Half width leaky wave antennas

Transcription

1 Hlf width leky wve ntenns G.M. Zelinski, G.A. Thiele, M.L. Hstriter, M.J. Hvrill nd A.J. Terzuoli Astrct: Leky trvelling wve ntenns tht use the first microstrip higher-order mode re nlysed. The ntenns investigted here re only hlf the width of previous leky wve designs nd utilise structure tht inherently suppresses the fundmentl mode. Since mode purity is ssured, the need for n elorte feed structure is eliminted. A mens for extrcting the complex propgtion constnt of leky wve ntenn is presented using the finite difference time domin (FDTD) method. Agreement is shown etween the resulting propgtion constnt nd nother estlished theoreticl method, the trnsverse resonnce method. Representtive mesured fr-field ptterns re included, which re consistent with the computed propgtion constnts. The properties of curving the leky wve structure re lso studied. Introduction Microstrip ntenns re ttrctive ecuse of their light weight, low profile nd low cost. These ntenns my e grouped into two clsses:. resonnt ptch, which is nrrownd with fixed min em, nd 2. nonresonnt leky wve ntenn, which typiclly hs wider ndwidth with frequency-steerle min em. A leky wve ntenn must e excited y higher-order mode [], since the fundmentl mode of microstrip does not produce fields tht decouple from the structure. If the fundmentl mode is not llowed to propgte, the next higher-order mode my dominte ove its cutoff frequency. Fig. shows the electric field lines due to the first higher-order mode EH, s defined y Bgy et l [2]. A phse reversl, or null, ppers long the centreline tht results in oppositely-directed E fields t the edges, llowing the fields to decouple nd rdite. In the lte 97s, Ermert [3, 4] ws the first to pulish the properties of higher-order microstrip modes. However, his work ws incomplete ecuse his longitudinl propgtion constnt consisted solely of phse constnt, ut neglected the lekge constnt. At out the sme time, Menzel [5] pulished pper on microstrip trnsmission line ntenn employing the first higher-order mode. He ssumed there ws meningful lekge constnt to llow the structure to rdite, ut he did not recognise tht he hd developed leky wve ntenn nd, thus, uilt it too short [6, 7]. Oliner [] further clrified the fct tht Menzel hd ctully uilt leky trvelling wve ntenn with complex propgtion constnt. # The Institution of Engineering nd Technology 27 doi:.49/iet-mp:26 Pper first received 2th Jnury nd in revised form st My 26 G.M. Zelinski is with the Air Force Reserch Lortory (AFRL) Wright- Ptterson AFB, OH G.A. Thiele is with the Electricl nd Computer Engineering Deprtment, University of Dyton, Dyton OH M.L. Hstriter, M.J. Hvrill nd A.J. Terzuoli re with the Deprtment of Electricl nd Computer Engineering, Air Force Institute of Technology, Wright-Ptterson AFB, OH E-mil: gregory.zelinskil@wpf.f.mil Since the lte 97s there hve een numer of ppers on microstrip leky wve propgtion. Leky wve propgtion hs een studied in [2], [8 ] nd leky wve ntenns in [ 7], lthough, the potentil of these ntenns hs not een fully explored. The performnce prmeters of trvelling wve ntenn cn e predicted s function of the wvenumer in the direction of propgtion within the structure. Referencing the min em to endfire (u ¼ 98 nd f ¼ 8), the guided wve phse constnt determines the direction of the min em, nd the guided wve ttenution constnt determines the emwidth of the min em. Both constnts together determine the leky wve ndwidth. Wlter [8] provides n excellent source for nlysis of trvelling wve ntenns. Determintion of the complex propgtion constnt proved quite difficult for the uthors using mesurements. While it my e possile to extrct ll prk propgtion constnt from fr-field mesurements, the ccurcy nd precision re questionle. Ner-field proing techniques show promise ut cn e