I. Intshayelelo
I-Fractals zizinto zemathematika ezibonisa iimpawu zokuzifanisa kwizikali ezahlukeneyo. Oku kuthetha ukuba xa usondeza ngaphakathi/ngaphandle kwimilo yefractal, indawo nganye yayo ibonakala ifana kakhulu neyonke; oko kukuthi, iipateni zejometri ezifanayo okanye izakhiwo ziphinda kumanqanaba ahlukeneyo okukhulisa (jonga imizekelo ye-fractal kuMfanekiso 1). Uninzi lweefractals zinemilo entsonkothileyo, eneenkcukacha, kunye nezintsokothe ngokungenasiphelo.
umfanekiso 1
Ingqikelelo yeefractals yaziswa yingcali yezibalo uBenoit B. Mandelbrot ngeminyaka yoo-1970, nangona imvelaphi yejometri yefractal inokulandelwa emva kumsebenzi wangaphambili weengcali zezibalo, ezifana noCantor (1870), von Koch (1904), uSierpinski (1915) ), uJulia (1918), uFatou (1926), noRichardson (1953).
U-Benoit B. Mandelbrot wafunda ubudlelwane phakathi kwe-fractals kunye nendalo ngokwazisa iintlobo ezintsha zeefractals ukulinganisa izakhiwo ezinzima, njengemithi, iintaba kunye nonxweme. Wayila igama elithi "fractal" elisuka kwisichazi sesiLatini elithi "fractus", elithetha "ukwaphuka" okanye "ukuqhekeka", oko kukuthi "ukuqhekeka" okanye "ukuqhekeka", oko kukuthi, izakhi ezaphukileyo okanye ezingaqhelekanga, ukuchaza iimilo zejometri ezingaqhelekanga neziqhekekileyo ezingenako ukuhlelwa ngokwejometri ye-Euclidean yemveli. Ukongeza, waphuhlisa imifuziselo zezibalo kunye algorithms ukuvelisa kunye nokufunda fractals, nto leyo eyakhokelela ekudalweni iseti odumileyo Mandelbrot, leyo mhlawumbi idume kakhulu kwaye ibukekayo imilo fractal entsonkothileyo kwaye ngokungenasiphelo ukuphinda iipateni (bona Figure 1d).
Umsebenzi kaMandelbrot awubanga nefuthe kwizibalo kuphela, kodwa ukwanezicelo kwiinkalo ezahlukeneyo ezifana nefiziksi, imizobo yekhompyuter, ibhayoloji, ezoqoqosho, kunye nobugcisa. Ngapha koko, ngenxa yokukwazi kwabo ukwenza imodeli kwaye bamele izakhiwo ezintsonkothileyo kunye nezifanayo, iifractals zinezicelo ezininzi ezitsha kwiinkalo ezahlukeneyo. Umzekelo, ziye zasetyenziswa ngokubanzi kwezi ndawo zilandelayo zesicelo, eziyimizekelo nje embalwa yokusetyenziswa kwazo ngokubanzi:
1. Imizobo yekhompyuter kunye noopopayi, ivelisa imbonakalo-mhlaba yendalo eyinyani nenomtsalane, imithi, amafu, kunye nokwenziwa;
2. Iteknoloji yoxinzelelo lwedatha ukunciphisa ubungakanani beefayile zedijithali;
3. Ukulungiswa komfanekiso kunye nomqondiso, ukukhupha iimpawu kwimifanekiso, ukufumanisa iipateni, kunye nokubonelela ngokucokisekileyo komfanekiso kunye neendlela zokuvuselela;
4. Ibhayoloji, echaza ukukhula kwezityalo kunye nentlangano ye-neurons kwingqondo;
5. Ithiyori ye-antenna kunye neemetamatariyali, ukuyila ii-eriyali ezidibeneyo/ii-multi-band kunye nee-metasurfaces ezintsha.
Okwangoku, ijometri ye-fractal iyaqhubeka ifumana usetyenziso olutsha kunye nolutsha kwiinkalo ezahlukeneyo zenzululwazi, ubugcisa kunye nethekhinoloji.
