SLOT EXCITED DIELECTRIC RESONATOR ANTENNA ABOVEA CAVITY - ANALYSIS AND EXPERIMENT

Robert Borowiec, Andrzej A. Kucharski, Piotr M. Slobodzian

Abstract: The integral equation - method of moments approach to analyzing a cavity backed, slotexcited dielectric resonator antenna is validated experimentally (by measure-ments). First, the closedrectangular metal box is considered to validate the cavity treatment. Then, the whole DRA structure,i.e. the cavity along with the slot and dielectric resonator, is tested to prove definitively correctness ofthe approach used.

I. Introduction

In recent authors' paper [1] the integral equation-method of moments (IE-MoM) approach to efficientanalyzing a dielectric resonator antenna (DRA) excited by a slot and backed by a rectangular cavity filled witha multilayered medium has been presented. The method of calculation, and especially the computer code, havebeen carefully validated by comparison to the data (results of investigation) published in the literature [2, 3].However, the data did not allow us to test full capabilities of the software developed. Although we testeda radiating slot and a hemispherical DRA over a rectangular cavity, the cavity itself was filled witha homogeneous medium (air), and hence it was not possible to check one of the main advantages of our method,namely its ability to take into account a layered structure of a microwave circuit enclosed inside the cavity. Thus,since the best method to validate the theory is to compare the result of calculations with experimental data,we have decided to curry out several practical tests. The paper briefly recalls the theory related to the IE-MoMmethod and describes the results of the experiment.

II. Outline of the computational method

The problem under consideration is illustrated in Fig. 1. A homogeneous DRA characterized by parameters 8d, Adis coupled to the microwave circuitry printed on a dielectric substrate, which is enclosed in a rectangular metalcavity. We also assume the infinite perfectly conducting screen under which the cavity is placed.

DR

Ed,/1d

|PEC

Jc

E4n, Hn

Fig. 1. A slot excited DRA placed over a cavity filled with multilayered structure.

The method of analysis is based on a multiple application of equivalence principle to split the original probleminto several simpler situations, i.e. the situations for which the Green's functions are known. The first step is theseparation of the cavity and upper half-space problems by shorting the slot and placing over and below it suitablemagnetic current distribution [4]. Next, the upper-half space is extended to the free-space by means of the imagetheory [5]. Finally, we apply the well known method of exterior/interior equivalence to analyze the isolateddielectric bodies [5]. The details of those steps can be find in [1]. By enforcing the boundary conditions over theslot, the surface of the dielectric and the metallizations inside the cavity, we get a set of coupled integralequations:

[Hd(-2Ms) + Hd(- J) + Hd ( M)]ta. = [Hc (Ms) + Hc (J)+ Hnc on Sa (1)

[Hd(-2Ms)+lHd(-J)+ Hd(-M)]t.= [He(J)+lHe(M)]tan, onSd (2)

*The authors are with the Wroclaw University of Technology, Institute of Telecommunications, Teleinformaticsand Acoustics, Wyb. Wyspiafiskiego 27, 50-370 Wroclaw, Poland, e-mail: e

[Ed(-2Ms) + Ed (-J) + Ed (- M)]t,,, = [Ee(J) + Ee (M)]t., on Sd

[E£ (Ms) + E, (Jc) + Einc Ian =0, on S,

(3)

(4)

In the above equations J andM denote equivalent currents flowing on the air/dielectric interface and reproducingcorrect fields in the upper half-space region (their negatives, together with the negative magnetic current over theslot, reproduce correct fields inside DRA), finally the positive magnetic current Ms over the slot, together withthe electric currents inside the cavity J, produce fields inside the cavity. The slot magnetic current in (1)-(3)is doubled as a result of the application of the image theory. Also, one must remember that J andM flow overthe surface of DRA and is image. The subscript "tan" stands for "tangential component", subscripts d, e, cdenote the environment in which the currents radiate (respectively: dielectric, external and cavity), Sc is thesurface of conductors (metallization) inside the cavity, Sa is the surface of the aperture, and finally Sd is thesurface of the (doubled) DRA.The set of equations (1)-(4) is solved by the method of moments. We have applied RWG basis functionsto approximate equivalent currents on the surface of the DRA, and simple roof-top functions spannedon rectangles, for the slot and metallization. This latter choice was dictated by the efficient calculation ofreaction integrals for the cavity environment. Finally, we have used the Galerkin' s testing procedure to transformthe initial equations into the corresponding set of linear equations. This set has been solved using standardmethods of linear algebra.

III. Experiment - measurement set-up

The experimental validation of the described method has been divided into several stages. First, a practicalmodel of the DRA above a rectangular cavity has been designed and built. The structure of the model, togetherwith its description, is shown in Fig. 2. In order to enable accurate modelling of the infinite ground plane,assumed in the theory, the practical model has been equipped with a finite size ground plane of suitably chosendimensions, as shown in Fig. 3. The figure also shows arrangement of the slot (aperture) made in the ground plane.

25.8

LDR:coCN

Dielectric resonator (Eccostock HiK 500)hDR=9 mm£gr=16tg6=0.002

Groundplane

-Li-L2_L3 E

E(.0

LC) V

Layer description:

L1: Foam (Rohacell 31HF)h1=5 mmEr1=1 .045tg6l=0.001 63

L2: Substrate (Ultralam 2000)h2=0.762 mmtr22 4tg62=0.002

L3: Airh3=44.9 mm8r3= 1tg63=0

Fig. 2. The structure of the cavity backed, slot excited DRA used in the experiment.

