Comparison of matching layers for automotive radome design

Transcription

1 Adv. Rdio Sci., 8, 9 5, 2 doi:.59/s9 Autho(s) 2. CC Attibu 3. License. Advnces Rdio Science Compon lyes utomotive dome design, R. H. Rsshe, E. M. Biebl 2 BMW Goup Resech Technology, Munich, Gemny 2 Technche Univesität München Fchgebiet Höchstfequenztechnik, Munich, Gemny Abstct. Hidden teg GHz sensos hd plstic pted fsci epesents chllengg tsk sce both electomgnetic c body design constts hve to met. Th ppe compes diffeent possibilities low-cost teg d sensos. Bsed on model sttified medi, study most impotnt pmetes such s bwidth, ngle tolences. Ou esults suggest plstic fsci, equiements futue d sensos cn met low-cost. Even metllic pts, equiements imposed moden GHz d sensos cn met unde cet condis. toduc Automotive d systems, ft toduced on custome mket lte 99s, show stedy tend fom comt (Advnced Dive Asstnce, shot ADAS) to sfety oiented vehicle funcs (Active Sfety, shot AS). Rdbsed systems tend to ddess scenios gowg complexity, tgetg ubn o city tffic thn highwy scenios, wee m pplic ecent yes. Re nge, zimuth ngle tget velocity key fetue to del demg scenios high complexity high dynmics (Rsshe, 27). Euopen Union, new fequency b fom to 8 GHz GHz b hs en llocted to enble futue ADAS AS systems eplcg peviously used 2 GHz ultwide b d sensos. stt development GHz b technology, Euopen funded poject Rd on Chip Cs" (shot RoCC) stted fll 28 (RoCC, 29). teg GHz sensos to moden cs epesents chllengg tsk sce electomgnetic c body design constts hve to met simultneously. Th poblem even moe evident when moe thn senso hs to tegted, cuse hidden teg sensos hd plstic bumpe ten equied. As cle fom both oeticl vestigs fom pevious expeience GHz d systems, ope se sensos hd pted, plstic fsci led to pemnce d if no optimiz sttified dome stuctues pemed. millimete wve egime, electomgnetic field popgtes qusi-opticlly, esults high loss fctos obstcles o medi le-sight. Th cse if d senso to tegted bumpe o hd o fsci c. pemnce d due to s tween bumpe senso. bumpe consts genelly substte some lyes pt. Th ppe detiled impotnt electomgnetic dome popeties bwidth, ngle tolences substte pted substtes. Addilly, cost teg should t mimum, th ppe consides low-cost possibilities hidden teg d sensos. 2 Mmticl model electomgnetic oy fields sttified medi cn deived fom plne wve ssump boundy condis electomgnetic wves (timehmonic conven e jωt ). Kut Altenbug (953) th oy deived. It cn found tody mny books optics, electomgnetics o micowve oy (Hecht, 25). cse pependicul cidence TE-wve (deiv TM-wves ccodgly) wd- bckwd wves e defed, suize ll wves sme diec (impotnt diffeence to o ppoches). deiv cn found Hecht (25) suy it Fitzek Rsshe (29). Fo ech lye i mteil pmetes n i s dex efc (k i ω/c n i espectively), d i s, Z i s wve impednce semi-fite lye followg chtetic mtix cn deived. Coespondence to: (fek.fitzek@bmw.de) Publhed Copenicus Publics on hlf URSI Lesusschuss de Bundesepublik Deutschl e.v.