Kwitekhnoloji ye-electromagnetic (EM), iimilo ze-fractal ziluncedo kakhulu kwizicelo ezifuna i-miniaturization, ukusuka kwii-eriyali ukuya kwi-metamatadium kunye neendawo ezikhethiweyo (FSS). Ukusebenzisa i-geometry ye-fractal kwii-eriyali eziqhelekileyo kunokunyusa ubude bawo bombane, ngaloo ndlela kuncitshiswe ubungakanani obupheleleyo besakhiwo se-resonant. Ukongeza, ubume obufanayo beemilo zefractal zenza ukuba zilungele ukuqonda ii-multi-band okanye i-broadband resonant structures. Ubunakho bendalo obuncinci be-fractals bunomtsalane ngakumbi ekuyileni ii-refleyiya, ii-eriyali zoluhlu olunezigaba, izinto zokufunxa i-metamaterial kunye ne-metasurfaces kwizicelo ezahlukeneyo. Ngapha koko, ukusebenzisa izinto ezincinci zoluhlu kunokuzisa iingenelo ezininzi, ezinjengokunciphisa ukudibanisa omnye komnye okanye ukukwazi ukusebenza ngoluhlu olunesithuba esincinci kakhulu, oko kuqinisekisa ukusebenza kakuhle kokuskena kunye namanqanaba aphezulu ozinzo lwe-angular.
Ngezi zizathu zikhankanywe ngasentla, ii-eriyali ze-fractal kunye ne-metasurfaces zimele iindawo ezimbini zophando ezinomdla kwicandelo le-electromagnetics eziye zatsala ingqalelo enkulu kwiminyaka yakutshanje. Zombini iikhonsepthi zibonelela ngeendlela ezizodwa zokusebenzisa kunye nokulawula amaza ombane we-electromagnetic, kunye noluhlu olubanzi lwezicelo kunxibelelwano olungenazingcingo, iinkqubo zeradar kunye nokuziva. Iipropathi zabo ezizifanisayo zibavumela ukuba babencinci ngobukhulu ngelixa begcina impendulo ebalaseleyo ye-electromagnetic. Oku kubumbana kunenzuzo ngakumbi kwizicelo ezithintelweyo kwindawo, njengezixhobo eziphathwayo, iithegi zeRFID, kunye neenkqubo ze-aerospace.
Ukusetyenziswa kwee-antenna ze-fractal kunye nee-metasurfaces zinamandla okuphucula kakhulu unxibelelwano olungenazingcingo, ukucinga, kunye neenkqubo ze-radar, njengoko zenza izixhobo ezidibeneyo, eziphezulu zokusebenza kunye nokusebenza okuphuculweyo. Ukongeza, ijometri ye-fractal isanda kusetyenziswa kuyilo lwezinzwa ze-microwave zokuxilongwa kwezinto, ngenxa yokukwazi ukusebenza kwiibhendi zamaza amaninzi kunye nokukwazi kwayo ukwenziwa i-miniaturized. Uphando oluqhubekayo kwezi ndawo luyaqhubeka nokuphonononga uyilo olutsha, imathiriyeli, kunye nobuchule bokwenza izinto ukuze baqonde amandla abo apheleleyo.
Eli phepha lijonge ukuphonononga uphando kunye nenkqubela phambili yesicelo see-antenna ze-fractal kunye ne-metasurfaces kwaye uthelekise ii-antenna ezikhoyo ezisekelwe kwi-fractal kunye ne-metasurfaces, ukugqamisa iinzuzo kunye nokulinganiselwa kwazo. Okokugqibela, kubonisiwe uhlalutyo olubanzi lweereyikhi ezintsha kunye neeyunithi ze-metamaterial, kwaye imingeni kunye nophuhliso lwexesha elizayo lezi zakhiwo ze-electromagnetic ziyaxoxwa.
2. I-FractalI-antennaIzinto
Ingqikelelo eqhelekileyo yeefractals inokusetyenziselwa ukuyila izinto ze-eriyali ezingaqhelekanga ezibonelela ngokusebenza ngcono kunee-eriyali eziqhelekileyo. Iimpawu ze-eriyali ye-Fractal inokuba yi-compact ngobukhulu kwaye ibe ne-multi-band kunye / okanye i-broadband.
Uyilo lwee-antenna eziqhekezayo ziquka ukuphinda iipateni ezithile zejometri kwizikali ezahlukeneyo ngaphakathi kwesakhiwo se-eriyali. Le pateni ifanayo isivumela ukuba sonyuse ubude be-eriyali kwindawo elinganiselweyo. Ukongeza, i-radiator ye-fractal inokufikelela kwiibhendi ezininzi kuba iinxalenye ezahlukeneyo ze-antenna zifana enye kwenye kwizikali ezahlukeneyo. Ke ngoko, izinto ze-antenna zefractal zinokubumbana kunye ne-multi-band, zibonelela ngokhuselo olubanzi lwefrikhwensi kunee-eriyali eziqhelekileyo.
