Optimization of a carton package containing thin metal foil, in order to prevent ionization caused by heating in a microwave oven

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1 Opmao of a cao package coag h meal fol ode o peve oao caused b heag a mcowave ove Mase of Scece hess omas Baegåd & Pä Söm coopeao wh ea Reca AB Decembe Depame of lecoscece

2 Absac I s possble o maufacue a cadboad package equvale o a b addg a h meal fol. hs kd of package has he advaages of beg lgh eas o shelf ad equg lmed space whe dsposed of. hs mase hess vesgaes he possbles o hea a ea Reca cao coag a h fol of meal a mcowave ove. hee s a poblem whe used a mcowave ove sce he meal fol causes oao. Dsc flashes appea fom wo specfc pas of he cao afe a sho me sde he ove. o vesgae he poblem wh oao a Fe-Dffeece me-doma (FD) model was made he pogam SMCAD. I ode o fd a soluo he popees ha cause oao have bee vesgaed b leaue sudes ad epemeal ess. he poblem wh oao s elaed o accumulao of he elecc feld a shap edges. Ioao ca be compleel peveed b mo chages of he cao.

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4 Ackowledgemes We would lke o hak ou supevsos va Josso ad Beg Adesso a ea Reca fo all he suppo whle dog hs mase hess poec. We would also lke o hak ou supevso Ades Kalsso a he Depame of lecoscece Lud fo all hs help.

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6 able of coes Ioduco 3. he poblem bef 3. he cao 3.3 Gude o eadg hs epo 5 heo 6. Compuaoal mehods 6. Advaages ad dsadvaages wh FDD 6.3 lecomagec felds 7. FDD-algohm 7.5 Sabl fo FDD.6 Mcowave ove.7 eag of wae.8 Wavelegh ad deph of peeao.9 Ioao gases 3 es mehod 3 3. pemeal appoach o he poblem op pefoao edge poblem he boom fold edge poblem Cause 3 3. es cases 3.. Oda cao wh pped op 3.. Oda cao cu ope Boom agles folded up o he sde Boom agles folded ou o he sde Boom folded ou Cao opeed ad lad o he sde Boom fold edge aleed Resed cao Cao wh cups of wae Pas of cao Slces cao empeaue measuemes Geeal empeaue of ees Choce of mehod 9 Compuaos SMCAD. Lea he pogam. Model desg.3 Smulaos. valuao ad pos pocessg

7 .5 Mehod fo usg SMCAD 5 Resul 5. Smulao esul 5.. Oda cao 5. pemeal esul empeaue ess Ioao es 6 6 Dscusso 8 6. Dscusso of smulaos Dscusso of smulao mehods Dscusso of smulao esuls 9 6. Dscusso of epemeal ess Dscusso of empeaue mehods Dscusso of empeaue esuls Dscusso of oao ess Dscusso of oao esuls Compaso of smulao esul ad epemeal esul 3 7 Cocluso Cocluso fom smulaos Cocluso fom epemeal ess Fuhe wok 3 Refeeces 35 Apped A quaos fo a leap fog algohm I B Deph of peeao ad wavelegh IV C empeaue VI D Pcues X Smbols XI

8 Ioduco. he poblem bef ea Reca s a compa wh he ea Pak goup wh he am o poduce packages equvale o a. he packages ae made of cadboad plasc ad a h meal fol. he dffcules o use meal obecs a mcowave ove s kow b mos people. Despe ha ea Reca s eesed makg he cao safe o hea mcowave oves. hs mase hess vesgaes he possbles o use a Reca cao a mcowave ove opeaoal a he fequec.5 G. he cao coas a h fol of meal poecg he food fom he suoudg amosphee. hee s a poblem whe he cao s heaed a mcowave ove sce he meal fol causes oao. Whe he poblem was peseed a compehesve plag was suggesed. I cossed of he followg pas choologc ode: Compue smulaos of a cao heaed a mcowave ove Vefcao of smulaos hough epemeal ess Suggesg soluos Vefcao of soluos wh compue smulaos Vefcao of soluos wh epemeal ess he used appoach s que smla o he suggesed plag wh he ecepo ha all suggesed soluos have bee vefed wh epemeal es ahe ha b compue smulaos. he compue smulaos have bee made wh he Fe-Dffeece me- Doma (FD) pogam SMCAD. Isead of ol suggesg ad esg possble soluos o he poblem a few es cases have bee eaed o fd he popees ha ae eleva fo oao.. he cao he pma obec ha has bee esed ad evaluaed s he ea Reca ml sadad cao (RC ) whch s show fgue.. he cao s fabcaed fom a lamae of pape plasc ad a h fol of alumum seveal dffee laes ad s a oall eoable package. Ou focus s o he alumum sce has he abl o wok as a aea fo mcowave fequeces. he alumum has beefs hs so of packages as a bae agas a ad lgh ad woks as a hea suface whe sealg he cao wh duco. Whe vesgag oao some pas of he cao ae ccal. hese pas ae he foldg a he boom ad he op edge whee he cao s pped ope see fgue.. 3

9 Fgue.. Oda ml caos. hese caos ae eas o shelf due o he shape. I hs epo pas of he cao have bee gve specfc ames. he foldg s show fgue.3 whee he agles ad he Boom fold edge ae vsble. agles efe o he wo agula pas of he foldg. Boom fold edge s he edge ha coecs he agle pas ad s pal hdde b hem. Fgue.. Cao beg pped ope alog he pefoao a he op. Fgue.3. hs pcue shows he wa he boom s folded o a oda cao. he agles ad he boom fold edge ae vsble.

10 .3 Gude o eadg hs epo I chape some heo s peseed fo he elecomagec felds he compuaoal mehod heag ad oao. I gves a ovevew of he heo ha s elaed o hs hess ad gves eamples of leaue fo eesve sudes. he mehods used hs hess have bee dvded o chape 3 ad chape epemeal mehods ae eaed chape 3 ad compuaoal mehods chape. he esuls ae peseed chape 5 hese esuls ad he mehods meoed eale ae dscussed chape 6. he coclusos ha ca be made ae summaed chape 7. A he ed of hs epo efeeces ca be foud as well as appedces fo calculaos ad pcues. Apped coas a ls of smbols fo quaes ha ae used he equaos hs hess. 5

11 heo. Compuaoal mehods hee ae mal hee dffee mahemacal mehods fo compug elecomagec pheomea a compue. Oe of hese mehods s called Mehod of Mome (MoM) ad s o commol used o calculae scaeg of waves. he emag wo mehods ae called Fe leme Mehod (FM) ad Fe-Dffeece me-doma (FDD). Boh of hese wo mehods ca be used fo smulaos of he felds heag a cao a mcowave ove. he mos obvous dffeece bewee FDD ad FM s he wa volumes ae epeseed he gd. I commo FDD-pogams a hee-dmesoal gd cosss of cubods ad he FM case eahedos ae used.. Advaages ad dsadvaages wh FDD he FDD mehod has a gea advaage o FM whe comes o calculao speed. he eplc aue of FDD eques less compuaoal esouces compaed o FM whe solvg a hee-dmesoal poblem wh cells. FM s a mplc mehod ha eques ma vesos. Depedg o he echque used o fd vese maces he ode of he compuaoal me ad he equed soage space ca be compaed able. (Rsma ). he fomao used dug calculao s pefeabl soed he compue memo. Memo usage Compuaoal me FDD 3 FM (dec) 5 7 FM (eave) 3 bewee ad 6 able.. Requed memo ad me fo solvg a poblem fo dffee compuaoal mehods. Ol he odes of he values ae gve he gd cosss of cells. h obecs ha ae o alged wh he aes ad o cubc obecs lke sphees wll esul a poo dsceao sce he gd cosss of ecagula cubc cells. he eases wa o educe hs eo bewee he model ad he gd s o ale he oveall cell se. Sce ha geal ceases he smulao me ohe aleaves ae cuel a wok. Oe aleave s o use a subgd o cease he esoluo locall he ccal oe. hs opo wll be mplemeed he o e eleased SMCAD V. (hp:// I seveal applcaos cludg smulao of mcowave oves s of ees o sud a bad of fequeces. Wh he usage of a ase pulse souce a sgle FDD smulao ca compue esuls fo mulple fequeces ol equg a addoal Foue asfomao o be made. ha s much moe effce ha FM whch would have o u a complee smulao fo each fequec. 6