time-consuming nd lorious [9]. To this end, this work vlidtes its findings y showing greement etween two independent estlished theoreticl methods, the finite difference time domin (FDTD) method nd the trnsverse resonnce method. Fig. shows design enhncement sed on Menzel s ntenn tht incorportes metl ifurction down the centerline to lock the fundmentl mode. Symmetry long this metl wll prompts the ppliction of imge theory. One entire side of the ntenn is now n imge of the other side, mking it redundnt nd not needed. The resulting modified ntenn in Fig. c is hlf the width of Menzel s ntenn. Menzel s originl full-width design, which uses seven slots cut from the conductor long the centreline to suppress the fundmentl mode, cn e seen in Fig. d. Menzel s ntenn requires gret effort to develop the pproprite slot structure nd feed to reduce the EH mode s much s possile. The use of shorting wll to reduce the size of microwve ptch ntenns is well known [2]. However, it is elieved tht the use of shorting wll hs not previously een pplied to microstrip leky wve ntenns to reduce their size. A purpose of this pper is to investigte the reduced size, or hlf-width (HW), microstrip leky wve ntenn. IET Microw. Antenns Propg., 27,, (2), pp Authorized licensed use limited to: Universidd de Crtgen. Downloded on July 2, 29 t 6:8 from IEEE Xplore. Restrictions pply.

2 Fig. The leky trvelling wve ntenns tht were nlysed Electric field pttern ssocited with the first higher-order mode of microstrip EH [2] Cross-section of the full-width (FW) ntenn, which incorportes metl ifurction long its entire midline c Cross-section of the hlf-width (HW) ntenn, with metl ifurction (wll) ttched to its entire right-hnd edge d Menzel s originl full-width ntenn [5], HW nd FW ntenns use feed structure similr to the Menzel ntenn, lthough, they do not require mtching stu Advntges of the hlf-width (HW) ntenn compred to the Menzel ntenn re: () no need to suppress the EH mode; () no slot cross-polrised rdition tht reduces rdition efficiency; (c) purer guided mode compred to the Menzel configurtion, which improves rdition efficiency; nd (d) potentilly less interction in n rry environment. 2 FDTD simultion 2. Determintion of nd stte in which the trvelling wve distriution hs constnt wvelength, only n ntenn length of l /2 in the ^x-direction is needed for determintion of the wvenumer. 2.2 The Computtionl domin The three ntenns of Fig. were investigted for performnce. An FDTD lgorithm [2] ws used employing 3-D centrl differencing Yee-cell formultion with unixil perfectlymtched lyer (UPML). The UPML ws -cell-thick, fourthorder polynomil grded nd PEC-cked on ll six fces. The loss mechnism ws normlised to free spce to llow lyers of unlike mterils within the PML. The ojective of the FDTD simultions ws to provide the propgtion constnt of the verticl component of the electric field E z inside the sustrte etween the top conductor nd the ottom ground plte. The E z dt ws retrieved from single row of cells stretching the length of the ntenn in the ^x-direction ner the open edge. The logrithm of the normlised mgnitude of the ^z-directed electric field from these cells creted wveform from which nd were extrcted using E z ¼ e ðþjþx ln E z ¼ x jx ðþ ln E z, normlized db λ β As shown in Fig. 2, is the slope of the peks of ln E z (shown s dotted line) nd is found from the seprtion of nulls using ¼ 2p l Provided the simultion runs long enough to ensure stedy 342 ð2þ Distnce from source, m Fig. 2 Nturl logrithm of the simultion dt used to determine the propgtion constnt in the x^-direction. is the slope of the dshed line nd l is the distnce etween three successive nulls IET Microw. Antenns Propg., Vol., No. 2, April 27 Authorized licensed use limited to: Universidd de Crtgen. Downloded on July 2, 29 t 6:8 from IEEE Xplore. Restrictions pply.