Ingqikelelo yee-eriyali ze-fractal inokulandelelwa emva ekupheleni kwe-1980s. Ngo-1986, uKim noJaggard babonise ukusetyenziswa kwe-fractal self-zifanayo kwi-antenna array synthesis.
Ngo-1988, ingcali yefiziksi uNathan Cohen wakha i-eriyali yokuqala ye-fractal yehlabathi. Ucebise ukuba ngokubandakanya i-geometry efana nayo kwisakhiwo se-antenna, ukusebenza kwayo kunye ne-miniaturization yamandla inokuphuculwa. Ngo-1995, uCohen waseka iFractal Antenna Systems Inc., eyaqala ukubonelela ngezisombululo ze-eriyali ezisekelwe kwi-fractal yokuqala yehlabathi.
Phakathi kwiminyaka yee-1990, uPuente et al. ubonise amandla amaninzi eefractals esebenzisa i-monopole kunye ne-dipole ye-Sierpinski.
Ukusukela oko umsebenzi kaCohen noPuente, iingenelo zendalo zee-antenna zefractal zitsale umdla omkhulu kubaphandi kunye neenjineli kwicandelo lonxibelelwano, okukhokelela ekuphononongeni ngakumbi kunye nophuhliso lwetekhnoloji ye-antenna yefractal.
Namhlanje, ii-antenna ze-fractal zisetyenziswa ngokubanzi kwiinkqubo zonxibelelwano ezingenazintambo, kubandakanywa neefowuni eziphathwayo, ii-router ze-Wi-Fi, kunye nonxibelelwano lwe-satellite. Ngapha koko, ii-eriyali ze-fractal zincinci, zininzi, kwaye zisebenza kakuhle kakhulu, zizenza zilungele izixhobo ezahlukeneyo ezingenazingcingo kunye neenethiwekhi.
La manani alandelayo abonisa ezinye ii-eriyali eziqhekekileyo ezisekwe kwiimilo ezaziwayo-kakuhle zefractal, eziyimizekelo nje embalwa yolungelelwaniso olwahlukeneyo oluxoxwe kuncwadi.
Ngokukodwa, i-Figure 2a ibonisa i-monopole ye-Sierpinski ecetywayo e-Puente, ekwazi ukubonelela ngokusebenza kwamaqela amaninzi. Unxantathu we-Sierpinski wenziwa ngokukhupha unxantathu oguquliweyo ophakathi kunxantathu oyintloko, njengoko kuboniswe kuMfanekiso 1b kunye noMzobo 2a. Le nkqubo ishiya oonxantathu abalinganayo kwisakhiwo, ngamnye unobude becala lesiqingatha sonxantathu wokuqala (jonga uMfanekiso 1b). Inkqubo efanayo yokuthabatha inokuphinda iphindwe koonxantathu abaseleyo. Ngoko ke, ngalinye lamalungu alo amathathu aphambili lilingana ncam nento yonke, kodwa ngokuphindwe kabini umlinganiselo, njalo njalo. Ngenxa yoku kufana okukhethekileyo, i-Sierpinski inokubonelela ngeebhendi zefrikhwensi ezininzi kuba iindawo ezahlukeneyo ze-eriyali zifana enye kwenye kwizikali ezahlukeneyo. Njengoko kuboniswe kuMfanekiso 2, iSierpinski monopole ecetywayo isebenza kwiibhendi ze-5. Ingabonwa ukuba nganye ye-sub-gaskets (izakhiwo zesangqa) kwi-Figure 2a yinguqu ye-scaled yesakhiwo sonke, ngaloo ndlela ibonelela ngeebhendi ezintlanu ezahlukeneyo zokusebenza, njengoko kuboniswe kwi-coefficient yokubonakalisa igalelo kwi-Figure 2b. Umzobo ubonisa kwakhona iiparameters ezinxulumene nebhendi nganye yefrikhwensi, kubandakanywa ixabiso lefrikhwensi fn (1 ≤ n ≤ 5) kwixabiso elincinci lelahleko yokubuyisela igalelo elilinganisiweyo (Lr), i-bandwidth ehambelanayo (Bwidth), kunye nomlinganiselo wokuphindaphinda phakathi iibhendi ezimbini ezikufutshane ezimeleneyo (δ = fn +1/fn). Umzobo we-2b ubonisa ukuba iibhendi ze-Sierpinski monopoles zi-logarithmically periodically isithuba nge-factor ye-2 (δ ≅ 2), ehambelana nomlinganiselo ofanayo wokulinganisa okhoyo kwizakhiwo ezifanayo kwi-fractal shape.