12 .3 lecomagec felds Mawell s equaos pla a mpoa pa all feld heo. he equaos ae called Faada s law Ampèe s law Posso s equao ad he codo of soleodal magec feld ad ae vewed as equao.-.. I Faada s law he magec cue des M has bee added. Addg he magec coducv gves a dual bewee Faada s law ad Ampèe s law. oweve oe should emembe ha a o-eo magec cue s mpossble sce magec chage does o es. B M (.) D J (.) D ρ (.3) B (.) I s aual o assume ha he volved maeals ae lea soopc ad odspesve. ha assumpo s vald fo a wde age of maeals ad s a ceo fo he cosuve elaos equao.5 ad.6. he cosuve elaos combao wh Mawell s equaos ca be used o deve a FDD-algohm. hs s doe wh gea deal aflove () ad s peseed befl chape. of hs epo. D B (.5) (.6) Felds behave a specfc wa close o coducve sufaces. Fo a pefec elecc coduco (PC) he elecc feld s omal o he suface ad he magec feld s ageal o he suface. hs behavou ca be deved fom Mawell s equaos as bouda codos.. FDD-algohm quao.7 ad.8 ca be ceaed b subsuo of equao.5 ad.6 o equao. ad.. quao.7 ad.8 ae ofe called Mawell s cul equaos ad ca be used o pedc vaaos of felds me gve ol he al felds ad cue deses. he cue deses ca be eaed as a combao of cue caused b felds ad addve souces as equao.9 ad.. 7

13 8 M (.7) J (.8) M M souce (.9) J J souce (.) If Caesa coodaes ae used equao.7 ad.8 ca be dvded o hee equaos each. hese ew equaos ca be used o epess he me devave of he se of dffee veco compoes as vewed equao.-.6. I equao.-.6 equao.9 ad. have bee used o dvde cue deses o dffee pes of cues. souce M (.) souce M (.) souce M (.3) souce J (.) souce J (.5) souce J (.6) I ode o ceae a algohm ha calculaes he feld vaaos he me mus be dvded o seps ad he space o cells. Fgue. s a eample of how he space ca be dvded o a mesh. hs mesh s ofe efeed o as he Yee space lace. Noe ha he feld compoes ae deoed such a wa ha each -compoe s suouded b fou -compoes ad each -compoe s suouded b fou -compoes.

14 Fgue.. Space dvded o a cubc mesh based o Caesa coodaes called he Yee space lace. A aba po he mesh wll have he dces k ad o epese poso he mesh as well as he me sep accodg o equao.7. Wh he same oao he devaves of me ad space ca be appomaed as equao.8 ad.9. he appomao equao. s useful ode o appomae feld segh a ukow me seps. ( k ) F F (.7) k F F k k F F k k F F k k (.8) (.9) F F k k F (.) k he equaos ha have bee peseed so fa hs chape ca be combed o a leap fog algohm. Whe he Yee space lace s chose he cul equaos ca be used o calculae boh he elecc ad magec felds gve he al values ad he souces. he elecc feld ad he magec feld ae calculaed aleag. he calculaos eque lmed usage of memo sce ol values fo he las me sep ae eeded o be saved. he fal equaos fo a leap fog algohm based o he devaos hs chape ae peseed apped A. 9

15 .5 Sabl fo FDD he gd FDD ca o be chose aba. he cubes ae o equed o have he same se bu hee s a lm fo he sabl ad a lm fo he hgh ode eos (Bodeso ). he equeme fo sabl lms ehe he dmesos of he smalles cell o he legh of he me sep. he codo s we equao. whee s he me sep ad cell m cell m ad cell m ae he dmesos of he smalles cell he gd. (.) c cell m cell m cell m I ode o lm hgh ode eos he dmesos of he cells should o be lage compaed o he legh of a wave he maeal. If he legh of a cell s /.5 of a wavelegh he eo due o paal cacellao of he spaal ad empoal eos he sabl lm s less ha % (Bodeso )..6 Mcowave ove he mos mpoa pa of a mcowave ove s he mageo. Whe a mageo s suppled wh a pulsed DC-volage geeaes elecomagec waves. he waves ae guded hough oe o moe wavegudes ha feed he mcowave cav. he geome of all wavegudes ae chose ode o suppo he fudameal mode m. cep fo he cav whee he obec ha s o be heaed s placed a mcowave ove geeall coas dffee mechasms o poduce a mulmode feld ad suppo ufom heag. Moe fomao abou fuco of mcowave oves ca be ead Rodd (986). Isde he mcowave ove waves geeaed b he mageo s deced o he ove cav hough oe o moe wavegudes. he dmeso of a squae wavegude ca be calculaed wh equao. ad.3 (Kalsso 996). he cu-off fequec gve b equao. should be chose lowe ha he mcowave fequec (usuall.5 G). he asvesal wave umbe fo a ecagula wavegude s gve b equao.3 (choose m ad fo he fudameal mode). a s he loges dmeso ad b s he shoes dmeso. k c f c (.) π m k π (.3) m a b

16 .7 eag of wae he fequec of a mcowave ove s usuall.5 G. ha fequec s chose o gve boh mamum heag ad ufom heag. Wae molecules ae dpoles whch allow dpole elaao. he deph of peeao wae s suffcel log compaed o he se of food obecs. ece absopo ad delecc loss due o dpole elaao ae he wo ma cobuos o he heag of wae a mcowave fequeces. Boh of hese effecs ae close o opmum a.5 G. Mcowave heag s somemes coecl eplaed as esoace of wae molecules bu hs occus a much hghe fequeces..8 Wavelegh ad deph of peeao I he vesgao of mcowave heag he deph of peeao (D p ) ca be used boh o pedc how much a obec s heaed ad f wll suffe fom cold spos. D p s he legh ha a wave wll popagae o a suface befoe s amplude has bee educed b a faco e -. he wavelegh (λ) dffee maeals s esseal ode o udesad basc pheomea sde he mcowave ove. Sce maeals have a vae of coducves ad eve some comple eleccal paamees he eases wa s o use mahemacal defos ode o calculae wavelegh ad deph of peeao. hus he deph ad he legh should be calculaed wh equao. ad.5 especvel. he comple popagao cosa s gve b equao.6. hese comple calculaos ca be edous whou he use of sofwae ha ca hadle comple values. A soluo o ha poblem s peseed apped B..9 Ioao gases D p Re( γ ) (.) π λ Im γ (.5) ( ω ) γ ω (.6) hee ae ma ccumsaces whch oao ca occu gases. A s he gas queso hee ad he dschage wll appea whe a chages fom a sulao o a coduco. he smples appoach o pedc a spak s o use owsed s beakdow ceo whch s saed equao.7 (Cooa 3b). hs ceo suggess ha wo coducos ae placed a a dsace d bewee each ohe ad a cosa elecc feld s appled as well as a cosa pessue. he umbe of oao collsos made b a eleco s deoed α o (whe avellg a u legh) ad s gve b equao.8 whee A ad B ae empcal cosas. α o s ofe efeed o as owsed s fs oao cosa ad γ o s efeed o as he secod oao cosa. γ o s he aveage umbe of elecos eleased b each posve o dug secoda oao.

