CHAPTER 3 MICROSTRIP PATCH ANTENNA

Transcription

1 CHAPTER 3 MICROSTRIP PATCH ANTENNA I this chapte, a itoductio to the Micostip Patch Atea is followed by its advatages ad disadvatages. Next, some feed modelig techiques ae discussed. Fially, a detailed explaatio of Micostip patch atea aalysis ad its theoy ae discussed, ad also the wokig mechaism is explaied. 3. Itoductio I its most basic fom, a Micostip patch atea cosists of a adiatig patch o oe side of a dielectic substate which has a goud plae o the othe side as show i Figue 3.. The patch is geeally made of coductig mateial such as coppe o gold ad ca take ay possible shape. The adiatig patch ad the feed lies ae usually photo etched o the dielectic substate. L Patch t h W Dielectic Substate Goud Plae Figue 3. Stuctue of a Micostip Patch Atea 3

2 I ode to simplify aalysis ad pefomace pedictio, the patch is geeally squae, ectagula, cicula, tiagula, elliptical o some othe commo shape as show i Figue 3.. Fo a ectagula patch, the legth L of the patch is usually λo < L < 0. 5λo, whee λ o is the fee-space wavelegth. The patch is selected to be vey thi such that t << λ (whee t is the patch thickess). The height h of the dielectic substate is usually λo h 0. 05λo. The dielectic costat of the substate ( ε ) is typically i the age. ε. o Squae Rectagula Dipole Cicula Tiagula Cicula Rig Elliptical Figue 3. Commo shapes of micostip patch elemets Micostip patch ateas adiate pimaily because of the figig fields betwee the patch edge ad the goud plae. Fo good atea pefomace, a thick dielectic substate havig a low dielectic costat is desiable sice this povides bette efficiecy, lage badwidth ad bette adiatio [5]. Howeve, such a cofiguatio leads to a lage atea size. I ode to desig a compact Micostip patch atea, highe dielectic costats must be used which ae less efficiet ad esult i aowe badwidth. Hece a compomise must be eached betwee atea dimesios ad atea pefomace. 3. Advatages ad Disadvatages Micostip patch ateas ae iceasig i populaity fo use i wieless applicatios due to thei low-pofile stuctue. Theefoe they ae extemely compatible fo embedded ateas i hadheld wieless devices such as cellula phoes, pages etc... The telemety ad 3

3 commuicatio ateas o missiles eed to be thi ad cofomal ad ae ofte Micostip patch ateas. Aothe aea whee they have bee used successfully is i Satellite commuicatio. Some of thei picipal advatages discussed by [5] ad Kuma ad Ray [9] ae give below: Light weight ad low volume. Low pofile plaa cofiguatio which ca be easily made cofomal to host suface. Low fabicatio cost, hece ca be maufactued i lage quatities. Suppots both, liea as well as cicula polaizatio. Ca be easily itegated with micowave itegated cicuits (MICs). Capable of dual ad tiple fequecy opeatios. Mechaically obust whe mouted o igid sufaces. Micostip patch ateas suffe fom a umbe of disadvatages as compaed to covetioal ateas. Some of thei majo disadvatages discussed by [9] ad Gag et al [0] ae give below: Naow badwidth Low efficiecy Low Gai Extaeous adiatio fom feeds ad juctios Poo ed fie adiato except tapeed slot ateas Low powe hadlig capacity. Suface wave excitatio Micostip patch ateas have a vey high atea quality facto (Q). Q epesets the losses associated with the atea ad a lage Q leads to aow badwidth ad low efficiecy. Q ca be educed by iceasig the thickess of the dielectic substate. But as the thickess iceases, a iceasig factio of the total powe deliveed by the souce goes ito a suface wave. This suface wave cotibutio ca be couted as a uwated powe loss sice it is ultimately scatteed at the dielectic beds ad causes degadatio of the atea chaacteistics. Howeve, suface waves ca be miimized by use of photoic badgap stuctues as discussed by Qia et al []. Othe poblems such as lowe gai ad lowe powe hadlig capacity ca be ovecome by usig a aay cofiguatio fo the elemets. 33

