Dielectric-loaded cavity-backed slot radiator analysis

R.Rov and V.F.Fusco

Ahslract: A dielectric-loaded cavity-backed slot aiitci i i ia is analyscd by the method of ~nomciits. Owing to the geometry, the dielectric matcrial can contact the inctal walls hence the problcni is formulatcd to includc polarisation currents on the dielectric body. In this way an analysis 01' the straictiirc can hc oblaincd in a single pass coniputiition. The papcl- shows tlic Liar-field riidiation pattcm, theoretical prcctlictions and experimental results for various dielectric material positions within the cavity.

1 Introduction

Unidircclioixal diclcctric radiator (UDR) anleiiiiias, as used in vcliiculiir sensors, and iisually consisting or a dielectric cubc placcd bctwceii two llat nietiillic plates, have been prc- viously analysed by iiniilytical methods [IM]. 111 this work we investigate the properties 01' a inodilicd UDR striicttirc where ii single diclcctril: cube is pliiccd in a rectangular cav- ity whose open aperture l'orins il narrow slot at the radiat- ing rrcquency of intcrcst. We analyse tlic structurc by setting up an integral cquation fit- (lie electric field i n terms or the difr'ercnt types ol'currcnts set tip within the structiirc and solve for these lield components using thc method 01' iiioniciits [SI. Integral cquations for B tlielcctric body liavc picviously been reported hy mirioi~s ~ut l io rs [6 81 by rcduc- iiig the whole body to equivalent surkicc currents. Tlic principle 01' this approach is to define two difr'crcnt prob- lems, oiic I'or the dielectric rcgion and another [or the air rcgion, indcpcndeiat OS Cacli other and then to cnlbrce the continuity 01' the Langential componcnts of the actual clcc- tric ;and miignctic licld at the iiitcrIBcc. However, Tor thc problem geometry of intcrest in this work an additional diG liculty aiiscs due to thc kict that the mctallic wiills of the structure ill-c touching the dielectric cuhe. With this in mind we formulated the problem to includc, to o w knowledge for the first tinic, tlic polarisation currents on the dielectric body. In this way wc show tllat it is possihlc to obtain an analysis of tlic structure using only a single-pass coinpulii- Lion.

2 Analysis

Using tlic co-ordinate systcin For tlic structurc shown i n Fig, I and assuming a suitahle cxci~ation soiirce, we ciin solve for the conduction current on the iilckd walls of the cavity and coiicurrcntly for the polarisation ci~rrciits on the dielectric body. To do this wc assiiinc an impressed current source at the location of the excitation probe shown in Fig. 1 wliicli Cor our work we express a s

j , = 6(?/ - c)h(i: - f i ) sin k ( a - :I;)z,~ ( I ) where d , is the unit vector ;!long the x-axis. The incident (or imprcssed) electric field E, or the sciittering surfaccs is given in terms or' the he-space Grccn r'unction [9] a s

The mclallic walls of the cavity and the dielectrjc cube scatter this field to give rise to ti total electric lield ,h7. = E; + E,v. Maxwell's cquiitioils at any point in spacc cBii be written a s v x 2,. = :juJDT wlierc d, is defined i!i ternis of the niagiieti? pcrincability qr' free spyc p0 as B , = N~ H , and V x IT./. =.ju I ) . , + ,l where /I1. is defined below in terms or the pcrinittivity of free spice F~ ;nid where ./ consists or the siim of the i!idnced currents J , on tlie scat- tering nick11 surfaces and J , cqn. 1 such that

+ - + .I = .I, + J;

The t o l ~ l electric displaceincnt vector d,. at any point is expressed in \erins of the electric susceptibility x, (9' tlie ppliirisation 1') of+lhc dielectric body a s [IO] D. - E,. = k,, -1- 1 ) ~ ~ ) R P Using these end setting I$., = V x we arrive at the special form 01' the kiclinholtz eqiialion which we tisc in this work

v"+pii= ,)UP - J zz . - ~ W X ~ E ~ J $ ? , - .I (4)

(3)

- + + +

(5) Tlic ctirrciit .I, in cqns. 3 and 5 is given [9] by

This lcads to a vector integral equalion for k r whose con?- ponents arc cxprcssctl in ierins of the known quantities Ei and i i oreq11s. I and 2 a s

This inlcgral cquiition is solved niimcrically using piilse basis f~~nctions and Galcrkin's mcthod of setting tlic testing functions equal to the basis f imiotts [SI. Once tlic lolal clccti-ic licld is obkiiticd wc cvaluatc tlic totiil currents Iironi eqns. ,6, I and 3, respectively, and l hcn cvaluatc the qu;iii- lily P from the relation P = fi!/. [IO]. Thus wlicii all tlic tcrnis in tlic right-hand side 01' cqn. 5 bccn cvtilualed, tlic far field at any poitil in Llic open spacc cxtcrnxl to tlic cavity ciiii bc ohtaincd by using cqn. 5.

here this probc position will bc maiiilaincd. Howcvcr, with the dielectric block at n = 0 (Fig. 4), tlic SdB hcaniwidths wcrc 69" incastired and 74" computed. For the dielectric block positioiicd a i ii = 55nim wc ohlain the ii~axin~iitii possible compression of the beani at this frcqiicncy Sor this slructurc using a diclcctric block of this size i t value of 62" for tlic 5dB beiimwid~h wiis prcdiclcd and mcasurcd (Fig. 5) . The cross-polar field lcvcl (llic z-compoiienl of I ? , ) was observed to be inore thin 25dB down with rcspcct LO thc copula lcvcl and lhis was roughly the same a s sliowi by tlic coiiipnlations (30dB). I n f ig , 6 the t'iill height dielectric hlock p1;iccd at tlic rediating apcrrurc was replaced with ii block wliosc hcighl was 3/4t, sitting on llic floor of the cavity at position n = S S m m . 'llic resulting prcdiclcd fir-licld I.iidialioii patkm is very similar to i l ic case wlicii no dielectric is pi-csciit (Fig. 2). When the diclcc- Lric was rcpositioncd at t i = 0 iio diffcrcnce in simulalcd rcspoiise was fountl rcliitivc 10 tlic iz = S S m m position.