17 Dffee appomaos of hs ca be foud Coa (3b). hs ceo suggess oao fo hgh values of α o ad γ o whch s elaed o hgh elecc feld () low pessue (p) ad a sgfca secoda oao pocess. o o d ( e ) α γ (.7) B p α A p e (.8) o owsed s beakdow ceo as saed equao.7 has lmed use whe appled o heag mcowave ove. hee ae o wo dsc coducos sde he ove ad addo he feld s aleag. he soluo o hs poblem s o sud cooa dschages whee he basc ceo ca be eeded as equao.9 (Cooa 3b). hs ew ceo saes ha oao mgh occu a ego aoud he coduco up o he dsace lm. lm s chose as he mamum dsace () whee he umbe of oao collsos α o s hghe he he umbe of aachme collsos η o fo he elecos. η o ca be calculaed wh equao.3 (Coa 3b) whee C ad D ae empcal cosas. Compag equao.8 ad.3 suggess ha a hgh feld ad a low pessue ove a log dsace wll cease he egal pa of equao.9. gh value of he egao combao wh a hgh value of he secoda oao pocess wll esul a beakdow. lm ( o - o ) α η d γ o e (.9) D p C p η o e (.3) quao.9 saes a beakdow ceo ha does o eque a ufom feld ad wo dsc coducos a fed dsace. he e sep would be o oduce felds ha va me. As log as he beakdow ceo s fulflled oao ca ake place. ve f s fulflled ol fo a sho me peod oao ca sa ad esul a spak. Isead of eag he feld as peodc me ca be eaed as mulple mpulses. Oe equeme fo beakdow s ha a fee eleco s pese whch s able o sa a avalache. A hs sa he feld mus have a segh above a ccal level ad ema hgh eough ul he dschage s complee. A me lag ca be defed whch epesses he me eeded fom he sa of oao wh a fee eleco o he fal beakdow (Coa 3b). hs s a smplfcao of he poblem sce he shape of he mpulse s o ake o cosdeao. Fee elecos ca be ceaed b cosmc adao o adoacv he goud. Sce he ceao of elecos s adom a sascal aue s added o he poblem. he e sep would be o use sascal mehods o defe peak values of he elecc feld ha leads o a cea pobabl ha a mpulse would esul beakdow. Defg hese values s o a pa of hs hess sce would eque a vas amou of measuemes ad mahemacal mehods.

18 3 es mehod 3. pemeal appoach o he poblem he poblem wh he cao s ha oao occus a he op pefoao ad he foldg a he boom of he cao. he spaks ol appea a he op whe he cao has bee pped ope usg he pefoao. A he boom he poblem occus whe s folded ad oed. ece ca be vewed as wo dffee poblems ha ca be solved sepaael. Dug he vesgao of he poblem a he boom he op should be cu ope wh scssos. I he same mae he poblem a he op should be suded whe he cao has bee ufolded ad cu ope a he boom f o ohe wa o peve oao s possble. Whe eeded he boom ca be eclosed wh ape o peve leakage of food. 3.. op pefoaed edge poblems I ode o make eas o ope he cao hee s a pefoao aoud he op. Whe he op s pped off he pefoao causes a ueveess of loose pape fbes ad a spk meal fol. Whe he cao s eposed o mcowaves oao appeas as spaks a he pefoao. he spaks ae uwaed b he cosume ad mus be peveed. 3.. he boom fold edge poblem he boom cosss of ma laes folded close ogehe. Due o he umbe of laes ad he low aflow he meal fol ca be seveel heaed whe he cao s used a mcowave ove. he foldg closel esembles a mcosp aea ad has shap edges. Ioao seems o alwas occu a he same spos. hese dschages ca leave maks a he boom of he ove ad eve se fe o he pape he boom foldg. A such dschage s uwaed fo a commecal poduc Cause hee s easo o beleve ha seveal facos cobue o oao. Some of he followg popees ca be foud wh leaue sudes whle ohes wee foud b dscussos. All of he followg popees should be cosdeed dug ess: empeaue of he meal fol ad he a Poso of he cao he ove Deco of he elecc feld Shap edges ad coes Suface cues he meal fol Legh of pas of he cao whch ae close o he esoace legh Dsace bewee he meal laes he feld segh sde he mcowave ove 3

19 Maeal popees of he cao A es case ca be chose ode o vesgae he cause of oao o ode o peve oao. I s aual o sa wh vesgag he cause ad lae usg hose esuls fdg a soluo ha peves he poblem. If a es case ol chages oe of he popees ca be used o coclude f ha pope causes oao o o. he opmal desg s a cao ha lms all he popees ha cobue o oao. Due o a lage umbe of possble es cases ol he mos eesg ae coveed hs hess. hose es cases ae peseed chape es cases o udesad he pheomea ha cause he oao he boom fold edge epemeal ess wee pefomed. I he ess a 9 W mcowave ove of he bad Whlpool was used whch s a sadad domesc mcowave ove. hee ae some seous poblems whe elecc sumes ae used sde a mcowave ove because mos cables wok as a aea fo mcowaves. heefoe ou ow seses ae he ol possble wa o check whe oao has occued. he followg pa of hs chape lss some mpoa es cases ha have bee pefomed. All es cases ecep fo oda caos wh pped op have bee opeed us below he pefoao wh scssos. Wh hs appoach he poblem has bee solaed o he boom foldg. 3.. Oda cao wh pped op hs s he cao as s oda wh a lamaed fol coag pape plasc ad a h lae of alumum. I coas ml ad s folded a wa a he boom whch ceaes wo agles o he ousde of he package whch ca be see fgue 3..he cao s pped alog he pefoaed le he same wa as he sucos ped o he cao. hee ae wo poblems ha occu o mos Oda cao wh pped op whe he ae eposed o mcowaves. he mos sevee oes ae he boom fold edge oao eplaed chape 3.. ad he oable bu o cucal op edge oaos eplaed chape 3...

