GHz down to 1.87 GHz, a change of 40 MHz or about 2%, centred at 1.89 GHz. At s=14mm, the top face of the DR coincides with the open top face of the cavity.

We can also observe that there was a slight bandwidth improvement when the DR was shifted upwards. From the initial value of 33MHz the bandwidth had expanded to about 40 MHz, an increment of more than 20%. This was to be expected, since more radiation losses are introduced by the upward movement of the DR due to more field escape.

Hence, it can be been that the structure can provide a straightforward frequency tuning by changing the vertical location of the DR within the cavity. In addition, this can also provide an effective bandwidth enhancement without any major structural modification, keeping cost low.


Effect of losses on the response and accuracy of simulation

For simplicity, the above analysis assumed a lossless structure that had neither conductor nor dielectric losses. In practise, this is not possible and there will always be such losses present. For those reasons the response of the structure is expected to deviate from the ideal behaviour when these losses are considered. Furthermore, a denser discretisation of the structure tends to improve the accuracy of the calculations, including the location of the resonant frequencies. The plot below compares the S11 response of the structure in three different occasions: Ideal (no losses) response, lossy response and fine meshing effect.

s11 dielectric resonator antenna losses ratiation


It can be seen that the introduction of losses smoothes the response. This is an indication of the Q-factor’s reduced value. For example, the sharp response in the no-loss response of the mode at 2.5 GHz is ‘absorbed’ when losses are considered. On the other hand, the higher number of meshcells improves the accuracy of the response and identifies more clearly any resonances.

It is possible to calculate the loaded Q-factor of a mode from the following equation:

Qo factor lossesATTENTION:this equation (Qo) appears to be wrong despite that it was found in book 'Dielectric Resonator Antennas' by Luk. The square root should be at the 'VSWR' on the denominator and not at 'VSWR-1' (see 'Antenna Theory' by Balanis for confirmation). The calculations that follow below need to be corrected. All other equations stated are correct. Sorry about this!


bandwidth fractional Q factor

The VSWR is the voltage standing wave ratio at the desired bandwidth and it is related with the Return Loss (R. L.) in dB, as follows:

return loss vs VSWR dielectric resonator antenna

The bandwidth is calculated at -10 dB, hence VSWR=1.925.

A better close-in at the response of mode HEM11 will us help proceed with the calculation:

Based on the above values,

BW(fractional) = (1.9082 MHz-1.8741 MHz)/1.891 MHz=34.1/1891=0.018032, so

Qo=27.3 .

The quantity Qo, contains radiation, conductor and dielectric losses as follows:

q factor equation dielectric resonator

The calculated Qo-factor for mode HEM11 appears to be below the estimated Q-factor shown on the graph at the top of this article, i.e. ≈30, for the isolated cylindrical DR. This is because of the presence of the conductive cavity, which introduces additional metallic losses lowering the Q-factor.

From this, we can also see that the presence of the cavity does not degrade the radiation properties of mode HEM11, compared to the case when the DR is isolated.


Dual mode operation – a probe fed DRA with corner screw

An idea, extracted from actual laboratory practises and implemented in cavity filters, has been applied to the open cavity DRA. Specifically, the use of a corner screw was considered in an attempt to excite two modes in orthogonal manner. This can allow the broadening of the bandwidth, since two near-by modes can add up constructively for this purpose. For this reason, the location of the feed probe was altered and a screw was inserted on the cavity as seen on the following figure (side face of cavity is transparent to view interior):

open cavity dielectric resonator antenna dual mode

open cavity dielectric resonator antenna top view

(top view of the enclosed DRA with the probe feed and corner screw shown)


There is a reason behind this alteration; the probe feed will orient the E-field lines of mode HEM11 in parallel to y-axis and normal to the cavity walls. The rectangular shape of the cavity can then support the same mode along x-axis, assuming that it can be excited properly through a coupling screw. So effectively, the feed excites mode HEM11 and then through the corner screw a second (identical) mode and orthogonal to the first is generated within the cavity, with the support of the cavity’s rectangular shape.

Such an idea, inspired from dielectric loaded cavities, is not known yet to have been applied in DRAs.

The distance of the corner screw from the dielectric body defines the amount of coupling between the two orthogonal modes. A number of simulations were performed to investigate this effect and the optimum results are shown below:

corner screw dual mode dielectric resonator antenna

(vary screw length, sensitivity)

Parameter ‘v’ is the length of the corner screw in mm projected inside the cavity. From this graph, we can immediately notice that it is possible to strongly couple two HEM11 modes together when v=17.3mm. Of course the other modes are also affected from the presence of the screw. The graph below compares the S11 response of the structure with and without the corner screw(l=22: no screw, v=17.1: with screw):

s11 dielectric resonator antenna dual mode bandwidth

(screw vs. no screw)

The -10dB bandwidth gets almost close to 100MHz (about 5.2% at 1.9 GHz) from about 33 MHz, resulting in a significant improvement over the previous geometry. The two coupled modes are located approximately at 1.88 GHz and 1.94 GHz. The magnetic field at the DR’s equatorial plane for these two frequencies are presented below:

  • HEM11 H-field 1st coupled mode
  • HEM11 H-field 2nd coupled mode


HEM11 dielectric resonator antenna 1st coupled mode


HEM11 dielectric resonator antenna 2nd coupled mode


It can be verified that the direction of the H-field lines on each figure reassembles that of mode HEM11. Additionally, by comparison, it is interesting to observe that their direction is orthogonal to each other and that the resonance at 1.88 GHz is due to the coupling screw, while the mode at 1.94 GHz is due to the probe feed (hint: H-field circulates around a probe feed).

The gain and the axial ratio at cutting planes φ=0 and φ=90 are shown below, for both coupled HEM11 modes.

far field pattern dielectric resonator antenna

axial ration dielectric resonator antenna

As in the case of single mode generation, the gain is almost 5dB for both modes. On the other hand, the value of the maximum axial ratio has dropped from 40dB, as mentioned in the single mode excitation, to 15 dB. This is an indication that the far field polarisation is more elliptic, compared to the previous (without screw) case when an almost linear characteristic was exhibited. The far field radiation pattern now contains two linear polarisations, but orthogonal to each other.

Hence, the open cavity DRA demonstrates an almost tripling in the bandwidth with the insertion of a corner screw and this is due to the dual coupling mechanism by exciting two orthogonal modes. As stated previously, only hybrid (HEMmn) modes have degeneracy properties, hence TM or TE modes cannot be used to achieve the dual-mode phenomenon with this method. The dual mode excitation with the presence of screw also results in a more elliptic polarisation.



The main properties of the open cavity DRA, can be summarised as follows:


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