Dielectric Resonator Antenna-Induced Conduction Current on the Metallic Ground Plane

Dielectric Resonator Antenna-Induced Conduction Current on the Metallic Ground PlaneInteresting observations on its impact and usefulnessRupam Kalyan Chakraborty, Debatosh Guha65map01-chakraborty-opener-3127528IMAGE LICENSED BY INGRAM PUBLISHINGThis article addresses the role of conduction current, caused by a dielectric resonator antenna (DRA) on its metallic ground plane (GP), in influencing its radiation and also in predicting accurate directivity patterns. Extraction of the surface current and its translation to the far field have been systematically studied using different methods. In contrast to what was reported earlier in [6], the conduction current alone is eventually found insufficient to predict the radiation successfully. An additional requirement of the passive DRA block to compensate fields over the front hemisphere has been identified, and an effective method of computation has been demonstrated. Measured and simulated data have been used as references to validate the method. A few examples have been furnished using different DRA shapes, feeding structures, and GP shapes with a special focus on different modes and polarizations. The provided method of computation will be helpful in understanding the physics of radiation from a DRA and interpreting its behavior under special conditions. This method shows that, by controlling the GP current and without disturbing the DRA resonance, the radiation patterns can be easily reconfigured.IntroductionDielectric resonators (DRs) are now quite popular for antenna applications and commonly deployed on metallic GPs [1], [2], [3]. The GP serves a threefold utility: 1) providing a solid platform for its deployment, 2) providing the desired electric boundary to support the modal fields inside the dielectric cavity, and 3) supporting the required feeding structures [1], [2], [3], [4], [5].An interesting observation shed light on the cause of radiation from a DRA [6]. In that study [6], a simple probe-fed rectangular DRA resonating in its dominant transverse electric

${(}{\text{TE}}_{{\delta}{11}}{)}$

mode with linear polarization was chosen. The work [6] obtained the simulated radiation patterns using [7] and compared them with the far-field patterns derived from the source, i.e., the GP current. It was believed that the electric fields or displacement currents inside the dielectric body have an insignificant role in determining the radiation; rather, the GP current alone serves as the sole source of radiation. No further confirmation or extension of that result has been reported so far.This article addresses the same topic to excavate a deeper insight through a systematic study involving a wide range of parameters like DRA geometries, feeding structures, and GP configurations. Unlike [6], our study includes different resonance modes as well as polarizations. Induced surface currents have been extracted using Computer Simulation Technology (CST) Microwave Studio [8] and then numerically treated as a source current to compute the radiation patterns under different physical conditions. Those results for each mode, polarization, and feed configuration have been thoroughly studied in comparison with the reference values obtained through simulation and/or measurements.More importantly, the present observations do not agree with those reported in [6]. The conduction current alone, as believed in [6], can predict a partial signature but not the physical radiation parameters. More realistic and accurate values can be obtained with a different method of computation. This new technique has been systematically studied, experimentally verified, and documented for possible future applications by others. A wide range of testing and comparisons has been furnished; thus, the article provides a deeper insight into interpreting the physics of radiation from a DRA. It also demonstrates that, by controlling the GP current but not the DRA resonance or mode, a designer can reconfigure or synthesize a desired radiation pattern.Analysis and ComputationThis investigation uses two typical DRA geometries, as shown in Figure 1, and two commonly used feeds, such as a coaxial probe and rectangular aperture. This study uses theoretical analysis followed by computation and comparisons of the predicted results with those produced by a standard electromagnetic (EM) simulator. The steps are as follows:

The analysis scheme of [6] is shown in Figure 2; the conduction current

${\bf{J}}_{\bf{c}}$

produced by a resonating DRA on its GP is used as the source of radiation. The rest is the traditional way of determining the far fields as

${\bf{E}}_{\theta}$

,

${\bf{E}}_{\varphi}$

and

${\bf{H}}_{\theta}$

,

${\bf{H}}_{\varphi}$

as functions of

${\bf{J}}_{\bf{c}}$

[9].