20 Fgue 3.. hs pcue llusaes a oda cao. 3.. Oda cao cu ope hs s he cao as meoed chape 3.. wh he ecepo ha he cao s cu ope a he op wh scssos. he foldg s show fgue 3.. he oao a he op s hee avoded wh a clea cu wh scssos. Rppg he cao ope would esul a ueve meal edge Boom agles folded up o he sde Isead of foldg he agles ude he package he ae folded up o he sde of he cao. hs ca be see fgue 3.. Oe wa o chage he fom of he boom fold s o use he same foldg echque ea Pak uses o seal he op. hs foldg chages he look of he package a wa ha makes look moe smmec wh he same foldg boh a he op ad he boom. Fgue 3.. hs pcue llusaes a oda cao wh he boom agles folded up o he sde. 5

21 3.. Boom agles folded ou o he sde Isead of foldg he agles udeeah he package he ae hee folded ou alog he boom. hs foldg s llusaed fgue 3.3. Wh hs chage he goal s o see f he esuls ae he same as he es case wh agles folded up o he sde o wh sadad fold wh agles a he boom. hs foldg s o a pefeable wa o make a cao bu ca gve fomao abou he aue of he poblem. Fgue 3.3. hs pcue llusaes a oda cao wh he boom agles folded ou o he sde Boom folded ou I hs es case he boom s folded ou ad he seam s pog dow as ca be see fgue 3.. he cao has o be balaced some wa whe s heaed upgh poso. Fgue 3.. hs pcue llusaes a oda cao wh he boom folded ou. 6

22 3..6 Cao opeed ad lad o he sde ee a oda ml cao lg o he sde as vewed fgue 3.5 s cosdeed. he op s closed wh adhesve ape ode o eclose he wae. Wh he cao placed o he sde he deco of he elecc feld s aleed elao o he cao. he cao s esed lag o boh of he boadsdes. Fgue 3.5. hs pcue llusaes a oda cao ha s lad o he sde. Adhesve ape has bee used o peve leakage of food Boom fold edge aleed he seam he boom s omall abou mm wde. he seam ca be shoeed whou leakg a flud. I s also eleva o es he cao whe he fold s shoccued. he boom fold edge ca be oed dffee was. Fgue 3.6 shows he fold edge bewee ad below he wo agles. he boom seam s he mos ccal pa of he cao whe comes o oao. I has some smlaes o a asmsso le ad s heefoe sesve fo small chages. Fgue 3.6. hs pcue shows he wa he boom s folded o a oda cao Resed cao he oda cao ca be esed o some ee. Fo hs es case he same kd of foldg he boom s used bu he foldg ad he cao s made smalle. 7

23 he esed cao was esed o see f hee wee a dffeeces esul bewee hs ad he lage ml cao. he wave pheomeo s lkel o chage whe he cao s esed Cao wh cups of wae A sadad cao flled wh wae ca be heaed wh addoal wae added sde he mcowave ove. he ea wae s added as a vag amou of cups wh a fed amou of wae. hs es was pefomed ode o see how mpoa he feld segh was he oao pocess. he ea wae absobs felds ad lowes he aveage feld segh. 3.. Pas of a cao he cao ca be cu o ma pas. hs es case coces pas heaed dvduall sde he mcowave ove. If he cao does o behave as a aea each pa of he cao ca be esed sepaael. If he pas ae cu ou wh scssos he ew edges ae o uecessa shap. 3.. Slces cao Cus ca be made he cao wh a kfe o scssos. he he cus should be made h eough o adhesve ape should be used o peve leakage. Cug ou pas of he meal ca peve suface cues. he coducv of fluds sde he cao should be ake o cosdeao sce mgh sho-ccu he slces. 3.3 empeaue measuemes 3.3. Geeal ea ca be asfeed wh coduco coveco ad adao. I addo coduco ad adao ca be used o measue empeaue (Gahm 996). Coduco s used whe a asduce s placed coac wh he measueme obec. Sce all obecs em hea adao a asduce ha absobs adao s a aleave empeaue of ees Oe possble easo fo he oao s ha he magec feld duces cues he meal fol. he cue heas he meal fol ad he empeaue cobues o possble oao. hs empeaue ca be compued a smulao calculaed aalcall o measued. SMCAD s o sued o compue he empeaue ad o ceae a ew model a dffee pogam s me cosumg. he aalcal calculaos eque seveal appomaos ad ae eaed apped C. 8

24 Uless he souces SMCAD ae chose wh gea cae he esuls wll ol be peseed wh elave feld segh. oweve SMCAD has a feaue ha calculaes specfc absopo ao (SAR) W/kg fo aba volumes. he empeaue chage of wae whch s heaed fo a specfc me ca be used o calculae he powe ha he wae s heaed wh. A compaso bewee hese wo powe values gves a omalsao value ha ca be used SMCAD o dspla absolue feld segh. quao ca be used fo hese calculaos Choce of mehod k m PReal heag (3.) SAR P Defaul scale m (3.) PDefaul scale k omalao P (3.3) Real heag No all mehods ae suable fo empeaue measueme sde a mcowave ove. If he asduce s placed sde he ove wll be eposed o elecomagec felds. he feld ca hea boh he asduce ad a wes coecg esulg faul values. I some eeme cases he asduce wll beak ad he wes mel o spak. If wes ae coecg bewee he sde ad he ousde of he ove he wok as a aea ad boh coduc ad adae mcowaves. ha would mal be haadous fo coeced elecocs bu also fo sesve equpme he oom. hee s a eas wa o avod all he poblems coeced o empeaue measueme dug mcowave heag. I s o smpl puchase a mcowave ove wh a bul dgal empeaue measueme sued fo heag of food. he he poblems have alead bee ake cae of b he desge. Aohe wa s moe epesve bu wll allow moe pecse ad vesale measueme. If hea adao s used hee s o eed fo meal coducos ad o elecocs sde he mcowave ove. A faed camea ca gve a oveall vew of he heag pocess. Ifaed dodes ca povde po measuemes combao wh a dgal eface. he meal gag ad he glass mgh affec he esul f he beam s foced o coss he wdow. A good choce s o use equpme wh a h fbe ha ca be peeae he ove hough a small hole. he poblem wh he alumum fol s s small mass ad ha s coveed wh plasc fol. hs ca be a poblem whe g o measue he empeaue eve ousde he mcowave ove. Sce he mass of he alumum s lmed a coac pobe has o be eve smalle o peve he asduce ad wg fom coolg of he fol. he aual aleave s a ouch-fee measueme. I boh cases s mpoa o emembe ha he empeaue of he alumum should be measued ad o he empeaue of he plasc. 9

25 he use of empeaue dcag caos s a cheap ad effecve mehod. Alhough lmed o measug ol he peak empeaue wh a low pecso hee ae seveal advaages. he caos do o seem o be affeced b mcowaves ad ca be used o measue empeaue ve specfc pos whou coolg of he measug obec. I also eques a mmum effo o appl caos o specfc pos.