3 The copper conductor ws modelled s zero-thickness perfect electric conductor (PEC) y setting the tngentil electric field to zero t the desired cell oundries. Sheen [22] demonstrted tht modelling microstrip ptch ntenn in this fshion ctully cuses the model to perform s if the PEC is extended one-hlf of cell further on ll open edges due to the FDTD method. This work supports his findings. Cre ws tken to ccurtely model the width of the ntenn in the ^y-direction y reducing the width of the FDTD ntenn model y one-hlf of cell for the HW ntenn nd one entire cell for the FW. The excittion mens ws hrd source, s defined y Tflove nd Hgness [2], nd ws modelled t the field point closest to the midpoint of the sustrte thickness. The source wveform ws constnt sinusoid with cuic growth over the first few periods to eliminte the prolemtic high-frequency components of rpid trnsitions. Simultions were run for every frequency point of interest. Hd computer resources ecome n issue, pulse wveform would hve een more elegnt solution tht would hve yielded the dt for ll frequencies in single tril. To isolte the forwrd trvelling wve, the reflections from the free spce oundries t the ends of the sustrte needed to e eliminted. This ws ccomplished y extending the sustrte directly into the UPML, nd modifying the ffected UPML cells to mtch the sustrte. The resulting grid spce for the full-width (FW) ntenn is seen in Fig. 3. The UPML sors ll outwrd propgting wves in the sustrte llowing the forwrd trvelling wve to develop exclusively. For the model of the FW ntenn, [dx : dy : dz] ¼ [.4722 :.546 :.574] mm grid discretistion ws used, which is roughly [3 : : ], with [Ny, Nz] ¼ [96, 5] cells in the ^y-nd ^z-directions, respectively. Note tht, in the ^y-direction, the ntenn width is mm ffi 4.84 mm, which is pproximtely one dy reduction from the ctul ntenn s width of 5 mm. The numer of cells in the ^x-direction vried with frequency. While it is possile to determine the propgtion constnt with s little s one-hlf l, it is esier to guge stedy stte from wveform progression with over two l in length. Likewise, the HW model lso used [.4722:.546:.574] mm discretistion with [48, 5] cells in the ^y-nd ^z-directions, respectively. In the ^y-direction, the ntenn width is mm ffi 7.42 mm, which is pproximtely one-hlf dy reduction from the ctul ntenn s width of 7.5 mm. Agin, the numer of cells in the ^x-direction vried with frequency. The stndrd CFL stility condition ws used to determine the time-step. Simultion times were s short s 5 min for the highest frequencies up to s long s 8 h for the lowest frequencies. Convergence ws met within.% of the extrcted wvenumer for ll trils. Resolution within the dielectric exceeded 5 cells per wvelength for ll HW nd FW trils. The sustrte modelled, Rogers Duroid 587 highfrequency lminte, hs nominl loss tngent of only.2 t GHz. FDTD trils demonstrted tht neglecting this loss in the nd of interest, 6 8 GHz, ffected the extrcted propgtion constnt y no more thn % nd freed nerly 5% of the memory. To further reduce memory demnds of the lrgest simultions, single precision ws used resulting in pproximtely 4% decrese in memory usge. These prmeters llowed ll simultions to e ccurtely run on 2.75 GHz PC with only GB of RAM. 2.3 Trnsverse resonnce pproximtion For comprison, trnsverse resonnce pproximtion ws creted following the work of Oliner nd Lee [6, 23] which they confirmed with steepest descent contour nlysis. Fig. 4 shows trnsmission line model tht is pplicle to the cross-section of the Menzel, FW nd HW ntenns. Ech structure cn e modelled s dielectric-filled prllel plte