This format of analysis guides in computing the surface current

${\bf{J}}_{\bf{c}}$

as a 2D matrix over the GP (each element being a vector

${\bf{J}}_{{\bf{c}}{\text{x}}} + {\bf{J}}_{{\bf{c}}{\text{y}}}$

) but in terms of the tangential magnetic fields

${\bf{H}}_{\bf{tan}}$

. We have utilized the finite integration technique (FIT) [10] and exploited the FIT numerical engine of CST Microwave Studio [8] to handle the problem numerically. Its “Near-Field Data Extraction Tool” efficiently accounts for the E- and H-fields on a defined boundary, and this feature has been applied over a subvolume enclosing the conducting ground to extract the E- and H-fields obeying

${\bf{E}}_{{\bf{tan}}{-}{x}} = {\bf{E}}_{{\bf{tan}}{-}{y}} = {0}$

with

${\bf{E}}_{z}$

nonzero, and

${\bf{H}}_{{\bf{tan}}{-}{x}} = {\bf{J}}_{{\bf{c}}{\text{y}}}$

,

${\bf{H}}_{{\bf{tan}}{-}{y}} = {-}{\bf{J}}_{{\bf{c}}{\text{x}}}$

. The electrical values are obtained as field source monitor (FSM) data files. The described scheme is schematically portrayed in Figure 3(a)–(c).

The far-field data are obtained by computing E and H at the far fields using the FIT engine of [8] with the FSM data (serving as

${\bf{J}}_{\bf{c}})$

as the input. The physical presence of the DRA is ignored. The far-field data, thus obtained, will be referred to as “computed [6].”

The computed results obtained in step 3 have been cross-verified using the plane wave spectrum method [11] to obtain the far-field transformation. For this purpose, a 2D fast Fourier transform has been executed in MATLAB [12], and it shows excellent mutual agreement with the computed results predicted by [8].

The proposed mode of analysis is different from that in [6], and it incorporates an additional field

${\boldsymbol{E}}_{\boldsymbol{s}}$

scattered by the dielectric body in determining the total radiated field E. This is schematically shown in Figure 4, indicating an “equivalent volume current”

${\bf{J}}_{\bf{d}}$

in the dielectric. This can be expressed as [9]

\[{\bf{J}}_{\bf{d}} = {j}{\omega}{(}{\epsilon}{-}{\epsilon}_{0}{)}{E} = {j}{\omega}{(}{\epsilon}{-}{\epsilon}_{0}{)}{(}{E}_{i} + {\boldsymbol{E}}_{s}{)}, \tag{1} \]

where

${\boldsymbol{E}}_{\bf{i}}$

is the electric field without considering any dielectric body to be present on top of the ground surface

${S'}_{g}$

and

${\boldsymbol{E}}_{\boldsymbol{s}}$

is the additional scattered field caused by the dielectric body. The field

${\boldsymbol{E}}_{\bf{i}}$

can be derived from the tangential magnetic field on the GP or the conduction current

${\bf{J}}_{\bf{c}}$

as

\begin{align*}{\boldsymbol{E}}_{\boldsymbol{i}} & = \frac{1}{j{\omega}{\epsilon}_{0}}{\nabla}\,{\times}\,{\boldsymbol{H}}_{\boldsymbol{i}}, \tag{2a} \\ {\bf{H}}_{\boldsymbol{i}} = {-}\frac{1}{{4}{\pi}}{\iint}{\left({\hat{\boldsymbol{R}}}\,{\times}\,{\bf{J}}_{\bf{c}}\right)} \frac{{1} + {jkR}}{{R}^{2}}{e}^{{-}{jkR}}{d}{S'}_{g}, \tag{2b} \end{align*}

where

${\boldsymbol{R}} = {\boldsymbol{r}}{-}{\boldsymbol{r}}'$

is the vector to the observation point r from the source point

${r}'$

. With

${\hat{\boldsymbol{R}}} = {\boldsymbol{R}} / {\left\vert{R}\right\vert}$

as the unit vector, and

${k} = {2}{\pi} / {\lambda}$

. The scattered field

${\boldsymbol{E}}_{\boldsymbol{s}}$

is expressed in terms of

${\bf{J}}_{\bf{d}}$

[13]:

\[{\boldsymbol{E}}_{\boldsymbol{s}} = {-}\frac{j{{\omega}{\mu}}_{0}}{{4}{\pi}}{\oiiint}\,{{\bf{J}}_{\bf{d}}\frac{{e}^{{-}{jkR}}}{R}\text{d}{\acute{v}}_{d}}{-}\frac{1}{{4}{\pi}{j}{{\omega}{\epsilon}}_{0}}{\nabla}{(}{\hat{\bf{n}}}'{.}{\bf{J}}_{\bf{d}}{)}\frac{{e}^{{-}{jkR}}}{R}{d}{\acute{s}}_{d}{.} \tag{3} \]