26 Compuaos SMCAD hs pa should o be cosdeed as a maual fo smulaos SMCAD sce hee ae some ccal pas of he smulao pocess ha ae o descbed hee. he pas ha ae o cluded hee ae bee ead he SMCAD Refeece Maual (hp:// Lea he pogam Whou a kowledge of SMCAD akes some me o ge o kow he pogam ad all he dffee feaues. A good sa s o use he SMCAD-lgh veso whch s much cheape ha he full veso howeve has some lmaos. he lgh veso s o able o ceae a gd lage ha mllo cells ad s o possble o wok wh moe ha volumes. Despe hese lmaos s possble o do some uoals ad pepaaos fo he eal wok b ug smplfed smulaos of he eal poblem.. Model desg SMCAD s a hee-dmesoal pogam whch gves he possbl o model obecs ve accuael. he cao s dffcul o model pefecl because of he sof maeals s made of ad he fac ha SMCAD has poblem wh cuved les ad volumes. hs poblem s based o ha he FDD mehod ol uses cubc cells ad ha a lo of cubc elemes ae equed o esemble cuved edges. Moe ad smalle cells gve bee esoluo bu o he ohe had esuls moe smulao me. I s o ol he umbe of elemes ha ae mpoa fo he smulao me bu also he se of he smalles cell whch decdes wha me sep ha wll be used accodg o equao.. If cells small eough o spl eve lae of he cao would be appled he smulaos would ake seveal weeks mal because of he small me sep. he soluo s o choose a eleme small eough o esemble he space bewee he hes laes o choose good esoluo us oe dmeso. hee ae hee dffee pes of souces whch ae called plae wave ecao souces edge souces ad wave po ecao souces. Dffee kds of sesos ca be used depede o he so of esuls ha shall be ecoded. Boh he souces ad sesos ae placed he model eve hough he ae o used o ale a phscal chaacescs..3 Smulaos Whe he ee model has bee desged he e sep s o swch he pogam o smulao mode. I smulao mode s possble o selec bewee wo pes of smulaos ase ad hamoc mode. he ase mode ca geeae a Gaussa pulse whch s a pulse wh a wavefom descbed b he Gaussa dsbuo. Wh hs kd of souces he smulao has eached a sable codo whe all sgs of he pulse

27 have dsappeaed. I hamoc mode he souces geeae a couous susodal sgal ha has o each a sead sae fo he smulao o be complee. I s hade o ge a hamoc smulao o covege.. valuao ad pos pocessg Pos-pocessg s he pa ha akes place afe a smulao s complee. I he pospocess meu hee ae seveal opos o how he esuls fom he smulaos ca be show. Fo eample he calculaed elecc feld ca be epeseed b aows o a colou scale whe vewed a plae. he felds ca eve be amaed fo a me peod. he sesos ae accessble a ee sucue a pogam meu. ach seso coas dffee quaes ad he esuls fom he compleed smulao ca be vsualed wh dagams. o deeme he covegece of he smulaos a leas oe volage seso should be placed he model. Oe choce s o have oe seso alged wh each as. Depede o he pe of smulao ha s pefomed he volage a hese sesos should ehe ake fom of a susodal sgal wh cosa amplude o fade ou. Oe of he mos mpoa facos he oao pocess s he magude of he elecc feld. he elecc feld ca be ploed SMCAD ove he ee seso volume whch gves fomao o whee ccal pos ad aeas ae. Wh a mesh coag small cells s ease o fd spos wh hgh felds due o he ceased esoluo. he esul s b defaul omaled o W pu powe. Nomalao gves he possbl o compae he esuls o eal. If he defaul value s used a compaso wll be scl elave whch meas s ol possble o see f oe cao desg s bee ha aohe. Wh kowledge of he acual pu powe s possble o make SMCAD calculae he absolue values of he felds. Calculao of hs omalao s eaed chape Mehod fo usg SMCAD I s aual o sve fo smulaos SMCAD ha ae as ealsc as possble whch hs case would eque a ee mcowave ove ad he use of hamoc waves. o lm he smulao aea s bee o ol model he cao hoveg above a small meallc boom wall. ase smulaos covege ease ha hamoc smulaos ad fo hs easo ase smulaos should be chose. A good wa o model he waves ha would have bee geeaed b he mageo s o use plae waves. If ol oe plae wave souce was used he esul would be ve depede o he agle ad polaao of he cde wave. I s o easoable o model he comple wave popagao sucue sde he ove cludg eflecos fom walls ad possbl a oag plae. Isead he bes choce s o use ma waves wh adom cde agles ad polaaos. If he umbe of souces s ceased fom s o welve he esuls va ve lle bewee he smulaos.

28 I ode o vef he esuls fo log smulaos a quck smulao ca be pefomed. Quck smulaos ca also be used o fd a fudameal eo he model o smulao paamees. As dscussed chape.5 hee s a lm o he mamum se of cells depede o he wavelegh he maeal. he wavelegh s sho deleccs such as wae equg hgh esoluo of a food he model. he smulao me ca be educed whe smulaos ae made whou food he cao. 3

29 5 Resul 5. Smulao esul he smulao esuls ae a mpoa pa he suggle o fd a vald eplaao o wha causes he oao especall he boom fold. he focus s o he elecc feld whch has bee suded deal afe smulaos. 5.. Oda cao he cases peseed fgue ae ake fom SMCAD ad llusaes he elecc feld dffee plaes. ach fgue epeses a h slce of he feld a a specfc hegh. he values show he fgues ae absolue ad omaled accodg o chape he mamum feld segh s foud a he boom coes of he cao. (f) Veco V/m om o 3.76e-9W a.5e9 epolaed Veco RMS Modulus lecc feld (V/m) Y As m X As m Fgue 5.. Pcue he --plae a he hegh of he op coes. gh elecc felds ca be see as bgh ellow aeas a some of he coes

30 Y As m (f) Veco V/m om o 3.76e-9W a.5e9 epolaed Veco RMS Modulus X As m 95 Fgue 5.. Pcue he --plae a he hegh of he boom coes. gh elecc felds ca be see a wo of he coes as ellow dos. Y As m (f) Veco V/m om o 3.76e-9W a.5e9 epolaed Veco RMS Modulus X As m lecc feld (V/m) lecc feld (V/m) Fgue 5.3. Pcue he --plae ha shows a sadg wave bewee he meal laes sde he boom seam. gh elecc felds ca be see he seam as a sadg wave pae ad he coes as dos

31 5. pemeal esul 5.. empeaue ess he empeaue dcag caos showed ha he meal fol go heaed up o almos C a mos aeas whe heaed wh mcowaves. hee wee some small aeas ha wee heaed above C hese aeas whee all close o he meal edges. he cease of empeaue he wae dug heag he mcowave ove was measued. he oda cao was heaed wh appomael 3 C pe mue. ha meas ha he oda cao would eque appomael mues whe heaed fom oom empeaue o 6 C. 5.. Ioao ess I ode o vef he SMCAD-smulaos ad fdg a soluo o he poblem epemeal ess wee pefomed wh eal caos a mcowave ove. he esuls fom he es cases meoed chape 3. ae lsed hee he same ode Accodg o ess he poso of he cao sde he mcowave ove ca o be used o peve oao. oweve a cao mgh dschage agas he ove walls f s placed oo close o a of hem. he eac dsace s had o ell sce s so small ha he cao almos ouches he wall. Oda cao wh pped op O almos eve package of he oda cao oao occus he boom fold ad a he pefoaed op. he oao he boom fold s sevee ad ca causes loud flashes ad bu pape. I mos cases appeas o boh agles a bu mak fom hs kd of oao ca be see fgue D.. A he pefoao he oao s moe dscee ad somemes dffcul o see bu s possble o hea ad obseve vsuall as bu pape fbes. Oda cao cu ope he oao poblems a he op dsappea fo he oda cao whe s cu ope wh scssos. oweve he poblem he boom foldg s o solved. Boom agles folded up o he sde Foldg he agles up o he sde s a cocep ha solves he poblem he boom fold. ece hee s o oao whe hs cao s cu ope. Boom agles folded ou o he sde Fo he es case wh boom agles folded ou o he sde oao sll occus. Bu maks appea a he same places o he agles as o he oda cao. 6