wveguide of dmittnce Y terminted t one end y short circuit nd the other end y dmittnce Y t. The E null generted in the EH mode y verticl wll or trnsverse slots is represented y short circuit. Y t is n pproximtion of the dmittnce of n open edge of microstrip developed y Chng nd Kuester [24, 25] using the Wiener Hopf technique to nlyse TEM wve tht is completely reflected. The trnsverse resonnce reltion G left ðyþg right ðyþ ¼ ð3þ must hold for ll points in the trnsverse ^y-direction. The reflection coefficient D due to the dmittnce of the end of the microstrip Y t is unity with phse shift x, s defined in [24, 25]. Referring to Fig. 4, t point y ¼ y just to the right of Y t GleftðyÞ ¼e jx ð4þ G right ðy Þ¼ e j2kw 2 ð5þ Fig. 3 2-D depiction of the 3-D computtionl spce used to model the FW ntenn ^y ^z slice of the FW ntenn extending into the UPML (not to scle); single source cell is mrked y n X; ^x ^z slice of Fig. 3 is outlined ^x ^z slice of the FW ntenn extending into the UPML (not to scle); ^y ^z slice of Fig. 3 is outlined The co-ordinte system is consistent with Fig. where k ¼ 2j is the complex wvenumer in the sustrte nd w is the width of the structure. Eqution (3) ecomes e jðx kwþ ¼ x kw ¼ +np n ¼ ; 3; 5;... ð6þ n ¼ for the EH mode. IET Microw. Antenns Propg., Vol., No. 2, April Authorized licensed use limited to: Universidd de Crtgen. Downloded on July 2, 29 t 6:8 from IEEE Xplore. Restrictions pply.

4 Fig. 4 Circuit model used with the trnsverse resonnce pproximtion Trnsmission line circuit tht pproximtes the dotted cross-section of ech of the three structures in () operting in mode EH Cross-sections of Menzel (top), FW (centre) nd HW (ottom) Fig. 5 shows tht the trnsverse resonnce pproximtion is in greement to within % of the FDTD-derived dt over the entire leky nd. 3 Results 3. Similrities/differences etween HW, FW, Menzel Generlly our simulted nd mesured results showed the HW ntenn to hve dvntges over the FW ntenn nd Menzel ntenn. At most leky nd frequencies, the Menzel configurtion used here hd noticely lrger crosspolristion (e.g. db t 6.2 GHz decresing to 2 db t 7.7 GHz) in the fr-field s typified y the mesurements in Fig. 6. This is due in prt to rdition y the nonresonnt slots used to suppress the fundmentl mode in the Menzel configurtion. The cross-polristion energy from the Menzel slots leds to decresed copolristion gin mesurements, s indicted in Fig. 6. The copolristion decrese of the Menzel configurtion is typiclly of the order of 3 db, lthough Fig. 6 shows n even greter reduction t 7.2 GHz. Further, the FDTD nlysis shows tht the slots in the Menzel design re not s effective in keeping the fundmentl mode suppressed s is the longitudinl wll in the FW nd HW ntenns. The copolristion mesurements show tht the HW ntenn, in which the wll ws fricted with vis spced less thn tenth of wvelength prt, hs slightly different minem loction nd n incresed ckloe. This difference is due to n uncertinty s to the effective width of the ntenn since the vis re of finite dimeter Mgnitude, db Angle from endfire, degrees HW (mesured) FW (mesured) Menzel (mesured) or β / k β / k Trnsverse Resonnce Approx FDTD Simultion Fig. 5 FDTD simultion of the HW is in greement with the trnsverse resonnce pproximtion 344 Mgnitude, db Angle from endfire, degrees HW (mesured) FW (mesured) Menzel (mesured) Fig. 6 Mesured fr-field ptterns of the HW, FW, nd Menzel ntenns t 7.2 GHz Cross-polrised Co-polrised IET Microw. Antenns Propg., Vol., No. 2, April Authorized licensed use limited to: Universidd de Crtgen. Downloded on July 2, 29 t 6:8 from IEEE Xplore. Restrictions pply.