4 3.3 Feed Techiques Micostip patch ateas ca be fed by a vaiety of methods. These methods ca be classified ito two categoies- cotactig ad o-cotactig. I the cotactig method, the RF powe is fed diectly to the adiatig patch usig a coectig elemet such as a micostip lie. I the o-cotactig scheme, electomagetic field couplig is doe to tasfe powe betwee the micostip lie ad the adiatig patch [5]. The fou most popula feed techiques used ae the micostip lie, coaxial pobe (both cotactig schemes), apetue couplig ad poximity couplig (both o-cotactig schemes) Micostip Lie Feed I this type of feed techique, a coductig stip is coected diectly to the edge of the micostip patch as show i Figue 3.3. The coductig stip is smalle i width as compaed to the patch ad this kid of feed aagemet has the advatage that the feed ca be etched o the same substate to povide a plaa stuctue. Micostip Feed Patch Substate Goud Plae Figue 3.3 Micostip Lie Feed The pupose of the iset cut i the patch is to match the impedace of the feed lie to the patch without the eed fo ay additioal matchig elemet. This is achieved by popely cotollig the iset positio. Hece this is a easy feedig scheme, sice it povides ease of 34

5 fabicatio ad simplicity i modelig as well as impedace matchig. Howeve as the thickess of the dielectic substate beig used, iceases, suface waves ad spuious feed adiatio also iceases, which hampes the badwidth of the atea [5]. The feed adiatio also leads to udesied coss polaized adiatio Coaxial Feed The Coaxial feed o pobe feed is a vey commo techique used fo feedig Micostip patch ateas. As see fom Figue 3.4, the ie coducto of the coaxial coecto exteds though the dielectic ad is soldeed to the adiatig patch, while the oute coducto is coected to the goud plae. Patch Substate Coaxial Coecto Goud Plae Figue 3.4 Pobe fed Rectagula Micostip Patch Atea The mai advatage of this type of feedig scheme is that the feed ca be placed at ay desied locatio iside the patch i ode to match with its iput impedace. This feed method is easy to fabicate ad has low spuious adiatio. Howeve, its majo disadvatage is that it 35

6 povides aow badwidth ad is difficult to model sice a hole has to be dilled i the substate ad the coecto potudes outside the goud plae, thus ot makig it completely plaa fo thick substates ( h > 0.0λ ). Also, fo thicke substates, the iceased pobe legth makes the o iput impedace moe iductive, leadig to matchig poblems [9]. It is see above that fo a thick dielectic substate, which povides boad badwidth, the micostip lie feed ad the coaxial feed suffe fom umeous disadvatages. The o-cotactig feed techiques which have bee discussed below, solve these poblems Apetue Coupled Feed I this type of feed techique, the adiatig patch ad the micostip feed lie ae sepaated by the goud plae as show i Figue 3.5. Couplig betwee the patch ad the feed lie is made though a slot o a apetue i the goud plae. Micostip Lie Patch Apetue/Slot Goud Plae Substate Substate Figue 3.5 Apetue-coupled feed The couplig apetue is usually ceteed ude the patch, leadig to lowe cosspolaizatio due to symmety of the cofiguatio. The amout of couplig fom the feed lie to the patch is detemied by the shape, size ad locatio of the apetue. Sice the goud plae sepaates the patch ad the feed lie, spuious adiatio is miimized. Geeally, a high dielectic 36

7 mateial is used fo the bottom substate ad a thick, low dielectic costat mateial is used fo the top substate to optimize adiatio fom the patch [5]. The majo disadvatage of this feed techique is that it is difficult to fabicate due to multiple layes, which also iceases the atea thickess. This feedig scheme also povides aow badwidth Poximity Coupled Feed This type of feed techique is also called as the electomagetic couplig scheme. As show i Figue 3.6, two dielectic substates ae used such that the feed lie is betwee the two substates ad the adiatig patch is o top of the uppe substate. The mai advatage of this feed techique is that it elimiates spuious feed adiatio ad povides vey high badwidth (as high as 3%) [5], due to oveall icease i the thickess of the micostip patch atea. This scheme also povides choices betwee two diffeet dielectic media, oe fo the patch ad oe fo the feed lie to optimize the idividual pefomaces. Patch Micostip Lie Substate Substate Figue 3.6 Poximity-coupled Feed Matchig ca be achieved by cotollig the legth of the feed lie ad the width-to-lie atio of the patch. The majo disadvatage of this feed scheme is that it is difficult to fabicate 37