2 5 et l.: Automotive dome design 2 et l.: Automotive Rdome [ M i] [ m i m i ] 2 i teil i () 2 mi pmetes n i s dex efc (k i ω/c [ n i espectively), d i s ], Z i s wve cos(ki d i ) j Z i s(k i d i ) impednce j Z semi-fite lye followg (2) chtetic mtix i s(k i cn d i ) cos(k deived. i d i ) ) b) c-) c) mplitude [ M i ] [ ] tnsmsion- m i m i 2 fctos lye i emdded tween m i 2 m i (). ) substte mteil bumpe (no ), b) substte. () ddil substte mteil lye, bumpe c-) substte (no ), tegted sub- semi-fite lyes i i + [ ] e defed s cos(k i d i ) j Z i s(k i d i ) stte lye ddil ( optimiz), lye, (c-) c) substte substte tegted tegted lye ( lye (ib pile) optimiz), (c) substte te- Z i+m i j (2) +mi 2 Z Z i s(k i d i ) i+z i m i 2 Z cos(k i d i i m i ) Z i+ m i +mi 2 +Z i+z i m i 2 +Z i m i (3) gted lye (ib pile). mplitude tnsmsion- fctos lye i emdded tween semi-fite lyes i i+ 2Z i+ model cn used to clculte vlues desied. pemed ee, whee n optimiz lgoithm eltive pemit- bsed e t defed Z i+ m i s +mi 2 +Z i+z i m i 2 +Z i m i () cn Z i+ m i + m i 2 Z i+ Z i m i 2 Z i m i tivity on diect sech method lye used. e optimized. Two diffeent Th simuls ppoch With se Z i+ equs, m i + mi 2 + tnsmsion Z i+ Z i m i 2 + Z i m i (3) fcto neglects cn pemed oughness whee mteil ssumes eltive pemittivity plne mteil. lye e optimized. Th ppoch i+ nonmgnetic, cn deived usg lods chctetic mtix 2 Z M i t. FoZ i+ multilye m i medi, chctetic medi mtices hve to multiplied + mi 2 + Z i+ Z i m i 2 ight ode. + Z i m i () neglects Fo ddil oughness mteil lye, bumpe ssumes mteils nonmgnetic, plne o pt) mteil. e not chnged. On o h, (substte With se equs, tnsmsion fcto n Fotegted ddil lye, lye, bumpe mteils substte (substte o pt) chnged e not ccodg chnged. to On o h, th lye. n cn deived usg lods chctetic mtix mteil 3M i. oy Fo multilye pctice medi, chctetic medi mtices Th tegted esults decesed lye, substte mte- mteil chnged bumpe. ccodg With th to tegted th lye. te- Th hve to multiplied ight ode. oy well kn fom tnsmsion le gted esults stuctue decesed optimiz substtecn mteil modeled. bumpe. Fo With ltte th eltive tegted pemittivity fixed tegted to, oy. im lwys to get high tnsmsion next to 3 low oy (powe pctice ). losses mteil whees stuctueit ee feedom optimiz cn tegted modeled. stuctue. Fo cn t compensted, esults decesed tnsmsion. Fo semi-fite lyes, methods hee cn 3. oy well kn fom tnsmsion le ltte eltive pemittivity fixed to, whees it oy. im lwys to get high tnsmsion next to ee tegted feedom stuctue tegted stuctue. used s well. Neveless, -wve pplics low (powe ). losses mteil constts should cefully consideed cn t compensted, esults decesed tnsmsion. Fo semi-fite lyes, methods hee cn 3. tegted tegted stuctue stuctued dielectic Fitzek Rsshe, 29). ib pile) cn ny stuctue fullfills Fo bumpe constent lye substte sevel lyes pt, e exts diffeent ops mtch- diec homogeneity used s well. Neveless, -wve pplics tegtedlimit p < stuctue λ/ p sstuctued cell size dielectic constts should cefully consideed ib pile) popg, cn ode ny stuctue to void psitic fullfills sctteg g. One to optimize substte. Fo effects. (Fitzek Rsshe, 29)). homogeneity Fo esy limit teg p < λ/ ib pile p s cellpossibility. size homogeneous mteil th esults multiple hlf-wvelengths. Fo sttified medi, tivity e Fo bumpe constent lye substte sevel diec exts popg, sevel methods ode to clculte to void psitic eltive sctteg pemit- lyes pt, e exts diffeent ops. effects. Fo suchesy stuctues teg (Bi, 23). ib pile Hee method possibility. bsed cn found mimiz coefficient on One to optimize substte. Fo homogeneous mteil th esults multiple e tnsmsion exts sevel lemethods models to clculte used eltive esultg pemittivity pemittivity such stuctues descid (Bi, 23). s Hee men method eltive bsed though ticl model. Th hs eltive ee feedom decesed substte chctetic hlf-wvelengths. Fo sttified medi, cn on tnsmsion impednces le models (Z µ used µ ) esultg fee mteil. Ano possibility n ddil lye found mimiz coefficient though spce eltive pemittivity substte descid dependg s on men tio ibs eltive plced diectly onto bumpe. Th mteil cn ticl