5 β / k.8 β / k or β / k Trnsverse Resonnce Approx FDTD Simultion or β / k Trnsverse Resonnce Approx FDTD Simultion Sustrte height, mm Width, mm Fig. 7 Simulted effects t 6.7 GHz of vrying the () height nd () conductor width with the other prmeters unchnged Dshed line in () is qudrtic lest squre of the FDTD dt points; Prmeters of the HW ntenn re h ¼.787 mm, r ¼ 2.33 nd w ¼ 7.5 mm nd merely pproximte solid wll. The effective width significntly ffects nd [26]. Slightly reducing the width of the HW y.5 mm mtched the nd of the FW nd Menzel ntenns seen in Fig. 6. Our simulted results confirmed tht nd of the FW nd HW ntenns were the sme, s nticipted y imge theory. Further, the FW ntenn induced fields in the pssive side tht degrded the 88 phse difference cross the width of the ntenn [26]. This resulted in decresed rdition efficiency (i.e. reduced mesured gin) for the FW ntenn reltive to HW ntenn with the sme, s evidenced in Fig Limittions of the trnsverse resonnce pproximtion The trnsverse resonnce model ws useful to get quick pproximtion; however, new model would e needed for geometries other thn those in Fig.. In ddition, the Y t pproximtion is not vlid when the microstrip is curved or tpered. Kuester et l. [25] stte pplicility to only electricllythin sustrtes in which h p v ffiffiffiffiffiffi m ð7þ shifted. The choice of sustrte mteril nd thickness is usully dictted y cost or vilility of mteril, therefore, the width is typiclly the prmeter to mnipulte. Fig. 7 illustrtes the reltionship etween the height, or thickness, of the sustrte nd the propgtion constnt. Like permittivity, the height of the sustrte is usully dictted y the mteril ville. All ntenns simulted nd fricted for this work used mteril tht ws.787 mm thick. As mentioned in the previous section, the trnsverse resonnce solution includes n pproximtion tht limits its pplicility to electriclly-thin sustrtes. The difference in etween FDTD nd trnsverse resonnce ecomes noticele for heights greter thn pproximtely.375l, which is. mm t 6.7 GHz. Fig. 7 shows tht the propgtion constnt is very sensitive to the width of the conductor strip. As little s. mm difference in width will cuse s much s % chnge in. This sensitivity to width requires dequte friction precision. 3.4 Effect of curvture on nd Shown in Fig. 8 is curved HW ntenn with its wll long the inside edge. Simultions were done t rdii of 3.36, 4.23, 5.32 nd 9.3 cm. 88 ws simulted when possile. Only For sustrte thickness h ¼.787 mm, (7) requires frequencies 4 GHz, which is five times higher thn the highest frequency of this leky nd. Fig. 7 shows tht FDTD nd trnsverse resonnce egin to disgree s the height of the sustrte increses pst the electriclly-thin criteri of (7), ner h ¼. mm t 6.7 GHz. 3.3 Modifying dimensions to meet ndwidth specifictions The leky ndwidth is defined y ¼ t the lower end nd ¼ k t the upper end []. Bndwidth round desired centre frequency f c cn e chieved y scling the width of the conducting strip, the height (or thickness) of the sustrte nd/or the permittivity of the sustrte. The ndwidth cn e incresed, to limited extent, y the selection of the sustrte mteril. As frction of the centre frequency, the percent ndwidth will e unffected y ltering the height nd width, lthough f c cn e redily Fig curved HW ntenn computtionl domin with the wll on the inside of the curve Source cell mrked y the X in the lower left of the figure; guided trvelling wve extrcted from the cells mrked y the dotted line long the open edge using ngulr position u with respect to the source cell IET Microw. Antenns Propg., Vol., No. 2, April Authorized licensed use limited to: Universidd de Crtgen. Downloded on July 2, 29 t 6:8 from IEEE Xplore. Restrictions pply.