Equations (1)–(3) express

${\bf{J}}_{\bf{d}}$

as a function of

${\bf{J}}_{\bf{c}}$

in the form of an integral equation as

\begin{align*} & \frac{1}{{j}{\omega}{(}{\epsilon}{-}{\epsilon}_{0}{)}}{\bf{J}}_{\bf{d}} + \frac{{j}{{\omega}{\mu}}_{0}}{{4}{\pi}}{\oiiint}\,{\bf{J}}_{\bf{d}} \frac{{e}^{{-}{jkR}}}{R}{d}{\acute{v}}_{d} + \frac{1}{{4}{\pi}{j}{{\omega}{\epsilon}}_{0}}{\nabla}{\oiint}\,{(}{\hat{\boldsymbol{n}}}' \cdot {\bf{J}}_{\bf{d}}{)} \\ & {\times}\,\frac{{e}^{{-}{jkR}}}{R}{d}{\acute{s}}_{d} = {-}\frac{1}{{j}{\omega}{4}{{\pi}{\epsilon}}_{0}}{\nabla}\,{\times}\,{\left\{{\iint}{\left({\hat{\boldsymbol{R}}}\,{\times}\,{\bf{J}}_{\bf{c}}\right)} \frac{{1} + {jkR}}{{R}^{2}}{e}^{{-}{jkR}}{d}{\acute{s}}_{g}\right\}}, \tag{4} \end{align*}

which needs to be solved numerically [10] to obtain

${\bf{J}}_{\bf{d}}$

as a function of

${\bf{J}}_{\bf{c}}$

. Thus, the combined knowledge of

${\bf{J}}_{\bf{d}}$

and

${\bf{J}}_{\bf{c}}$

helps in determining the total vector potential

\begin{align*}{\bf{A}}_{\bf{tot}} & = \frac{{\mu}_{0}}{{4}{\pi}}{\left[{\iint}{\bf{J}}_{\bf{c}} \frac{{e}^{{-}{jkR}}}{R}{d}{\acute{s}}_{g} + {\oiiint}\,{\bf{J}}_{\bf{d}} \frac{{e}^{{-}{jkR}}}{R}{d}{\acute{v}}_{d}\right]} \\ & {\approx}\,\frac{{\mu}_{0}}{{4}{\pi}}{e}^{{-}{jkr}}{\boldsymbol{N}}, \tag{5a} \end{align*}

where

\[{N} = {\iint}{\bf{J}}_{\bf{c}}{e}^{{jk}{r}'{\cos}{\psi}}{d}{\acute{s}}_{g} + {\oiiint}\,{\bf{J}}_{\bf{d}}{e}^{{jk}{r}'{\cos}{\psi}}{d}{\acute{v}}_{d}, \tag{5b} \]

and hence in computing the far fields. An approximation considering

${R}\approx{r}$

in the amplitude term and

${R}\approx{r}{-}{r}'\cos{\psi}$

in the phase term results in

\begin{align*}{E}_{\theta}\,&\,{\approx}\,{-}\frac{{j}{\eta}{ke}^{{-}{jkr}}}{{4}{\pi}{r}}{N}_{\theta}, \tag{6} \\ {E}_{\varphi}\,& \,{\approx}\,{-}\frac{{j}{\eta}{ke}^{{-}{jkr}}}{{4}{\pi}{r}}{N}_{\varphi}{.} \tag{7} \end{align*}

Here

${r}$

and

${r}'$

represent the distances of observation and source points, respectively, from a reference with

${\Psi}$

as the angle between

${\boldsymbol{r}}$

and

${\boldsymbol{r}}'$

.

We have repeated step 2 to extract the FSM data file bearing

${\bf{J}}_{\bf{c}}$

followed by step 3 but in the presence of the DRA body, as in Figure 3(d). Thus, the FIT engine [8] numerically takes care of solving (4) to determine

${\bf{J}}_{\bf{d}}$

and finally (5)–(7) to determine

${\bf{E}}_{\theta}$

and

${\bf{E}}_{\varphi}$

. The resulting data will be referred to as computed [present].