model. Th hs ee feedom - decesed substte substte spce cn substte eched. dependg on tio ibs bs. chctetic Hence, impednces eltive pemittivity (Z tween µ hve desied eltive pemittivity, hs µ ),s fee ees feedom. One could lso conside tificil mteil. Ano possibility n ddil lye bs. ( Hence, eltive pemittivity tween stuctues o even metmteils s n ddil,s plced diectly onto bumpe. Th mteil cn tb Z substte cnsubstte eched. lye, s mentid bove, low-cost focus th ppe, se ops e not consideed. ( +t ibz ) 2 (5) hve desied eltive pemittivity, hs t b +t ib ees feedom. One could lso conside tificil tb Z substte stuctues thid o even metmteils op s comb n ddil se + t ib Z ) 2 If ibs (t ib ) e pedefed due to mnufctug constts, cn esily ib (5) t lye, methods. s mentid ee, bove, low-cost stuctue ib pile) focus th ppe, b + t clculte ssembled to subtte se mteil ops e not bumpe. consideed. Becuse bs (t If b ) to ech desied vlue ibs (t ib ) e pedefed s clculted due to mnufctug constts, cn esily clculte ovell thid op stys constnt, comb th se method optimiz lgoithm. hs methods. ees ee, feedom stuctue (depth eltive ib pile) pemittivity Figue bs 2 (t b ) to ech desied vlue eltive pemittivity s clculted ssembled to tegted subtte stuctue). mteil Figue depicts bumpe. Becuse diffeent vesus tio optimiz bs to lgoithm. ibs constnt ib. possibilities. ovell Fo ll stys constnt, methods th ticl method It Figue cn 2 seen vi eltive eltive pemittivity pemittivity model hs cn ees used to clculte feedom (depth vlues eltive pemittivity desied n vesus cesed tio b bs to (esultg ibs constnt highe ib. vlues). tegted ee, stuctue). n optimiz Figue depicts lgoithm diffeent bsed lowe, It cn thn seen smlle vlues vi eltive b. pemittivity Th on possibilities. diect sech Fo method ll used. methods Two diffeent ticl simuls n n cesed impotnt b design possibility (esultg lte on. highe vlues) Adv. Rdio Sci., 8, 9 5, 2

3 et l.: Automotive Rdome 3 et l.: et Automotive l.: Automotive Rdome Rdome 3 3 et l.: Automotive dome design eltive eltive pemittivity pemittivity eltive pemittivity pemittivity ib pile b / ib pemittivity pemittivity ib pile ib pile b b / ib / ib lye / () Optimiz lye fequency / lye / 2. Pemittivity ib pile () Optimiz fequency 2. Pemittivity ib pile. () Optimiz () Optimiz fequency fequency 2. Pemittivity 2. Pemittivity ib pile ib pile. lowe, thn smlle vlues b. Th 2. n impotnt Compon design possibility lte lyes on lowe, lowe, thn thnsmlle smlle vlues vlues b. b. Th Th 2. Fo compon se diffeent ppoches optimiz lgoithm vulized gphs ll 2. n impotnt impotnt design design possibility possibility lte on. lte on Compon lyes ees feedom. Th mens ll thick- FoCompon ness compon Compon lye, sell diffeent lyes lyes ppoches eltive pemittivities optimiz elgoithm. Obviously vulized th cn not gphs d ll elly ll pos- Fo ees sibilities, Fo compon feedom. dcete compon Th se vlues mens se diffeent e chosen diffeent ppoches ll steps ppoches. eltive miz lgoithm pemittivity. optimiz opti- lgoithm lye, vulized ll vulized eltive gphs gphs pemittivities ll ll ees e. Th feedom. ees Obviously d Th feedom. th cn mens fequency Thnot mens d f ll.5 elly GHz ll ibilities, pos- so dcete lye, consideed bwidth B 8 GHz. Fo bwidth vlues ll lye, e llchosen eltive steps pemittivities eltive. pemittivities lye / e (meng wost cse) eltive. epemittivity. Obviously th cn not d elly ll possibilities, Th. Obviously th cn not d elly ll possibilities, Optimiz bwidth b consideed evlu. st d so dcete bwidth so vlues dcete fequency e chosen vlues tken f e chosen.5 steps n ngle GHz steps vi.. Optimiz lye bwidth / lye / eltive pemittivity. 