6 Tle : Summry of curvture trils Stright Rdius (cm) Arc length (cm) N/A Lrgest l possile (cm) N/A Lowest f possile (GHz) N/A Approx. ndwidth (GHz) Bndwidth is the frequency difference etween ¼ nd ¼ k o 98 ws simulted for the 9.3 cm rdius model due to vilility of computing resources. All curved HW ntenn models used grid discretistion of [dx :dy :dz] ¼ [.236 :.236 :.574] mm, which is [.5 :.5 : ]. The size of the FDTD computtionl domin for the ntenn modelled with rdius of 3.36 cm ws [Nx, Ny, Nz]¼ [337, 84, 5], resulting in 3 4 cells, not including the PML. Similrly, the 4.23 cm rdius used 4 45 cells, the 5.32 cm rdius used cells nd the 9.3 cm rdius used cells. The size of the computtionl domin of ll curved simultions necessitted only single precision, due to the GB memory limittion. Like the stright ntenn models, the length of the curved ntenns needs to e longer thn one-hlf l to extrct the wvenumer. No sugridding of the curved edges ws necessry since the resolution for ll FDTD trils of curved ntenns ws over cells per wvelength in the dielectric. The curvture trils re summrised in Tle. Fig. 9 shows tht curvture increses ndwidth somewht y flttening, predominntly for the lower frequencies, while keeping reltively unffected. As the rdius of curvture decreses, the ndwidth increses. Curvture with the wll on the outside hmpers the ility of the ntenn to set up only the EH mode. As seen in Fig., 88 rc of rdius 4.23 cm produces destructive interference indicting the presence of one or more other modes. 3.5 Effect of multiple elements on nd The min em of trvelling wve ntenn is frequency-steerle in the longitudinl direction from ner endfire to ner rodside. A liner rry of HW elements is, therefore, le to scn in two dimensions. A first step to developing such n rry is to determine the effect of spcing etween neighouring elements. Two elements were simulted next to ech other t 7.2 GHz. The results were nerly identicl regrdless of whether the second element ws excited or not. The impct on the propgtion.8 β / k.8 β / k or β / k.6.4 Trnsverse Resonnce Stright 9 o Curve or β / k.6.4 Trnsverse Resonnce Stright 8 o Curve β / k.8 β / k or β / k.6.4 Trnsverse Resonnce Stright 8 o Curve or β / k.6.4 Trnsverse Resonnce Stright 8 o Curve.2.2 c d Fig. 9 FDTD simulted dt for curved HW ntenn with rdius of () 93 mm () 53 mm (c) 42 mm (d) 34 mm For comprison, the single precision curved dt is plotted longside the single precision stright dt 346 IET Microw. Antenns Propg., Vol., No. 2, April 27 Authorized licensed use limited to: Universidd de Crtgen. Downloded on July 2, 29 t 6:8 from IEEE Xplore. Restrictions pply.