The DRA under test has been deployed on a metallic GP, excited by a suitable feeding process, and the directivity values have been obtained as a function of the elevation angle. The finite-element-method-based EM simulator [7] has been used to obtain the simulated results, and they will be referred to as simulated. The provided comprehensive flowchart (see Figure 5) would help in visualizing the steps of the preceding analysis and studies.

chakraborty01-3127528Figure 1. Rectangular and cylindrical DR structures.chakraborty02-3127528Figure 2. The basis of analysis [6]: the conduction current induced by a resonant DRA on its GP serving as the sole source to predict the far fields.chakraborty03-3127528Figure 3. Different schemes for obtaining the radiation parameters. (a) Simulation by the EM simulation tool. (b) Computation on the basis of GP current as source [6]. (c) Computation on the basis of near fields obeying E_tan_-x = E_tan_-y = 0 with E_z nonzero and H_tan_-x = J_c_y, H_tan_-y= −J_c_x and resulting in the same output as (b). (d) The proposed mode of computation.chakraborty04-3127528Figure 4. The proposed mode of analysis: scattering by the dielectric body with relative permittivity f_r is accounted for in terms of the “equivalent volume current” J_d inside the dielectric along with the conduction current J_c induced on the GP.chakraborty05-3127528Figure 5. The flowchart of the theoretical studies.Results and Comparative Study: Different DRA Shapes, Feeds, Modes, and PolarizationsA set of representative results has been generated and furnished for a varying range of DRA geometries, modes of resonance, GP sizes and shapes, and different feeding structures.Linearly Polarized CoaxIAL-fed DRAsA pair of cylindrical DRA (CDRA) and rectangular DRA samples with

${a} = {b} = {r} = {h} = {10}{\text{ mm}}$

and

${\varepsilon}_{r} = {10}$

will resonate with their respective fundamental mode (

${\text{HEM}}_{{11}{\delta}}$

in CDRA and

${\text{TE}}_{{\delta}{11}}$

in rectangular DRA) at around 3.9–3.7 GHz. This is ensured by the simulated data obtained using step 1 and depicted in Figure 6. Their computed directivity values are compared with the simulated curves, as depicted in Figures 7 and 8. Figure 7 also embodies their 3D versions for a representative comparison. Note that they have been examined in a linear scale. The source current alone [6] produces identical radiations over both hemispheres (upper and lower) and, as such, predicts relatively weak directivity in the realistic broadside region. However, the proposed method of computation using source current in the presence of the DR block is able to compute a very close approximation with the simulated data. As conjectured, scattered fields through the DR block enable one to compensate the deficiency and maintain a close approximation with the ideal equivalent radiating aperture. Even then, our computed peak directivity is marginally overestimated by 0.1 − 0.2 relative to the simulated values, which could be attributed to their inherent marginal difference in interpreting equivalent apertures.chakraborty06-3127528Figure 6. Simulated S₁₁ indicating resonance frequencies of two test antennas. a = b = r = h = 10 mm with GP size ≈ λ × λ (77 mm × 77 mm).chakraborty07-3127528Figure 7. The computed directivity for the dominant mode in CDRA: (a) and (b) 2D patterns across the principal radiation planes and (c) 3D views of radiation. Parameters are as in Figure 6.chakraborty08-3127528Figure 8. The computed directivity for the dominant mode in a rectangular DRA for (a) E-plane and (b) H-plane. Parameters are as in Figure 6.Figure 9 examines the DRA fields under two different conditions: Figure 9(a) gives the simulated modal fields at resonance, and Figure 9(b) shows the same when the surface current scatters through the passive DRA block, i.e., as in Figure 3(d). They appear similar but with different orders of field intensity. This is reflected when the cross-polarized radiations are examined in Figure 10. The results are quite informative. Negligibly small orthogonal currents can hardly scatter through the DRA body and estimate the cross-polarized radiations. Rather they indicate relatively larger radiations toward the back hemisphere. This is also true for the copolarized fields, as is evident from both the 2D and 3D plots in Figure 7.chakraborty09-3127528Figure 9. The electric field portrayed in a CDRA due to the HEM₁₁_δ mode. (a) When simulated with a high-frequency structure simulator and a vertical probe as feed [as in Figure 3(a)]. (b) When computed as in Figure 3(d) using the FIT engine of [8]. Parameters are as in Figure 6.chakraborty10-3127528Figure 10. The H-plane cross-polarized radiations of a CDRA resonating with HEM₁₁_d mode. Computed [6] values are insignificantly small and hence not visible. Parameters are as in Figure 6.Aperture-Coupled DRAsThe previous investigation has been verified by changing the feed from the probe to the aperture coupling. Both the rectangular and cylindrical structures resonate exactly at 3.68 GHz, revealing identical radiation data. A set of representative results for the cylindrical geometry is furnished in Figure 11. They repeat the same results as obtained in Figure 7(a)–(c) and ensure consistent reproducibility of the proposed mode of computation.chakraborty11-3127528Figure 11. The directivity computed for an aperture-coupled CDRA: (a) E-plane and (b) H-plane. Parameters are as in Figure 6.Verification with Higher-Order ModesThe reproducibility is examined for predicting the radiation caused by a higher resonance mode, e.g.,

