A Nw Mthod to Calculat Elctoagntic Ipdanc Matching Dg in On-Lay Micowav Absobs* MA Zhi( 马治 ), CAO Chn-Tao( 曹晨涛 ), LIU Qing-Fang( 刘青芳 ), WANG Jian-Bo( 王建波 )** Ky Laboatoy fo Magntis and Magntic Matials of Ministy of Education, Lanzhou Univsity, Lanzhou 730000 *Suppotd by th Fundantal Rsach Funds fo th Cntal Univsitis und Gant No. lzujbky-2011-54, National Natual Scinc Foundation of China und Gant No. 11074101 and National Scinc Fund fo Distinguishd Young Scholas und Gant No. 50925103. **Cosponding autho. Eail : wangjb@lzu.du.cn; az09@lzu.du.cn. Tl: 0931-8914171 Fax: 0931-8914160 A dlta-function thod was poposd to quantitativly valuat th lctoagntic ipdanc atching dg. Masud lctoagntic paats of α-f/f 3 B/Y 2 O 3 nanocoposits a applid to calculat th atching dg by th thod. Copad with flction loss and quat-wav pincipl thoy, th thod accuatly vals th intinsic chanis of icowav tansission and flction poptis. A possibl honycob stuctu with poising high-pfoanc icowav absoption accoding to th thod is also poposd. PACS: 84.37.+q, 41.20.Jb,77.22.Ch 1
In cnt yas, du to th incasingly sious lctoagntic (EM) intfnc causd by th apid dvlopnt of wilss counications and high fquncy cicuit dvics in th gigahtz ang, significant sach ffots hav bn invstd in th ppaation of vaious stuctud agntic (o dilctic) atials fo th icowav absoption applications. [1-5] In paticula, th agntic o dilctic coposits with high-pfoanc icowav absoption poptis hav bn intnsivly invstigatd. [6-13] It is found that stong icowav absoption of nanocoposits ainly sults fo pop EM ipdanc atching. [2, 14-17] Th chaactistic ipdanc of th absobing atial should b ad qual to that of th f spac to achiv zo-flction. Howv, until now, th was no good thod to accuatly calculat th EM ipdanc atching dg du to too any paats should b considd in dsigning th boad-band icowav absobs. [18] To solv th abov pobl, w dvlopd a dlta-function thod as an ffctiv tool fo valuating th EM ipdanc atching dg. Th nw appoach not only can povid a quantitativ analysis of EM ipdanc atching dg but also can giv guid to dsign icowav absobing atials with btt pfoanc in a boad fquncy ang. Figu 1(a) shows th tooidal sapls (7.0 outsid diat and 3.04 inn diat) which a usually usd in asuing th scatting paats. Th al and iaginay pat of th lativ coplx pittivity/pability a usually dtind 2
fo th coplx scatting paats using th Nicolson Ross odl by th vcto ntwok analyz [19] = 1/ ) ( - j ) = ( / ) (1- j tand ) (1) ( 0 0 = 1/ ) ( - j ) = ( / ) (1- j tand ) (2) ( 0 0 Wh ε is th lativ coplx pittivity, µ is th lativ coplx pability. Tanδ is dilctic dissipation facto, tanδ is agntic dissipation facto. Th dpndncs of icowav absoption on th fquncy, thicknss and th lativ EM paats a obtaind basd on on-lay icowav absobs odl [20-21] (s Fig. 1(b)). Th input ipdanc Z in at th ai atial intfac was calculatd fo asud coplx pittivity (ε ) and pability (µ ) at th givn thicknss basd on tansission lin thoy [22] Z in = Z / tanh( j2pfd / ) (3) 0 c Wh Z 0 =377 W is th intinsic ipdanc of f spac, f is th icowav fquncy, c is th spd of light and d is th thicknss of th absobs. Th flction loss (RL) of absobs backd with a pfct conducto in th on-lay odl can b wittn as RL db) = 20log ( Z - Z )/( Z ) (4) ( 10 in 0 in+ Z0 [20, 22] Accoding to th abov quations, th RL valu was iplicitly dtind by d, f, µ and ε. Th dip in RL indicats th icowav absobing pow of th atials. Whn Z in appoachs Z 0, RL gadually appoachs -. Th condition that an EM wav is 3