7 Wll on the INSIDE of the curve Wll on hte OUTSIDE of the curve E z, normlized.2.2 Actul Error Position long curve, degrees from source Element spcing, frction of λ.8 Wll on the INSIDE of the curve Wll on hte OUTSIDE of the curve.6 β / k E z, normlized Reltive error, % Position long curve, degrees from source Element spcing, frction of λ Fig. FDTD simultions of curved HW ntenn with the wll on the outside produces field distriutions, suggesting the presence of multiple modes 6.4 GHz 7.4 GHz constnt y neighouring element is shown in Fig.. There is miniml interction etween elements if they re seprted y t lest.25 l nd virtully no interction if the spcing is over.4 l. 4 Conclusions The hlf-width (HW) leky wve ntenn ws shown to e n improvement over the previously reported full-width (FW) ntenn s well s the originl Menzel ntenn in the following wys:. The verticl wll used in the HW nd FW ntenns ws found to e etter t suppressing the fundmentl mode thn the slots in the Menzel ntenn. 2. Since the mode purity in the HW nd FW ntenns is ssured y the verticl wll, the feeding of these two ntenns is simplified; for exmple, just simple mtched microstrip trnsmission line is required for the HW ntenn or 88 hyrid nd mtched trnsmission line for the FW ntenn. 3. The slots in the Menzel configurtion were found, in the pttern mesurements nd in the FDTD modelling, to contriute noticely to cross-polristion. The crosspolristion of the HW pttern ws typiclly found to e 3 6 db lower thn tht of the Menzel design. Fig. Impct of neighoring element on the HW ntenn s propgtion constnt Actul error of jj (dshed line is qudrtic lest squre) Reltive error of (dshed line is liner lest squre) from plcing nother element frction of wvelength from the open end of the ntenn in FDTD simultions For oth figures, the error is with respect to the guided wvenumer of single element 4. With the verticl wll used here, imge theory suggests tht one-hlf of the FW ntenn my e discrded. In fct, it ws found in the FDTD computtions nd in the pttern mesurements, tht the presence of the pssive side reduced the rdition efficiency, since the unintentionl excittion of the pssive side degrded the 88 phse difference cross the width of the FW ntenn. 5. Our FDTD modelling indictes tht there ws no effect oserved on the propgtion constnt of prllel HW elements if the spcing distnce ws greter thn.4 l. This reltion simplifies design in n rry environment 6. The (H-plne) curved HW ws investigted nd found to retin mode purity. It is unlikely tht FW (with verticl wll) or Menzel design could chieve this. As function of (H-plne) HW curvture, no significnt impct to ws noticed compred to the stright cse. However, the plot showed significnt flttening, prticulrly t lower frequencies. Flttening without ffecting results in ndwidth increse. The primry tool in this investigtion ws threedimensionl FDTD modelling, the results of which greed with the trnsverse resonnce method. Experimentl IET Microw. Antenns Propg., Vol., No. 2, April Authorized licensed use limited to: Universidd de Crtgen. Downloded on July 2, 29 t 6:8 from IEEE Xplore. Restrictions pply.

8 mesurements were confined to fr-field ptterns ecuse previous work [9] indicted tht the FDTD results for the complex propgtion constnt were more ccurte thn could resonly e expected from experimentl proe mesurements. A method ws introduced in Section 2. to extrct the complex propgtion constnt from FDTD dt. It is elieved tht this method hs not een previously developed. In ddition, severl mens were found to decrese the numer of FDTD cells required to ccurtely model the ntenns investigted here. This llowed elorte simultions using only stndrd desktop PC with GB of memory. Thus, high-performnce computing resources, which re typiclly required for such simultions, were not needed nd not used. 5 Acknowledgments The uthors would like to cknowledge the technicl support y Dr. D. Jnning nd the mesurement support of J. Rdcliffe, oth of the Air Force Reserch Lortory (AFRL) Rdition nd Scttering Compct Antenn Lortory (RASCAL) fcility. The foundtion FDTD code ws grciously furnished y Dr. S Hgness nd K Willis of the University of Wisconsin Computtionl Electromgnetics Lortory. Although their code ws extensively rewritten nd modified for our purposes, it provided n excellent strting point for our work. The views expressed in this rticle re those of the uthors nd do not reflect the officil policy or position of the United Sttes Air Force, Deprtment of Defense, or the United Sttes Government. 6 References Oliner, A.A.: Lekge from higher modes on microstrip line with pplictions to ntenns, Rdio Sci., 987, 22, (6), pp Bgy, J.S., Nyquist, D.P., Lee, C.-H., nd Yun, Y.: Identifiction of propgtion regimes on integrted microstrip trnsmission lines, IEEE Trns. Microw. Theory Tech., 993, 4, (), pp Ermert, H.: Guided modes nd rdition chrcteristics of covered microstrip lines, Arch. Elektron. Uertrg. technik, 976, 3, (2), pp Ermert, H.: Guiding nd rdition chrcteristics of plnr wveguides, Microw. Opt. 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