3. Fequency bwidth. consideed eltive ngebwidth pemittivity. ±. B With 8 moe GHz. exct Fo bwidth ( stepsize Th Th.) d d lgoithm fequency fequency tolence f.5 GHz f.5 GHz Optimiz bwidth (meng wost cse) 3. Fequency bwidth Optimiz vi- consideed bwidth σ bwidth ±. B. evlu. bwidth consideed b consideed s B Fo 8 GHz. 8 ddil Fo GHz. st Fo bwidth bwidth lye vi ffects (meng (meng wost cse) wost th lye. cse) Fo 3. Fequency fequency (f bwidth.5 GHz). Consi 3. Fequency bwidth (B 8 GHz) im- bwidth tken ngle vi b nge consideed ±. optimiz With evlu. moe (tegted exct stlye) ( vi- lgoithm ffects tolence tken ngle subtte vi mteil vi- 7 lye Th vied chieved tween eltive pemittivity (itil con- b consideed evlu. st stepsize Consi povement low-cost bout mteils esultg eltive pemittivity eflec-.) bwidth nge bwidth tken n ngle vi bumpe. ±. With vi moe exct tegted stuctue ( stepsize (tegted Consi low-cost mteils eltive pemittivity s σ ±.. Fo ddil lye di) nge ±. With moe exct ( stepsize Consi It cn low-cost d mteils.7 seen. eltive pemittivity eltive pemittivity.) lgoithm lye) ffects tolence on h vis substte σ ±. mteil. Fo on o ddil h ou cse lye thickdi) 3. It cn seen eltive pe- lye vied tween (itil con- vi ffects th lye. Fo.) lgoithm tolence vis σ ±.. Fo ddil lye di) 3. It cn seen eltive pe- ngul 2.6 lye vied tween d..3 Hee (itil con- optimiz (tegted lye) vi ffects subtte mteil quency ness comb (f.5 GHz). fom Consi bwidth e used eflec- to cn vlues decesed eltive bout pemittivity 5 db thick- fe- vi ness ffects bs. th lye. Fo mittivity 2.6 d.3 vi ffects th lye. Fo mittivity 2.6 d.3 optimiz (tegted lye) vi ffects subtte mteil quency (f.5 GHz). Consi eflec- cn decesed bout 5 db fe- bumpe..addil vi optimiz tegted (tegted lye stuctue substte (tegted show hviou. b (B comb 8 GHz) mentid impovement e lso lye) vi ffects subtte mteil quency (f.5 GHz). Consi eflec- cn decesed bout 5 db fe- lye) ffects on h gives bout st esultg ngul. Hence, -7 bumpe. esults vi nddil tegted stuctue lye (tegted b (B 8 GHz) impovement substte mteil on o h ou cse bs. still low d.7. b subtte Th chieved coefficient eltive pemittivity n ngle ± 2. bumpe. vi tegted stuctue (tegted b (B 8 GHz) impovement mteil lye) ffects bumpe (no pt h consideed yet) e bout esultg -7 lye) ffects on h bout esultg -7 substte mteil 3 b. on se o figues h ft ou(+), cse st (dimond) lst bs. (x) gph e lwys highlighted to see fluence 7 db c seen.7t. edges b (/8 GHz) s Th ove fequency. chieved eltive pemittivity coefficient 2.bout ngul Figue (). Hee substte mteil on o h ou cse bs. e. d Next.7 to. tolence Th chieved eltive pemittivity 2.. Addil lye substte vlues eltive pemittivity clculted cesg eltive pemittivity. substte mteil hs comb ngul fom bwidth Figue e used (). to show Hee vi. Addil eltive pemittivity lye nge substte ngul σ ±.. Figue hviou. esults n ddil lye (). Hee,s 6.6i sub-ntte mteil bumpe (no pt consideed yet) e st esult ngul bwidth vlues eltive pemittivity. Addil bout d s 3. lyeconsi substte low-cost mteils Figue eltive n 3() ddil pemittivity 3. se lye figues lye sub- ft vied mum.2 hviou. comb tegted coefficient comb fom lye bwidth mentid ngle substte e ± e lsoused gives still to show comb low 2 fom vlues comb mentid e lso gives. eltive pemittivity e Hence, used to mxi- show esults tte (+), st mteil tween (dimond) esults bumpe (itil nlst ddil (x) condi) (no gph pt e consideed lwys 3. lye highlighted It cn yet) e seensub- mteil fluence Figue eltive 3() cesg pemittivity bumpe 3. eltive (no se pt 2.6 pemittivity. figues consideed ft yet) e mum quency. esults st esult coefficient n tegted ngul coefficient ngle. lye ± bout Hence, -7 sub- still db mxi- low st esult hviou. Figue ngul comb. mentid Hence, e ove mxi- fe- lso gives to seette (+), substte st d (dimond) mteil.3figue hs lst eltive 3() (x) gph cn pemittivity 3. e decesed lwys se highlighted figues bout nge 5 dbft low cn tte mum mteil seen t Figue edges bumpe coefficient (g b no (/8 pt nngle consideed) GHz) s ove ± clculted e. low Next to Figue tolence coefficient bout -7 vi- dbove fe- e fequency. still to,s see (+), 6 st fluence (dimond).6i cesg lst (x) eltive gph bout pemittivity. e lwys d s 3highlighted. substte towww.dv-dio-sci.net/8/9/2/ see mteil fluence hs eltive cesg pemittivity eltive pemittivity. nge cn quency. seen t edges Adv. b Rdio (/8 Sci., coefficient 8, GHz) 9 5, s 2 clculted e. cn seen Next t to edges tolence b (/8 GHz) vi- s clcu- bout -7 db,s substte 6 mteil.6i hs eltive pemittivity bout d s 3. nge,s 6.6i bout d s 3. lted e. Next to tolence vi- mx. mx. mx. mx mx mx.