copltly absobd by th absobing diu on th idal conducto could b wittn as: 1 / tanh( j2p fd / c) = / (5) Equation (5) is a coplx function (both th lft and th ight sid of th quation should hav a al pat and an iaginay pat). To obtain al function, al and iaginay pats of th lativ pittivity and pability a intoducd to quation (5). [18] Accoding to th tigonotic function and coplx quation thoy, finally, th following quations could b divd fo th quation (5): ì - 4pfd sin[( d + d ) / 2] ïcosq = cosh( ) ï + c í ï d + 4 d pfd sin[( d+ d ) / 2] ï sinq = tan sinh( ) î 2 c (6) Wh q could b psntd by q 4 pfd cos( d / 2+ d / 2) c = (7) Th quation (6) is quivalnt to th coplx function (5). In od to valuat th EM ipdanc atching dg, th abov two quations should b visd into only on quation. Accoding to sin 2 q+cos 2 q=1, quation (6) could b wittn and siplifid as th following sipl quation: sinh 2 ( Kfd ) = M, wh K and M could b dtind by th lativ coplx pittivity and pability: K sin[( d + d ) / 2] = 4p / c (8) 4
M 4 = (9) 2 d -d 2 2 ( - ) + (tan ) ( + ) 2 Now, th EM ipdanc atching dg could b dscibd as a dlta-functiond = sinh 2 ( Kfd) - M. H, th dlta-function psnts th ipdanc atching dg. It ans that th high absoption (wh RL appoachs - ) at a ctain thicknss is th sult of btt EM ipdanc atching, wh dlta valu should gadually appoachs zo. Th sall dlta valu iplis btt EM ipdanc atching. By th thod, onc th pittivity and pability w obtaind fo th xpint, lik asud by th vcto ntwok analyz, th EM ipdanc atching dg could b accuatly valuatd and quantificationally analyzd by th dlta valus. In od to judg th ffctivnss of th thod and daw a copaison, al EM paats asud in al atials a applid to calculat th atching dg. Sinc pittivity/pability of α-f/f 3 B/Y 2 O 3 nanocoposits showd alost constant ov th plottd fquncy ang (1-10 GHz, ε =15-0.6j, µ =1.25-0.5j), [23] th data a usd in latt calculations. W hypothsizd that th pittivity and pability w aintain constant ov whol 0.1-18 GHz ang. Th calculatd flction loss and dlta valus a shown in Fig. 2(a) and (b). It can b sn that flction loss and dlta valus show sa tndncy. Th copaison of ths two aps concluds that wh th flction loss blow -8 db, th dlta valus should b sall than 0.2. It is al that th dlta valus wll psnt th EM ipdanc atching dg and th thod is ffctiv. 5
In Fig. 2(a) and (b), it can futh b noticd that th iniu RL and dlta valus shift towads a high fquncy sid if th sapl thicknss is ducd. This can b undstood basd on quat-wav pincipl [1], which is wittn as: 2 d = ( n / 4) c /[ f ( ) 1/ ]. Wh n is odd nub, µ and ε a th odul of µ and ε, spctivly. Sinc th thicknss d is invsly popotional to fquncy f, th abov cition is satisfid at ducd thicknss fo high fquncis. Th high absoption at ducd thicknss is th sult of total cancllation, wh RL and dlta valus should also b ducd, satisfying th abov citia pfctly. Fig. 2(c) shows th atching thicknss and atching fquncis basd on th abov quat-wav pincipl. Th filld gions iplid th ons wh th flction loss o th dlta-function valus achs thi iniu valus. Fo th copaison in Fig. 2(a) to (c), it is found that th flction loss was cucially dtind by th quat-wav pincipl at th givn dilctic and agntic paats. In thos cosponding gions, th EM ipdanc atching was wll achivd, whn th flction loss blow -8 db, th dlta valus should b sall than 0.2 and n should b qual to 9. Th abov analysis also iplis that th good icowav absoption popty of th agntic atials was ainly a sult of stuctu ffct whn th atials a ctain. In oth wods, whn EM ipdanc of absobs was uch btt atchd ov a boad-band fquncy ang, th thicknss of absobing atials should soothly dcas as fquncy continuous incass. So w think that th stuctu of th 6