32 he boom folded ou he oao ha occued whe he boom s folded ou was dsc. Dug oao some of hese caos eve made maks o he sde of he ove. Cao opeed ad lad o sde A cao opeed ad lad o sde solves he boom fold poblem wh o ohe chages ecep posog compaed o he oda cao. hs s o a ealsc wa o solve he poblem bu s possble o daw some eesg coclusos. Boom fold edge aleed he es case wh boom fold edge aleed allows ma appoaches. Cug of a h pa of he edge wh scssos ofe peves oao bu does o gve elable esuls. Pg he edge ogehe wh hea lms he oao poblems bu ol f he pessue s eve. hs echque s a b uelable. Resed cao hs cao s much smalle ha he sadad cao bu shows he same behavou as he ml cao all kd of maes. he same oao poblems appea he boom fold ad a he op pefoao. Cao wh cups of wae B addg ad emovg cups of wae dug heag he oveall feld segh ca be aleed o some ee. A oda cao heaed ogehe wh cups of wae cleal showed ha he feld segh ca be loweed o a po whee oao does o occu. Wh hee cups of wae he feld segh has bee loweed eough o peve he oao he boom fold. Wh wo cups he oao sas aga. he powe dsbued o he cav s pobabl a ve mpoa faco hs es case. Pas of a cao eag dvdual pas of a cao sde he ove gves adom ad upedcable esuls depede o geome of he cu ou obec. If pa of he foldg s heaed mgh o cause oao as he case wh he ee cao. I addo pas of he cao ha usuall ae ouble fee ca gve poblems. Cuved shapes gve oveall bee oao mmu. Slces cao As a es case slces ca be cu ma was. Cug ou pas of he meal geeall ol ceaes poblems a he ew edges. he esuls whe cug ou pas of he cao seem adom ad upedcable. 7

33 6 Dscusso 6. Dscusso of smulaos 6.. Dscusso of smulao mehods I s o possble o model he cao sde a complee mcowave ove SMCAD wh easoable accuac ad compuao me. ve whe modellg ol a cao whou mcowave ove he smulaos ake oo log me o allow opmao ess. he mao easo fo log smulao me s he lm o me sep as see equao.. I ode o esolve small deals he foldg he me sep ges sho esulg oo ma smulao seps. If he esoluo s chose oo low ol aveages of small aeas ae avalable ahe ha he value of he felds specfc pos. Oe wa o avod he poblem wh smulao me s o use ma compues ad ug mulple smulaos a oce. A small pogam called SMLAB ca be used o u smulaos whou gaphcal eface o almos a kd of compue. he dea would be o pepae all smulaos o a sgle compue usg SMCAD ad o u smulaos o ohe compues wh SMLAB. Ufouael hs was o a opo hs poec sce he umbe of compues was lmed ad SMLAB was o pa of he lcese package avalable. I hs poec he mos mpoa applcao of SMCAD s fo compeheso. I a eal sage of opmao SMCAD ca be used o fd ccal pos whee felds accumulae. A few smulaos SMCAD ca gve a udesadg of wave pheomea ad feld accumulao whch s of gea use dug epemeal opmao. I addo due o lmed measug equpme SMCAD s eeded ode o fd a value of he felds sde a mcowave ove. he usage of SMCAD was chose eal hs poec sce he ogal poblem descpo suggesed a compaso bewee sofwae smulao ad epemeal ess. oweve ued ou ha he sofwae dd o have he mao ole dug opmao. I ehe case has bee ve educaoal o lea usg SMCAD ad sudg he smulao esuls. Smulaos based o he same model wh dffee esoluo gve almos he same esuls. he ol oceable dffeece s he esoluo of he esul. he umbe of cells eeded dug smulao ca be educed b o cludg a food he model. Resuls fom mos of hese smulaos va lle compaed o oda smulaos. Seveal smulaos have bee u wh dffee souces wh adom agles of cdece. I he esuls fom hese smulaos he ccal pos ae he same bu he muual values of he feld segh va bewee he coes. he vaao of feld 8

34 segh a he ccal po s pobabl depede o whee he souces amplf ad aeuae each ohe. 6.. Dscusso of smulao esuls As see some fgues fo eample fgue 5. he felds geeall accumulae a shap coes. he fgues ca be a b cocevg sce he cao coes ae modelled much shape ha he ae eal. he coes ae modelled shap sce he gd SMCAD s based o cubes. he feld segh a some ccal pos s compaable o he beakdow poeal of a whch s appomael 3 6 V/m (Cooa 3a). Whe a small amou of cells ae used he esoluo s lmed. he mamum felds a ccal pos wll show lowe values whe he esoluo s low sce a aveage value s dsplaed sead of he value a a specfc po. I fgue 5.3 a sadg wave ca be cleal see whch s mos lkel caused b a asmsso le effec. hee s also easo o beleve ha he foldg a he boom of he cao ca wok as a folded mcosp aea. Combg hese wo effecs ca epla he ccal feld accumulao a he foldg edges. he fequec of mcowaves geeaed b a mageo ca dffe slghl. o vesgae f hs wll affec oao a smulao ca be u wh mulple fequeces. Smulaos a eghboug fequeces gve almos decal esuls ad have bee lef ou of hs epo. 6. Dscusso of epemeal ess 6.. Dscusso of empeaue mehod he poblems coceg empeaue measuemes have bee eaed chape Measuemes sde he mcowave ove have bee made wh empeaue dcag caos. hese caos wee fs esed agas a depede ouch-fee hemomee dug he heag of a fg pa. he caos poved o be accuae empeaue ad boh legble ad quck chage of colou. Some smple ess sde he ove dcae ha mcowaves wll o effec he chemcal eacos a hamful wa. he measueme of he food empeaue does o eed o be made a complcaed wa. Smpl akg he cao ou of he ove sg ad addg a hemomee poved o be accuae eough. he smplc of coducve hemomees leaves few souces of eo. Coolg of he food agas a ca be eglgble due o he sho me akes o make a measueme. he hemomee wll cool he food bu hs effec s lmed due o he se of he hemomee elave o he food. 6.. Dscusso of empeaue esuls he measued empeaues seem easoable ad compl o some ee wh calculaos made apped C. Sce hgh empeaues ol wee measued a edges he heag s lkel o be caused b accumulao of felds. 9