${\text{HEM}}_{{21}{\delta}}$

occurring in the same CDRA. The excitation mechanism follows the same approach as in [14] using a pair of balanced probes. The computed directivity plots, shown in Figure 12, indicate excellent agreement of our values with the simulated ones. The signature of the pattern can be traced by computed [6] but again with an almost equal magnitude of back radiations.chakraborty12-3127528Figure 12. The directivity due to higher-order HEM₂₁_d mode in a CDRA fed by a balanced dual probe [14]: (a) E-plane and (b) H-plane. Parameters are as in Figure 6.Verification for Circularly Polarized DesignThe reliability of the proposed computation has been checked with a circularly polarized (CP) design using a CDRA with comb-shaped vertical serrations and excited by a vertical probe [15]. The computed and simulated results are shown in Figure 13, establishing the proposed concept as equally valid and reliable for a CP DRA.chakraborty13-3127528Figure 13. The directivity plots of a CP design reproduced from [15]; the geometry is shown as an inset. (a) xz-plane and (b) yz-plane. Parameters are as in [15].ExperimentsSimulated radiation data have been considered as the reference in the previous study. Experimental verification on the basis of a set of prototypes has been documented. CDRA geometries have been chosen based on the availability in our laboratory. Both coaxial probe and aperture-coupled feeds have been tested. The prototypes are shown in Figure 14, and their measured gain values are compared with the computed and simulated parameters in Figure 15. The directivity has been extracted from the measured gain using the measured radiation efficiency of the DRA [16]. The Wheeler cap method employed by Debatosh Guha in [16] revealed it to be 96% for a prove-fed CDRA (see [16, Table 2]). Figure 15 reveals excellent mutual agreement with the simulated prediction along with our computed values for both principal planes. For the aperture-fed geometry, our computation overestimates the peak value by about 0.5, which does not occur with the probe-fed geometry. It might be possible to investigate the actual reason through a more in-depth study of the surface current using a high-end computation facility.chakraborty14-3127528Figure 14. Prototypes of CDRAs fed by (a) coaxial probe and (b) aperture coupling. f_r = 10, r = h = 10 mm, GP: 60 mm × 45 mm.chakraborty15-3127528Figure 15. The measured directivity of a CDRA bearing different feeding techniques compared with the simulated and computed data: using vertical coaxial probe for (a) E-plane and (b) H-plane and using aperture-coupled feed for (c) E-plane and (d) H-plane.For Intentionally Modified GP CurrentsAn examination has been performed by considerably changing the GP size and hence the modified distribution of the surface current. The simulated results are shown in Figure 16 to visualize with

${\lambda}\,{\times}\,{\lambda}$

and

${2}{\lambda}\,{\times}\,{2}{\lambda}{GP}$

sizes. All investigations furnished for Figures 6–15 are with the

${\lambda}\,{\times}\,{\lambda}{GP}$

. Figure 17 shows the radiation with an enhanced GP. The pattern changes to broadside null, and the simulated prediction is exactly followed by the computed data. Such a change is realizable only through a large-scale modification of the source current. As observed earlier, the current alone [6] fails in computing the realistic parameters.chakraborty16-3127528Figure 16. The simulated surface current for HEM₁₁_d mode with varying GP sizes: (a) λ × m and (b) 2λ × 2m. Other parameters are as in Figure 6.chakraborty17-3127528Figure 17. The directivity computed with a larger-sized GP measuring 2λ × 2m. (a) E-plane and (b) H-plane. Parameters are as in Figure 6.The typical requirement indicates a compact GP size; hence, we have tested a rectangular DRA deployed on a