4 l.: Automotive Rdome et l.:etautomotive Rdome l.: Automotive Rdome et l.:etautomotive Rdome 52.. mx. mx. mx. mx () 2 ngle / ngle / () Angul Angul ngle / ngle / () -3 σ -.σ -. σ σ σ +. σ +. σ -.σ -. σ σ σ +. σ lence lence fequency / GHz / fequency GHz fequency / GHz / GHz fequency lence. Angul tolence lye / lye / () Optimiz / fequency Optimiz lye fequency lye /.9 () Optimiz fequency () Optimiz fequency mx. mx. () Angul () Angul mx. mx... () Optimiz fequency () Angul et l.: Automotive dome design lye / lye / Optimiz bwidth Optimiz lye bwidth Optimiz bwidth Rdome / lye / et l.: Automotive 5. Fequency bwidth. tolence lence lence. Angul tolence. Angul bwidth bwidth 5. Fequency Optimiz bwidth 5. Fequency Optimiz bwidth. Angul tolence. Angul 5 tolence b. Th d sme mteil 5. Fequency bwidth 5. Fequency bwidth mx. σ e.. e- bwidth no impovement conceng diffeence bove mentid σ±. ±.. bwidth no impovement conceng duc substte mteil. figues low ngul nge.nge. Nevelow ngul Neve σ esults. bwidth no) impovement conceng optimiz, cuse less σ±. ±.. no impovement conceng bwidth smlle nge ±3 eflecless smlle nge ±3 ) eflec lye vied. Th esults delow ngul nge. Nevelow ngul nge. Neve low cove ngul.2.2 tegted lye substte low cove ngul tegted lye substte cesed subtte mteil bumpe. nge less smlle ±3 ) eflecless smlle nge ±3, ) eflec ends upnge no, nge ends up no.,., itil condi epesented eltive pemittivity low cove ngul.2 tegted lye substte low cove ngul.2 tegted lye substte lowlow esults ntegted lyelye educes ceses ceses esults n tegted subtte subtteeduces, nely sme s substte mteil ngenge ends up no, Conceng., ends up no., bout 2, Conceng mteil bumpe (g no pt consideed) e de bout 2 mteil bumpe (g no pt consideed) e de. fequency educes low ceses esults n tegted lye subtte educes low ceses esults n tegted lye subtte ngul th. Th Figue 5() 5. Th d sme mngul th. Th Figue 5. Th d. sme m. bwidth 5(). d.7 ledy bout 2 mteil e. bumpe (g no pt consideed) e de stge bout 2Conceng Conceng mteil (g no pt consideed) e de- ledy th meng "" teilteil bumpe diffeence mentid stge th meng e. diffeence bove mentid b bove bout 2 db "" ngul th. Th Figue 5() 5. Th d sme mngul th. Th Figue 5() 5. Th d sme mnot dtct. Sec.3 th dcussed. Neveeduc substte mteil. figues ngul dtct. Sec.3 th dcussed. Nevenot educ substte mteil. figues lowe thn ddil lye ledy th stge meng "" teil e. diffeence bove mentid th "" meng "" teil cuse bove mentid we hve s. esults optimiz, nglestge / "" less we ledy hve s. e. esults cuse less diffeence 6. optimiz, bnot dtct. Sec.3 th dcussed. Neveeduc substte mteil. figues not dtct. Sec.3 th dcussed. Neveeduc substte mteil. figues esults tolence e Figues 7() lye vied. Th esults width no impovement conceng mxiesults tolence e Figues 7() lye vied. Th esults hve "" s. optimiz, cuse 6.we Angul. we hve "" s. esults optimiz, less 7 Hee e mentid decesed subtte mteil cuse bumpe. mumesults nge. Neveless less decesed ngul subtte mteil bumpe. Angul.. Hee e mentid 6. esults tolence e Figues 7() lye vied. Th esults esults tolence e Figues 7() lye vied. Th esults coheence tween highe pemittivity smlle vi itil condi epesented eltive pemittivsmlle nge ±3 ) coheence tween highe pemittivity smlle vi itil condi epesented eltive pemittiv. 7.. Hee e mentid itydecesed subtte mteil bumpe. low cove ngul nge. 7 cn.. cn pemittivity seen. decesed mbumpe. ity, nely subtte sme smteil substte eltive eltive pemittivity Hee seen. e mentid, nely sme s substte mtween highe pemittivity smlle viends up no,., educes coheence coheence ledy tween th stge meng " not d- vi condi epesented eltive pemittiv highe pemittivity smlle itil condi epesented eltive pemittivteilitil fequency teil fequency low ceses eflectct. Sect..3 th dcussed. Neveless eltive pemittivity cn seen. ity, nely sme s s m- m.3 Dcussion eltive pemittivity cn seen. σ -. we ity, nely sme.7 substte bwidth. dsubstte. Dcussion substte mteils bwidth.3 substte mteils. d.7. hve " s. esults bout 2 Conceng ngul σ teil b bout teil fequency fequency b bout σ +. th. Th tolence e 7 thn ddil d Dcussion substte mteils s comg fom fom. bumpe dbbwidth lowe thn ddil... lye. d lye..7 Dcussion mteils substte s comg bumpe dbbwidth lowe b bout ngul Figue 6. cn not defed - b bout cn not defed ngul Figue 6. comg fom fom bumpe db lowe thn lye.lye. Adv. Rdiothn Sci., 8, 9 5, db lowe ddil 2 ddil s s comg bumpe cn not -ngul Figue 6. cn notdefed defed ngul Figue 6.