*

/

Slot

50Q SMAconnector

Strip

Cavity

40 mmI' op

I

Ground plane _ _ _

40.0 mm

l ~ 4.0mmII

1270mm ECavity outline 27E

66

Slot IF

2.1 mm Strip i

Fig. 3. The finite size ground plane and the slot arrangement for the antenna practical model.The strip layout and its dimensioning is also given in the drawing.

The thickness of the aperture is equal to the thickness of the ground plane, thus in order to come as close aspossible with the zero thickness requirement assumed in the theory the ground plane was made of a sheet ofcopper foil of 35 gm thick.At the second stage, first the input impedance of the strip on a single dielectric layer embedded in the closedcavity has been measured in order to validate the computer code responsible for the cavity numerical modellingitself. Since the theory assumes infinite conductivity of the cavity walls (a = ) the input impedance has beenmeasured twice: first time, for the cavity made of brass (o = 1.57 107 [S]) and second time, for the silver-platedcavity (o= 6.3 107[S]). The results of the two measurements have allowed us to assess the influence of thesimplifying assumption made in the theory. In the second part of the experiment, the input impedance of thewhole antenna structure, shown in Fig. 2, has been measured and compared with the results of calculations (thesilver-plated cavity has been used). It is worth mentioning that in this case the results of measurements hasturned out to be very sensitive to the way the dielectric resonator was fixed on the ground plane. The mainreason for this phenomenon is an air-gap, which arises in the DR-ground junction (this fact has been very oftenreferred in the literature). The problem has been eliminated by sticking the DR with the ground planeby a resin-based glue.All the measurements during the experiment have been performed with the use of the vector network analyserR3860A (Advantest) and the antenna analyzer Site Master S400 (Anritsu).

IV. Results

The validation of the computational method described in this paper is based on the comparison between themeasured and calculated return loss (|S 12 ) at the input port installed in the cavity's wall. In this way, thecomparison is insensitive to phase errors, which can easily arise during the input impedance measurements.The comparison of the results for the closed cavity with a single strip is shown in Fig. 4, where the influence ofthe cavity wall conductivity is clearly visible. The increase in conductivity results in the vertical shift of thecurve, so it seems that in the limit a -* the measurements should tend quite close to the results ofcomputation. Nevertheless, we are still not sure about correctness of the results of computations due todiscrepancy between the results, even though we take the silver-plated cavity results for comparison. Therefore,the results of our computations have been compared with the results obtained with the use of other"computational tool", namely commercial EM software, Sonnet by Sonnet Software Inc. The results are givenalso in Fig. 4 and show excellent agreement between results obtained with the computational method developedby the authors. Hence, we can finally conclude that the computer code responsible for the cavity modellingyields valid results and the discrepancy between the measured and calculated curves, seen in Fig. 4, can beattributed mainly to the finite conductivity of the cavity walls (in some degree also to the finite thickness of theslot). Finally, the computational method has been validated for the whole structure of the dielectric resonatorantenna. The results of comparison between the measured and calculated data is shown in Fig. 5, and a verygood agreement can be again observed. The small discrepancy can be attributed mainly to the problemsmentioned earlier.

0,0

-1,0

cncn0

a)oy -2,0

-3,05000 6000 7000 8000 9000

Frequency [MHz]

Fig. 4. The comparison between the results of computations and measurements for the closed cavity.

0

-2

-4

0 -6cncno -8

a, -10

-12

-14

-16 -2000 2200 2400 2600 2800

Frequency [MHz]3000

Fig. 5. The comparison between the results of computations and measurements for the DRA.

V. Conclusion

The developed MoM solution enabling efficient analysis of slot excited DRA over a cavity filled with amultilayered medium has been validated experimentally. Both the results for the closed cavity, and for the DRAhave been presented. In this paper we have concentrated on the comparison concerning circuit quantities (returnloss), however more sophisticated measurements including radiation patterns calculations and measurements areconducted and the results will be published in the nearest future.

References:

[1] A. Kucharski, P. Slobodzian, Analysis of a Slot Excited DRA above a Cavity Filled with a Multilayered Medium,International Conference on Electromagnetics in Advanced Applications, ICEAA-2005, 12-16 Sept., Torino, Italy,pp.253-255.

[2] S. Hashemi-Yeganeh, C. Birtcher, Theoretical and Experimental Studies of Cavity-Backed Slot Antenna Excited by aNarrow Strip, IEEE Trans. Antennas Propagat., vol.41, no.2, 1993, pp.236-41.

[3] K.Y. Chow, K.W. Leung, Cavity-Backed Slot-Coupled Dielectric Resonator Antenna Excited by a Narrow Strip, IEEETrans. Antennas Propagat., vol.-50, no.3, 2002, pp.404-405.

[4] R.F. Harrington, J.R. Mautz, Electromagnetic Transmission Through an Aperture in a Conducting Plane, Archiv-fur-Elektronik-und-Uebertragungstechnik, vol.3 1, Feb. 1977, pp. 81-87.

[5] R.F. Harrington, Time-harmonic electromagneticfields. McGraw-Hill Book Company, 1961.