35 Sce a pcal mcowave ove s suppled wh he powe 9 W he mageo geeaes mcowaves wh heag capac of he same ode. he mageo geeaes waves depede of wha s sde he ove. hs leads o a suplus of powe whe a sadad cao wh a lo of sheldg alumum fol s used elave a o shelded amou of wae. hs powe wll o some ee be efleced back o he mageo ad educe s lfeme (Vollme ) Dscusso of oao ess All oao ess wee pefomed he same mcowave ove. Usg he same ove s useful whe compag dffee caos ad makes ease o daw coclusos. A dsadvaage s ha he fal esuls ca o be geealed o he same ee bu sce mos mcowave oves ae smla hs s a mo poblem. I ode o cofm he vald of each es case he fuco of he ove was vefed bewee eve es. A eas wa o vef he ove s o check he me akes o hea a specfc amou of wae o a specfc empeaue. As alead meoed ol he mos eesg es cases ae coveed hs epo. All es cases meoed have bee esed seveal mes boh wh ad whou small chages. he umbe of ess ad he small chages made bewee he ess ae o coveed due o he vas amou of daa ha would have o be lsed ad eplaed. Due o he lmed daa lsed some esuls suggesos ad coclusos mgh seem a b fa feched. he es cases have bee chose o daw coclusos of he popees meoed chape he ol pope ha has o bee full cosdeed s he maeal pope. Ol lmed vaaos of maeal popees have bee avalable ad was o eough o daw a coclusos. Movg a cao aoud ca be used o es f he posog ca peve oao. hs has o bee eaed as a specfc es case. 6.. Dscusso of oao esuls Dschages bewee he cao ad he walls he mcowave ove ol occu whe he dsace s small. he walls sde he ove ae coeced o he same goud ha s used fo he suppl volage of he ove whch mgh ecouage hs kd of dschages. hs kd of dschage has o bee eamed hs hess sce s aual o place he cao he cee of he ove dug heag. As ca be see SMCAD felds ed o accumulae a shap coes ad edges. Whe he cao s pped ope small edges ae ceaed b he pefoao compaed o whe s cu ope b scssos. Such edges ae oo small ad adom o be smulaed SMCAD. A compaso bewee he cases whe he oda cao s opeed wh ad whou pefoao suggess ha he accumulao of felds s he cause of oao a he op of he cao. 3

36 Ufoldg he edges as Boom agles folded ou o he sde mgh cease he edge poblems. O he ohe had he ohe popees ae chaged as well. I hs case he edge poblems seem o be he doma faco sce oao occus a he edge of he agles as he es case oda cao cu ope. Whe he es case Boom agles folded ou o he sde s heaed he mcowave ove hee s sll a poblem wh oao. Whe he foldg s made hs wa he empeaue a he edges s educed due o bee cculao of a addo he possbl of dschage bewee meal laes a he boom s lmed. Sce oao sll occus s lkel ha empeaue ad dsace bewee laes ca o be used o peve oao. Ufoldg he cao a dffee wa esuls a ew es case called boom folded ou. Smlal hs es case also has poblems wh oao. hs es case has good a cculao ad lmed amou of adace meal laes bu has a dffee deco of he foldg edge compaed o he felds. ve f he empeaue ad dsace bewee laes ae eleva he chage of feld deco does o seem o be eough o peve oao fo hs es case. he ol sgfca dffeece bewee Resed cao ad he oda cao s he se. Sce he es esuls ae compleel smla fo hese wo cases s suggesed ha he legh of dvdual pas s uelaed o oao. he mao dffeece bewee Cao opeed ad lad o he sde ad he sadad cao s he deco of he feld compoes a he foldg. hs es case s a soluo o he oao poblem bu s o suable as a commecal poduc fo seveal easos. hs es cleal shows ha he deco of he feld compoes s a eleva pope. Boom agles folded up o he sde s oe possble soluo o he oao poblem. he mao dffeece bewee hs es case ad he oda cao s he deco of he elecc feld elao o he caos agle edges. Compag o Boom agles folded ou o he sde hs effec aloe seems o be eough o peve oao. he boom fold edge ca be aleed ma was ha peve oao. he cue mache pocess esuls a edge ha has small beds ad s shaped lke a ho aea a he opeg. Whehe he edge s sho-ccued o o vaes bewee he maufacued caos. he echques used Boom fold edge aleed wee eve pefeced o compaed o possble soluos fo mass poduco. I seems lke aleao of he boom edge ca be a smple ad effecve soluo o he oao poblem a he boom. he wo es cases Pas of cao ad Slces cao show ha he dffee pas of he cao ca o be eaed dvduall. he cao ca be compaed o a aea whee suface cues pla a dscve ole. I s had o epea epemeal ess coceg suface cues ad ecevg he same esul. Opmaos of hs kd should pefeabl be made wh sofwae smulaos. Fom he epemeal ess ha have bee pefomed s clea ha chages ha ale suface cues ca affec oao. hose 3

37 kds of chages geeall gve ol ew poblems ahe ha solvg he al poblem whe opmao s made wh epemeal ess. 6.3 Compaso of smulao esul ad epemeal esul Sce he feld segh gve b SMCAD s close o he beakdow volage s lkel ha oao wll occu fo he oda cao. hs comples wh he epemeal esuls whee oao fac does occu. he spos wh ccal felds SMCAD do o agee wh whee oao does occu epemeal ess. hs s pobabl ol elaed o lms he SMCAD-model. Spos ad edges wh hgh feld segh ca easl be foud SMCAD ad s aual ha he magec feld duces suface cues ha hea he meal. he spos ad edges wh hgh felds foud SMCAD also have hghe empeaue epemeal ess. Whe food wh bad cculao s heaed a ove cold ad ho spos ca be foud. hese ho ad cold spos ca be foud SMCAD as pas of he food wh moe o less heag felds. 3

38 7 Cocluso hee ae ma facos especall maufacug aspecs o ake o cosdeao. hs complcaes he possbl o pese a complee soluo. he lsed coclusos wll o solve he poblem compleel fo ea Reca should ahe be used as a goud fo fuhe wok. 7. Cocluso fom smulaos I s dffcul o use SMCAD as a opmao ool whe smulag a h meal cao. hs s mal because of he log smulao me due o he fe esoluo equed hs hess. lecc felds accumulae a shap meal edges. SMCAD s able o gve a absolue value of he feld segh a mcowave ove f a omalao mehod s used as chape I s evde ha he smulao esuls do o mach he eal pefecl. he mos obvous faco ha affecs he esuls s he dffeeces bewee he hee-dmesoal model made he compue ad he eal cao. he cell appomao SMCAD s a mpoa faco cobug o a esul ha dffes fom eal. 7. Cocluso fom epemeal ess Ioao he boom fold ca be avoded wh a dffee foldg o wh a dffee maufacug mehod of he boom seam see chape 6... he deco of he elecc feld s also mpoa fo he oao pocess he boom fold. Ioao s sogl elaed o shap edges ad hgh elecc felds as descbed chape.9. hs s mpoa boh he op pefoao poblem as well as he boom fold poblem. hee ae wo possble soluos based o a Oda cao cu ope ad oe ha s aacve a maufacug aspec. A cao wh he boom fold agles fold up o he sde wll solve he oao poblem ad s a soluo ha s possble fo maufacug. If he cao s lad o he sde hee s o oao poblem hough s o a good soluo fo he uses. gh empeaue ca be measued a specfc pos whe he alumum fol he cao s eposed o mcowaves. he meal s heaed a edges b accumulao of felds ad he poblem wh oao cao be peveed b educg he empeaue. Nehe ca he se of he cao be used o peve oao. 33

39 7.3 Fuhe wok he pefoao a he op edge of a ope cao s o suable fo use mcowave oves uless he fagmes of alumum fol o he elecc behavou s aleed. I s dffcul o avod oao whe hee s a pefoao wh small shap edges. hs s a aea whee moe wok has o be doe ehe o fd a ew soluo o o ale he esg pefoao. Aleg he boom fold has show good esuls ad s a pomsg wa o solve he poblem he boom fold ad should heefoe be fuhe evaluaed. he me akes o hea he food a oda cao s oo log ad mgh damage he mcowave ove. hee should be moe vesgao o how he ove s affeced befoe s peseed as a commecal poduc wh he ecommedao o use a mcowave ove. 3