5 6. Angul et l.: Automotive Rdome 6. Angul et l.: Automotive Rdome fequency / GHz 2 3 ngle / 8 () lence el. / GHz -3 fequency 2pemittivity 3 ngle / 8.8 () lence el. pemittivity. 6. Angul () lence el. pemittivity. 6. Angul σ -. σ σ +. σ -. σ σ σ -. σ σ +. σ -. 8 σ 8 σ +. mx. mx lye / Optimiz / bwidth lye / lye / bwidth () Optimiz fequency 8. Fequency Optimiz bwidth lye () Optimiz fequency () Optimiz fequency 8. Fequency bwidth pmetes. detiled bove cn clculted. Addilly, evlu pmetes. detiled bove cn tegted lye supeio ove ddil clculted. Addilly, evlu lye conceng tegtedbecuse supeio ove ddil bwidth. thlye stong equiement futue lyeconceng d sensos, evlu focused on tegted mtchbwidth. Becuse th stong equiement futue g lyes followg sec. d sensos, evlu focused on tegted lyes followglye sec.. tegted substte pt mx. mx. mx. mx σ -. σ σ +. σ -. σ σ +. et l.: Automotive dome design 5 () Optimiz fequency. tegted lye substte pt n tegted lye subtte esults mteil bumpe metllic lye / pt (pemittivity -7 lence el. pemittivity. 8 8 Optimiz lye subtte 8 metllic pt n condi depends on substte s bwidth >tegted esults lence el.pemittivity.8 fequency fequency / GHz / GHz.6.65 Optimiz bwidth mteil bumpe metllic pt (pemittivity pemittivity) e Figue 8() 8. sub 7. lence. lye / metllic 8. Fequency bwidth. depends on substte s pt > condi 8 8 stte mteil sme s e slightly de lence pemittivity el. pemittivity el... ()7. lence lence fequency / GHz Optimiz 2.7 bwidth 8.cesed Fequency bwidth pemittivity) e Figue 8. sub ds.8() Ag, tegted 7b.. Hee e mentid coheence. tegted lye substte pt stte mteil sme e substte slightly de lye esults s educ mte 7.lence lence el. pemittivity. () tween highe pemittivity smlle vi eltive Fequency bwidth cesed d. Ag, tegted s out kg senso equiements. Neveless it 8.il. figues 2.7 coextent oppemittivity cn seen. esults lye n tegted lye pmetes substte subttecnmtedetiled bove esults educ to defe cost func fom senso equiementsmteil timiz epesents til condi. bumpe metllic pt (pemittivity clculted. Addilly, evlu out.3kg senso Neveless it figues il. show figues s coextent op clely defes equiements.. ge e cesed subdcussion substte mteils metllic pt > condi depends on substte s tegted supeio ovepmetes condi. ddil detiled bove cn to defe cost func fom senso equiementspemittivity) timiz epesents lye e 9 9b. til substte lye conceng clculted. Addilly, evlu s comg fom bumpe clely defes. ge figues show s e cesed -3 mteil sme s e slightly decesed sub cn not defed - bwidth. Ag, stong futue tegted lye supeio ove ddil Becuse ds 2.7th. equiement tegted out kg senso equiements. Neveless it d sensos, evlu focused on tegted lye conceng lye esults educ substte mteil. mtch -3 to defe cost func fom senso equiements bwidth. gfigues lyesbecuse followg sec. th stong equiement futue coextent optimiz clely defes. ge d sensos, epesents til condi. showmtch evlu focused onfigues tegted detiled bove cn σ -.pmetes s e cesed substte substte mteil. tegted lye pt g lyes followg sec. σ fequency / GHz clculted. Addilly, evlu +. tegted lye supeioσσ ove ddil lye conceng σ fequency / GHz σ +. futue bwidth. Becuse th stong equiement -7 8 lence el. pemittivity.8 mtchd sensos, evlu focused on tegted fequency / GHz g lyes followg sec. 7. lence lence el. pemittivity. metllic pt. fequency. esults bwidth lye d.8 n tegted lye subtte. tegted substte pt b bout mteil bumpe metllic pt (pemittivity ngul 9 st metllic pt condi depends