on-lay icowav absob should b not unifo but hav a pop gadint. Th botto gaph in Fig. 3 shows on possibl honycob stuctu of on-lay icowav absobs. Basd on th fo analysis, th cuvatu of inn sufac of th honycob stuctu should satisfy so quints. Th top ight gaph in Fig. 3 illustats th sction of th honycob stuctus and th d box shows an lnt of th honycob stuctus. Th top lft gaph iplis that lnt of th honycob stuctu should hav an optiu gadint, which should b dsignd to fully satisfy th dlta function o appoxiatly satisfy th quat-wav pincipl. It is poising that this optiu honycob stuctu will hav a btt icowav absoption pfoanc. Futho, oth stuctus also could b dsignd accoding to this viw fo anti-em intfnc tchnology inducd by th wilss counication quipnt, sinc ost of th wilss counication quipnts a woking in 2 4 GHz. Th stuctus also could b adaptd to th ada wav absoption gion, sinc th woking fquncy of ost ada is in 8 18 GHz. In conclusion, a dlta-function thod was poposd to calculat th EM ipdanc atching dg. It is donstatd that this thod is usful to analyz th EM ipdanc atching dg and can b usd to dsign lightwight high-pfoanc icowav absobs. Basd on this function thod, it is asi to obtain th optiu gadint cuvs fo dsigning th honycob-shapd o oth shapd icowav absobing atials. Th sults in this wok a hlpful fo invstigating th optiu 7
stuctus of icowav absob in pactic and would bnfit th dsign of lightwight high-pfoanc icowav absobs in th futu. Rfncs [1] Yusoff A N, Abdullah M H, Ahad S H, Jusoh S F, Manso A A and Haid S A A 2002 J. Appl. Phys. 92 876 [2] Li Z W, Lin G Q and Kong L B 2008 IEEE Tans. Magn.44 2255 [3] Sakai K, Asano N, Wada Y and Yoshikado S 2010 J. Eu. Ca. Soc. 30 347 [4] Ni Y, H H H, Gong R Z and Zhang X C 2007 J. Magn. Magn. Mat. 310 13 [5] Yi H B, Wn F S, Qiao L and Li F S 2009 J. Appl. Phys. 106 103922 [6] Liu X G, Li B, Gng D Y, Cui W B, Yang F, Xi Z G, t al. 2009 Cabon 47 470 [7] Cao M S, Song W L, Hou Z L, Wn B and Yuan J 2010 Cabon 48 788 [8] Dong X L, Zhang X F, Huang H and Zuo F 2008 Appl. Phys. Ltt. 92 013127 [9] Li B W, Shn Y, Yu Z X and Nan C W 2007 J. Magn. Magn. Mat. 313 322 [10] Wu M Z, H H H, Zhao Z S and Yao X 2000 J. Phys. D: Appl. Phys. 33 2398 [11] Yan S J, Zhn L, Xu C Y, Jiang J T and Shao W Z 2010 J. Phys. D: Appl. Phys. 43 245003 [12] Yan L G, Wang J B, Han X H, Rn Y, Liu Q F and Li F S 2010 Nanotchnol. 21 095708 8
[13] Xi L, Wang Z, Zuo Y L and Shi X N 2011 Nanotchnol. 22 045707 [14] Liu X G, Gng D Y, Mng H, Shang P J and Zhang Z D 2008 Appl. Phys. Ltt. 92 173117 [15] Kang Y Q, Cao M S, Yuan J and Shi X L 2009 Mat. Ltt. 63 1344 [16] Yan S J, Zhn L, Xu C Y, Jiang J T, Shao W Z and Tang J K 2011 J. Magn. Magn. Mat. 323 515 [17] Han R, Han X H, Qiao L, Wang T and Li F S 2011 Physica B 406 1932 [18] Huang Y Q, Yuan J, Song W L, Wn B, Fang X Y and Cao M S 2010 Chin. Phys. Ltt. 27 027702 [19] Nicolson A M and Ross G F 1970 IEEE Tans. Instu. Mas. 19 377 [20] Ki S S, Jo S B, Choi K K, Ki J M and Chun K S 1991 IEEE Tans. Magn. MAG-27 5462 [21] Shin J Y and Oh J H 1993 IEEE Tans. Magn. 29 3437 [22] Kwon H J, Shin J Y and Oh J H 1994 J. Appl. Phys. 75 6109 [23] Liu J R, Itoh M and Machida K 2003 Appl. Phys. Ltt. 83 4017 9
Figu captions: Fig. 1 (a) Coaxial sapl usd in asuing th coplx scatting paats, and (b) on lay icowav absobs odl was usd to calculat th lctoagntic ipdanc atchs dg. Fig. 2 (a) Calculatd icowav flction loss ap by quation (4), (b) calculatd dlta valus ap and (c) calculatd quat-wav pincipl ap. Th lativ pittivity and pability w hypothsizd at constant ov 0.1-18 GHz (ε =15-0.6j, µ =1.25-0.5j). Fig. 3 Optiu honycob stuctus w dsignd fo high-pfoanc icowav absobs. Th botto gaph givs th 3D honycob stuctus. Th top ight gaph shows th sction of th pfct honycob stuctus and th top lft gaph shows th gadint of th honycob lnt should satisfy th dlta function. 10
Fig. 1. 11
Fig. 2. 12
Fig. 3. 13