40 Refeeces Bodeso Ades - Rlades homas - Igelsöm Pä (). COMPUAIONAL LCROMAGNICS School of leccal ad Compue geeg Göebog. Cheg Davd K (983). FILD AND WAV LCRORMAGNICS Addso-Wesle Publshg Compa Ic. Cooa Veo (3a). Ble Så fugea aues fveke Uppsala Uvese Uppsala. Cooa Veo (3b) he Lghg Flash MPG Books Lmed Bodm. Gahm Lea - Jubk as-gua - Laube Aleade (996). Mode dusell mäekk KFS AB Lud. Kalsso Ades - Ksese Gehad (996). Mkovågseo Luds ekska ögskola Lud. Rsma Pe O - Cleuch-Macsak Malgoaa (). LCROMAGNIC MODLLING FOR MIROWAV AING APPLICAIONS Mcowaves Rada ad Weless Commucaos vol Rodd Des (986). Mcowave echolog Pece-all glewood Clffs. Schmd & Pae geeg AG (--) FAURS: SOLVRS: FDD NANCMNS hp:// Schmd & Pae geeg AG (--) SMCAD Refeece Maual hp:// aflove Alle - agess Susa C (). Compuaoal lecodamcs: he Fe- Dffeece me-doma Mehod ARC OUS Nowood. Vollme Mchael - Möllma Klaus-Pee - Kasäd Delef (). Mcowave ove epemes wh meals ad lgh souces Phscs ducao 39 (6) s

41

42 I Apped A quaos fo a leap fog algohm quaos fo a leap fog algohm based o he Yee space lace ae peseed below. Devao of hese equaos s made aflove () ad s peseed befl chape.. k souce k k k k k k k k k k k k k J k souce k k k k k k k k k k k k k J

43 II k souce k k k k k k k k k k k k k J k souce k k 3 k 3 k k k k k k k k k k M

44 III k souce k 3 k k k k k k k k k k k k M k souce k k k k 3 k k k k k k k k k M

45 Apped B Deph of peeao ad wavelegh quao. ad.5 ae vald fo comple values. If o appomao s made calculaos based o hese equaos ae edous o compue b had. If o sofwae s avalable ha ca hadle comple values he followg bef devao s useful. he devao s based o equao. ad.5 whch ae epeaed hee as equao B. ad equao B.. he equao D p Re( γ ) (B.) π λ Im γ (B.) γ ω ( ω ) ca be ewe as γ '' ( ω ) ' ω ω usg he oao. ' '' Sce hs epesso fo γ ow s he oo of a eal value ad a maga value he elao ( a b) c d c d a ± a ± a b a b ca be appled. Usg hs elao γ ca be we wh dsc eal pa ad maga pa as IV

46 V '' ' ' '' ' ' ω ω ω ω ω ω ω ω γ ± ± hs equao ca be used o ewe equao B. equao B. usg ol eal valued quaes. ha meas ha D p ad λ ca be calculaed eacl whou sofwae ha hadles comple umbes wh he equaos below. '' ' ' p ω ω ω ω ± D '' ' ' ω ω ω ω π λ ±

47 Apped C empeaue calculaed wh he hea equao empeaue of he meal he cao ca be calculaed aalcall wh he hea equao. he calculaos wll eque a smple sucue of laes some bouda codos empeaue a boudaes ad hemal popees of he maeals. A smple sucue of laes s peseed fgue C.. he hea equao s saed equao C. whee Ξ s he souce em. Fgue C.. A sucue of laes epeseg a pa of he cao. he fgue s dvded o fou aeas. he laes ae a meal pape ad a eumeaed fom lef o gh. k Ξ (C.) Due o he deph of peeao meal compaed o pape ol he meal s heaed decl b mcowaves. Fo smplc sce he hckess of he meal lae s compaable o he deph of peeao heag of he meal s cosdeed ufom a all dephs. he a aoud he cao s cosdeed o have good cculao ad hece has cosa empeaue. Wh hese appomaos he empeaue () fgue C. has o sasf equaos C.. he equemes of equaos C. gves empeaue vaao o he fom of equaos C.3. he empeaues a ad a ae cosdeed kow ad he coeffces a a 3 b ad b 3 ae he ol ukows. VI

48 VII < < < < < Ξ < d d l l k (C.) < < < < < Ξ < d a d l b a l b a k a 3 3 (C.3) he e sep s o oduce bouda codos. ea asfe due o coveco s o ake o cosdeao whch lms he hea asfe o coduco ad adao. Coduco occus bewee he pape ad he meal ad foces boh he empeaue ad he fs devave o be cosa a he bouda. Sce a has lmed hea coducv ol adao s cosdeed a he wo emag boudaes. he hea adao s depede o he empeaue dffeece a he bouda ad he maeal popees. he bouda codos ae summaed equaos C.. () () () () d d k α d l k l k l l k α (C.) A ssem of equaos ca be ceaed b subsug equaos C.3 o equaos C.. he esulg ssem of equaos s we equaos C.5 o ma fom. I s ecommeded o solve he ma ssem wh a pogam such as MALAB bu ca be doe b had. Oce he ukows ae calculaed he empeaue a a aba po s gve b equaos C.3. he calculaos eque ha he maeal popees dmesos of laes ad he souce ae kow.

49 VIII Ξ Ξ α α α α α k a l k l k a b b a a k k d k k l l k (C.5) hee ae wo kds of maeal popees volved he soluo of he hea equao. k s he hemal coducv ad ca be foud fo mos maeals. he emssv α s ael saed leaue bu ca be calculaed fom he emsso faco e. he bouda codo equao C.6 has bee used equaos C.. hs bouda codo s ol a appomao based o equao C.7. quao C.6 s ease o use bu s ol vald fo small vaaos of empeaue. k α (C.6) e k B (C.7) he appomao used s show below. Noe ha e whee e s he case fo a black bod. he elaoshp bewee α ad e gve equao C.8 B s he cosa Bolma s equao e k 3 B e k e k e k e k 3 B 3 B 3 B 3 B α α e 3 B α (C.8)

50 he value of he souce em deoed Ξ s had o boh measue ad deve. Wh some assumpos ad appomaos a value whch seems easoable ca be calculaed. he mcowaves heag he cao ca be cosdeed o be cde evel fom all agles. akg he aea o accou ha meas appomael mes moe mcowave powe wll appoach he cao walls compaed o he food suface. Due o he smla bewee a wave gude ad he opeg a he op of he cao he walls ge appomael a addoal faco moe powe. Sce he deph of peeao s smalle ha he hckess of he maeals all waves asmed o he sufaces ca be cosdeed absobed. he lages dffeece s ha mos of he cde powe s efleced a he meal suface whle a fa shae of he waves peeae he food suface. he ao bewee he asmed feld powe ad he cde feld powe ca be calculaed wh equao C. wh he use of equao C.9. he devao of equao C. ca be made wh smple feld heo. Summag all he popees gves a value ode of -. Gve he powe he mcowave ove geeaes wo pece hea he cao walls ahe ha he food. Dvdg ha powe wh he oal volume of he meal fol gves a appomae value ha ca be used as Ξ. Ohe moe accuae calculaos fo Ξ ae possble bu hs mehod has he advaage of beg smple ad ol usg basc elaos whou edous devaos. η ω ω P η P η η Re Re ( η ) ( η ) (C.9) (C.) IX

51 Apped D Pcues Fgue D.. A oda cao whee oao has lef bu maks. X