on substte s esults n lye subtte >tegted s bwidth. eflecpemittivity) e Figue 8() 8. submteil bumpe metllic pt (pemittivity n ngul nge ± bout.5 stte mteil sme s e slightly metllic pt > condi depends on substte s Th cn optimized eltive pemittivity.6decesed d 2.7.8() Ag, tegted pemittivity) e Figue 8. sublow 6 s highe s b. 7. lence lyeesults s educ mtestte mteil sme e substte slightly de Fo pts < diffes. il. figues d 2.7 coextent opcesed. Ag, tegted s timiztie esults til condi.mte epesents educ substte figues show s e cesed subil. figues coextent 8,9 5, Adv. Rdio Sci., 2optimiz epesents til condi. figues show s e cesed sub- -7 out kg senso equiements. Neveless it to defe cost func fom senso equiements clely defes equiements.. ge it out kg senso Neveless to defe cost func fom senso equiements clely defes. ge

6 6 et l.: Automotive Rdome 6 low db even metllic l.: Automotive pts. Metllic Rdome pts hve 5 et l.: Automotive dome design. highest pemittivities ll pts, consi low db even metllic pts. Metllic pts hve.6 wost cse. It clely ngul 5. highest pemittivities ll pts, consi Conclusions tolences ply n impotnt ole design.6 wost cse. It clely ngul Th nppe compes diffeent lye. possibilities Ag n "" low-cost teg exts tolences d specific sensos senso ply n equiements. impotnt GHz ole b. s- design sumps n model descid lye. Ag e n plne "" wve cident on exts non-mgnetic, specific plne senso mteil equiements. out oughness. It 5 Conclusions plstic fsci, bwidth equiements B 8 GHz, ngul equiements ± tolence 5ThConclusions fluences ppe compes σ ±. diffeent cn possibilities met coextently low-cost teg. d Thsensos cn elized usg GHz ibb. pile s- low-cost Th ppe compes diffeent possibilities low-cost teg pted non-mgnetic, fsci d sensos bwidth plne mteil equiement out GHzcn oughness. b. met It s (tegted sumps lye). model descid e plne wve cident ngle / Fo sumps plstic model fsci, descid low e bwidth plne wve equiements cident () Angul ngle / optimiz on B non-mgnetic, (tegted 8 GHz, plne ngul mteil lye) equiements out delivesoughness. ± stit () Angul tolence consi fluences plsticfsci, mentid σ ±. eliz bwidth cn possibilities. metequiements coextently () Angul Becuse B low-cost ngul 8. GHz, Th ngul cn equiements tolence elized usg ± ib pile bsed (tegted on th evlu, y lye). suffe fom equiement σ -. etolence fluences σ ±. cn met coextently σ 5 σ +. Fo GHz pted low-cost bwidth. fsci. Neveless bwidth Th cn equiement elized usg cn ib po- file (tegted educed low dblye). unde cet condis. met -. cn σ low optim ngul tolence fluence consideed futue wok. An ovell σ +. Fo optimiz pted fsci (tegted bwidth equiement lye) delives cn met st low cn consi found kg mentid detiledeliz equiements possibilities. futue optimiz Becuse d sensos. ngul (tegted lye) tolence delives st consi mentid eliz possibilities. e bsed th evlu, y suffe fom equiement Ackledgements. Becuse 5 GHz bwidth. ngul uthos Neveless wh to thnk Gemn tolence Fedel Mty e cnbsed Educ educed th low evlu, Resech db (BMBF) y unde suffe cet fom fundg condis. equiement RoCC 5jot GHz poject. optim bwidth. ngul Neveless tolence fluence consideed futue wok. An ovell cn educed low db unde cet condis. 8 8 fequency / GHz Refeences optim cn found ngul kg detiled equiements tolence fluence futue d consideed sensos. futue wok. An ovell lence 8 8 lence fequency / GHz Alitlo, P., Luukkn, cn found O., Vehms, kgj., detiled Tetykov, equiements S. A.: 9. Angul tolence. Impednce-Mtched futue Ackledgements. Micowve d sensos. uthos Lens, wh 7, 87 9, to thnk 28. Gemn Fedel 9. Angul tolence lence Bi, S., Richte, J., Mtius, S., Schmidt, L.