-201 -70 -35 0 35 70

11, deg.

11, den.

~ ' ~ ~ ~ l i ~ ~ ~ ~ l , ~ ~ ~ ~ i ~ l ~ / ~ ~ ~ ~ i i ~ ~ ~ ~ ~ . ~ , / i ~ ~ di//wwi Imh, lowiims 6, = 2.25 Fig. 3 . .., ., . I . ~ IS. ~ 20 - I. = io . ~ 20. /, ~ IS. /,/ ~ i i

3 Computed and experimental results

The diincnsion 01' the cavity nidiating aperture arc 15 x 70nni1, i.e. O.I25&, x O.SS&,,, and ils depth is 7Onnii. Tlm operating Trcqiicncy is 2.SGllz. The CO-polar ;izi~nnlhiil radiation pattern, tlic doininanL u-coinponeiil of I fiinction of H as sliowii in fig. I with it polypropylene diclecil-ic cube of dielcclric cotiskint = 2.25 and 15mni side sytntnctrically posilioncd i n tlic cavity and ils y-position varied, was measured i n an ancclioic cliambcr. The position of lhe excitation probc ( I , , /n) is dclincd in Fig. I . Conipiitcd results obtained using the formulation described in Section 2 arc also prcscnlcd along with the experimenlal rcsiills for tlic cases 01' a dielectric positioned at various locations as shown in Fig. L . 111 all CRSCS, where present, the diclectric block is positioncd along tlic y-;ixis so thal its face was parallel to the riidialing hacc O T lhc cavity. The rcsult- ing radiation pattern and prediclion Tor tlic probe-Ted cavity witliout dielectric prcseiit is given in Fig. 2. The 5dB heamwidth with no dielectric present was 93" ineasurcd and 90" compiitcd. The clioicc of localion of the feed probe lcads LO shaping of the far-licld patterns. Some samplc locations arc shown i n Fig. 3 it1 tlic prcscncc of the dielec- tric block dcfincd i n Fig. I, The position for iniixiiniini beam symmctry for minitnuni sidelobe level was located at iz = 55, I , = 15, J I I = 20. For the rest of thc work presented

IIlR P~i~i.-hIi~ra~~. Av,c~,uJ,,,s I'i.oi,os IVd 147, I\'<,. 3, . / c r r r 2llllf~

~ 7 0 4 5 0 36 70 ( I , dog.

-20 -70 LIII_, -36 0 35 70

11, deg.

I97

7'bc reason for this can bc obtaincd by invesligating tlic radiating aperture current distribution. Hcrc, since l l ie tlielectric is only partially filling lhc spice, little intcrniil ficld pcrturhation is occurring. l f the dielectric cons(ant or the material i s increased then lbc perturbation will bc inore pronounced.

An interesting feature in these results i s tliiit the coiiipu- tatioii predicts tlic experinicnlal shape of' l hc iniiiii beam to a lcvcl of approxiiixilcly 5dR below the pcak OS thc pattern. Also, thcrc is a narrowing or the bcam iii the prcscncc or the tiill-height diclcctric cube, i.e. thc dielectric cuhe iicls its ii focusing cleiiiciit. With tlic iivaibble coni- puling facility, the problem geometry quanlised to I nini resolution, the subscqucnt nuiiicrical reprcsctilation requires a dcnsc niiilrix OS the order 2100 x 2100 rcquir- ing eight iiiiiiulcs or CPU time wlieii computed on a Dec- Alpha computer (or its complete solution and about 250MB RAM. The method of iiiatrix solution was LU decomposition [I I]. In the above results we used ti coni- incrcial software package [I21 based 011 a finite clcniciit inclhod (FEM) with absorbing houndary conditions. In every case il was round that the FEM forintilation f i i i led 10 predict adequately tl ic amount of beam compression (Figs. 2 and 4-6).

11 i s difficult to commcnl a s to why this should be. How- ever, wc note that, as described in [13], Lhc way in which the conliniiily of electric ficld aod nnignelic field is 1101'-

inally applied in an I'EM solution may lcad to a spurious condition of continuity of the norinal elcctric conipoiicnl field. In the problem under consideration hcrc there is ii

discontinuity in the normal electric ficld which arises from a n abrupt change in the dielectric constant iii the cavity body due to the prcscncc of the dielectric inscrl. A solution used in FEM to accommodate this effccl is l o Soniiulalc l h e problem in terins OS magnetic lield which i s continuous cvcrywlicrc II 31. Further investigation of this aspect i s beyond tlic scope 01' this paper.

4 Conclusions

The method or compul;ilion proposed here allows direct trcatment of a dielectric which is in conpact with a inclal siirfiia. ?'lie procedure wbicli pi-oduccs iiii analysis iii a sin- gle-pass calculation has hccn sliowii l o account Tor tlic cxpcritiicntal ohservations. 'rllc restills presented tire more physically representative than those obtained l'roiii FEM solution.

5 Acknowledgments

We thank EPSRC (UK) GRIL32XM/1<5X449 for giving fiilaiicial support Tor the invcstigation

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