${0.22}{\lambda}\,{\times}\,{0.22}{\lambda}{GP}$

, as examined in Figure 18. An excellent agreement with the simulated data is truly significant in endorsing the ability of our computation even if the GP size is very small. But considering the optimum gain and patterns, the recommended GP size would be about

${\lambda}\,{\times}\,{\lambda}$

.chakraborty18-3127528Figure 18. The directivity of a probe-fed rectangular DRA (2.44 GHz) with a highly compact GP (0.22λ × 0.22m), as used in [17]. (a) E-plane and (b) H-plane. Parameters are as in [17, Fig. 7(d)].This study is significantly important as it predicts the possibility of modifying the DRA radiation patterns by controlling or synthesizing the GP current. A representative study has been executed in Figure 19, which actually repeats the configuration of Figure 14(a) after introducing a pair of physical defects on the GP. The configuration now looks like that in Figure 19(a), and the resulting perturbed surface current is shown in Figure 19(b). Its computed and simulated directivity patterns [Figure 19(c) and (d)] are completely changed compared to those in Figure 15(a) obtained with its conventional counterpart [Figure 14(a)]. Here also, the proposed method of computation closely corroborates the simulation. Thus, any radiation caused by a single or multielement DRA bearing a conventional or engineered GP can easily be interpreted in terms of its surface conduction current.chakraborty19-3127528Figure 19. A CDRA on a λ × m GP with a pair of major defects and resulting radiation characteristics. (a) The antenna geometry bearing two 8 mm × 30 mm rectangular slots, (b) a simulated portrayal of the surface current, (c) the directivity over the E-plane, and (d) the directivity over the H-plane. DRA parameters are as in Figure 6.ConclusionsThis article gives a clear insight about the cause of radiation from a DRA and a way to compute the accurate radiation values in terms of the source parameters. It establishes the fact that accurate modal fields can be reproduced in a DRA by its compatible GP surface current. Indeed, the surface current bears the signature of the modal fields as well as the radiation patterns. With this insight, a designer can synthesize any desired current distributions in the GP and also predict the radiation. This would help in interpreting any disorder if present in the radiation from a DRA.AcknowledgmentsThis work was supported in part by the India National Academy of Engineering/Department of Science and Technology-Science and Engineering Research Board, Government of India, and the Center of Advanced Study in Radio Physics and Electronics, University of Calcutta. The authors gratefully acknowledge the useful suggestions received from the associate editor and the reviewers. They are also thankful to Dr. Chandrakanta Kumar of the Indian Space Research Organisation, Government of India, and Dr. Chandreyee Sarkar of the Birla Institute of Technology, Mesra, India, for their help and support during the work.Author InformationRupam Kalyan Chakraborty (rupamkalyan@gmail.com) is an algorithm design engineer at Signalchip Innovations, Bengaluru, 560 043, India. He received his M.Tech. degrees in microwave engineering and signal processing from the University of Calcutta, Calcutta, India, and the Indian Institute of Science, Bangalore, India, respectively. He is a Student Member of IEEE.Debatosh Guha (dguha@ieee.org) is a professor at the Institute of Radio Physics and Electronics, University of Calcutta, Calcutta, 700 009, India. His research interests include both printed and dielectric resonator antennas. He is a Fellow of IEEE and the Indian Academies of Sciences and Engineering.References[1] K. M. Luk and K. W. Leung, Eds. Dielectric Resonator Antennas. Baldock, U.K.: Research Studies Press, 2003.[2] A. Petosa, Dielectric Resonator Antenna Handbook, 1st ed. Norwood, MA, USA: Artech House, 2007.[3] R. K. Mongia and P. Bhartia, “Dielectric resonator antennas–A review and general design relations for resonant frequency and bandwidth,” Int. J. Microw. Millimeter-Wave Comput. 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