-P.: tificil dielectics nti--cotgs, : Euopen Mi- Mty Educ Resech (BMBF) fundg Neveless educed ngul nge ± Ackledgements. RoCC jot poject. uthos wh to thnk Gemn Fedel 9. Angul tolence ngul nge bwidth mteil e low metllic pt. tolence flec RoCC jot Reduc poject. sttified medi, Antenns Wieless cowve Confeence, 33d, Octo 23, pp. 5 8, 23. Fitzek, Mty F. Rsshe, Educ R. H.: Resech Automotive (BMBF) Rdome fundg Re- stte mxmimum fequency low bwidth 7 Fo σ esult stte mteil d bwidth.8 metllic. cn pt. checked Hecht, E.: Optik, Oldenboug Wsenschftsvelg, 25. Popg Refeences Lettes, IEEE, 8, 29. b fequency bout b bwidth low ngul 9() d.8 st. s bwidth. Poc. Impednce-Mtched IRE tenl Conven Micowve Recod, Lens, vol. 7, 87 9, 2, pp. 6 53, 28. Js, Refeences Alitlo, E. P., Cohn, Luukkn, S.: SufceO., Vehms, dielectic J., Tetykov, lenses, : S. A.: Figue.5 Dcussion pted mteils b bout ngul 95. Alitlo, S. Bi, P., J. Richte, Luukkn, S. Mtius, O., Vehms, L.-P. J., Schmidt, Tetykov, S. A.: tificil dielectics S. K.: Wellenusitung Micowve nti--cotgs, Lens, geschichteten 7, 87 9, Medien Euopen 28. Mi- n ngul nge ± Kut Altenbug, Impednce-Mtched Figue bout evlu 9().5 Th st diffeent cn s optimized pmetes bwidth show eltive it. to educe.6 low n ngul nge highe bwidth s ± 953. Fitzek, tificil F. dielectics Rsshe, nti--cotgs, R. H.: Automotive Rdome Euopen -Mi- Re- pemittivity i S. Bi, cowve senkechtem J. Richte, Confeence, Efll S. [...], Mtius, 23. Annlen 33d, de L.-P. Oct. Physik, 23, Schmidt, pp. 8, , - low bout.5 b. even Th Neveless cn metllic optimized pts. educed Metllic ngul eltive pts nge pemittivity hve ± highest.6 pemittivities low ll pts, highe ngul s consid- nge Rd Fitzek, Popg Rsshe, cowve flec R. H.: Reduc Confeence, Funcl 23. Requiements sttified 33d, medi, Oct. Futue 23, Antenns pp. Automotive 5 8. Wieless Systems, F. Rsshe, : Lettes, Poc. IEEE, R. H.: 8, Euopen Automotive 29. Rd Rdome Confeence, - Reflec E.: Optik, Reduc Oldenboug sttified Wsenschftsvelg, medi, Antenns25. Wieless eg bwidth wost b. cse. Neveless e It low clely educed tolence ngul nge ± mxmimum tolences Munich, Gemny, 27. Hecht, ply n low impotnt -7 Fo ngul ole σ nge RoCC pess elese, Js, Popg E. Cohn, Lettes, S.: IEEE, Sufce 8, 29. dielectic lenses, : design esult bwidth bwidth e low lye. Ag cn tolence "" checked 29. Hecht, Poc. E.: IRE Optik, tenl Oldenboug Conven Wsenschftsvelg, Recod, vol , pp. 6 53, mxmimum exts specific senso b low equiements. low -7 Fo σ Js, 95. E. Cohn, S.: Sufce dielectic lenses, : esult bwidth cn checked Kut Poc. Altenbug, IRE tenl S. K.: Wellenusitung Conven Recod, geschichteten vol. 2, pp. Medien 6 53,.5 Dcussion pted mteils b low 95. i senkechtem Efll [...], vol. 8, Annlen de Physik, 953. Kut Rsshe, Altenbug, R. H.: S. Funcl K.: Wellenusitung Requiements geschichteten Futue Automotive Medien.5 Dcussion pted mteils i senkechtem Efll [...], vol. 8, Annlen de Physik, 953. evlu diffeent pmetes show it to educe bwidth Rd Systems, : Poc. Euopen Rd Confeence, Rsshe, Munich, R. Gemny, H.: Funcl 27. Requiements Futue Automotive evlu diffeent pmetes show it Fo to pts educe < diffes. bwidth 29. RoCC Rdpess Systems, elese, : Poc. Euopen Rd Confeence, Munich, Gemny, 27. Adv. Rdio Sci., 8, 9 5, 2 RoCC pess elese, Fo pts < diffes. 29. mx. mx.