umfanekiso 2
Umzobo 3a ubonisa i-eriyali encinci yocingo olude olusekwe kwigophe le-Koch fractal. Le eriyali icetywayo ukubonisa indlela yokusebenzisa iipropathi zokuzalisa indawo yeemilo zefractal ukuyila ii-eriyali ezincinci. Enyanisweni, ukunciphisa ubukhulu bee-eriyali yinjongo yokugqibela yenani elikhulu lezicelo, ngakumbi ezo zibandakanya ii-terminals ezihambayo. I-monopole ye-Koch idalwe ngokusebenzisa indlela yokwakha i-fractal eboniswe kuMzobo 3a. I-iteration yokuqala i-K0 yi-monopole ethe tye. Ukuphindaphinda okulandelayo kwe-K1 kufunyanwa ngokusebenzisa inguqu efanayo kwi-K0, kubandakanywa ukukala ngesinye kwisithathu kunye nokujikeleza ngo-0 °, 60 °, -60 °, kunye no-0 °, ngokulandelanayo. Le nkqubo iphinda iphindwe ngokuphindaphindiweyo ukufumana izinto ezilandelayo Ki (2 ≤ i ≤ 5). Umzobo we-3a ubonisa inguqu ephindwe kahlanu ye-monopole ye-Koch (oko kukuthi, i-K5) kunye nobude be-h obulingana no-6 cm, kodwa ubude obupheleleyo bunikezelwa ngefomula l = h · (4/3) 5 = 25.3 cm. Ii-eriyali ezintlanu ezihambelana nokuphindaphinda ezintlanu zokuqala ze-Koch curve ziye zaqatshelwa (jonga uMfanekiso 3a). Zomibini iimvavanyo kunye nedatha zibonisa ukuba i-monopole ye-Koch fractal inokuphucula ukusebenza kwe-monopole yendabuko (jonga uMzobo 3b). Oku kuphakamisa ukuba kunokwenzeka ukuba "ukunciphisa" ii-eriyali eziqhekekileyo, uzivumele ukuba zilingane kwimithamo emincinci ngelixa ugcina ukusebenza kakuhle.
umfanekiso 3
Umzobo we-4a ubonisa i-eriyali ye-fractal esekelwe kwiseti ye-Cantor, esetyenziselwa ukuyila i-eriyali ebanzi yokusetyenziswa kokuvuna amandla. Ipropati ekhethekileyo yee-eriyali ze-fractal ezizisa ii-resonances ezininzi ezikufutshane zisetyenziselwa ukubonelela nge-bandwidth ebanzi kunee-eriyali eziqhelekileyo. Njengoko kuboniswe kwi-Figure 1a, idizayini yeCantor fractal set ilula kakhulu: umgca ochanekileyo wokuqala ukopishwe kwaye uhlukaniswe ngamacandelo amathathu alinganayo, apho icandelo leziko lisuswa; Inkqubo efanayo ke isetyenziswa ngokuphindaphindiweyo kumacandelo asanda kuveliswa. Amanyathelo okuphindaphinda i-fractal aphinda aphindwe kuze kube yilapho i-antenna bandwidth (BW) ye-0.8-2.2 GHz iphunyeziwe (oko kukuthi, i-98% BW). Umzobo we-4 ubonisa ifoto yeprototype ye-eriyali eqaphelekayo (Umfanekiso 4a) kunye ne-coefficient yokubonisa igalelo layo (Umfanekiso 4b).
umfanekiso 4
Umzobo wesi-5 unika imizekelo eyongezelelekileyo yee-eriyali ze-fractal, kuquka i-eriyali ye-monopole esekwe kwigophe likaHilbert, i-eriyali esekwe eMandelbrot esekelwe kwi-microstrip, kunye nesiqithi sase-Koch (okanye "i-snowflake") i-fractal patch.
umfanekiso 5
Okokugqibela, umzobo wesi-6 ubonisa ulungelelwaniso olwahlukileyo lwefractal yezinto zoluhlu, kubandakanywa iSierpinski carpet planar arrays, Cantor ring arrays, Cantor linear arrays, kunye ne fractal tree. La malungiselelo aluncedo ekuveliseni ii-arrays ezimbalwa kunye/okanye ukuphumeza ukusebenza kweebhendi ezininzi.
umfanekiso 6
Ukuze ufunde ngakumbi ngee-eriyali, nceda undwendwele:
Ixesha lokuposa: Jul-26-2024