8 because of the two dielectic layes which eed pope aligmet. Also, thee is a icease i the oveall thickess of the atea. Table 3. below summaizes the chaacteistics of the diffeet feed techiques. Chaacteistics Table 3. Compaig the diffeet feed techiques [4] Micostip Lie Coaxial Feed Apetue Feed coupled Feed Poximity coupled Feed Spuious feed Moe Moe Less Miimum adiatio Reliability Bette Poo due to soldeig Good Good Ease of fabicatio Impedace Matchig Badwidth (achieved with impedace matchig) Easy Soldeig ad dillig eeded Aligmet equied Aligmet equied Easy Easy Easy Easy -5% -5% -5% 3% 3.4 Methods of Aalysis The most popula models fo the aalysis of Micostip patch ateas ae the tasmissio lie model, cavity model, ad full wave model [5] (which iclude pimaily itegal equatios/momet Method). The tasmissio lie model is the simplest of all ad it gives good physical isight but it is less accuate. The cavity model is moe accuate ad gives good physical isight but is complex i atue. The full wave models ae extemely accuate, vesatile ad ca teat sigle elemets, fiite ad ifiite aays, stacked elemets, abitay shaped elemets ad couplig. These give less isight as compaed to the two models metioed above ad ae fa moe complex i atue. 38

9 3.4. Tasmissio Lie Model This model epesets the micostip atea by two slots of width W ad height h, sepaated by a tasmissio lie of legth L. The micostip is essetially a ohomogeeous lie of two dielectics, typically the substate ad ai. Stip coducto Dielectic Substate h W Goud Plae Figue 3.7 Micostip Lie Figue 3.8 Electic Field Lies Hece, as see fom Figue 3.8, most of the electic field lies eside i the substate ad pats of some lies i ai. As a esult, this tasmissio lie caot suppot pue tasveseelectic-magetic (TEM) mode of tasmissio, sice the phase velocities would be diffeet i the ai ad the substate. Istead, the domiat mode of popagatio would be the quasi-tem mode. Hece, a effective dielectic costat ( ε eff ) must be obtaied i ode to accout fo the figig ad the wave popagatio i the lie. The value of ε eff is slightly less the ε because the figig fields aoud the peiphey of the patch ae ot cofied i the dielectic substate but ae also spead i the ai as show i Figue 3.8 above. The expessio fo ε eff is give by Balais [] as: Whee ε eff = Effective dielectic costat ε + ε h ε eff = + + (3.) W ε = Dielectic costat of substate h = Height of dielectic substate W = Width of the patch 39

10 Coside Figue 3.9 below, which shows a ectagula micostip patch atea of legth L, width W estig o a substate of height h. The co-odiate axis is selected such that the legth is alog the x diectio, width is alog the y diectio ad the height is alog the z diectio. Micostip Feed Patch W L h Substate Goud Plae z y Figue 3.9 Micostip Patch Atea x I ode to opeate i the fudametal TM 0 mode, the legth of the patch must be slightly less tha λ / whee λ is the wavelegth i the dielectic medium ad is equal to λ o / ε eff whee λ o is the fee space wavelegth. The TM 0 mode implies that the field vaies oe λ / cycle alog the legth, ad thee is o vaiatio alog the width of the patch. I the Figue 3.0 show below, the micostip patch atea is epeseted by two slots, sepaated by a tasmissio lie of legth L ad ope cicuited at both the eds. Alog the width of the patch, the voltage is maximum ad cuet is miimum due to the ope eds. The fields at the edges ca be esolved ito omal ad tagetial compoets with espect to the goud plae. 40

11 Radiatig Slots Goud Plae L E V EH Patch EH W L E V h L Goud Plae Patch Figue 3.0 Top View of Atea Figue 3. Side View of Atea It is see fom Figue 3. that the omal compoets of the electic field at the two edges alog the width ae i opposite diectios ad thus out of phase sice the patch is λ / log ad hece they cacel each othe i the boadside diectio. The tagetial compoets (see i Figue 3.), which ae i phase, meas that the esultig fields combie to give maximum adiated field omal to the suface of the stuctue. Hece the edges alog the width ca be epeseted as two adiatig slots, which ae λ / apat ad excited i phase ad adiatig i the half space above the goud plae. The figig fields alog the width ca be modeled as adiatig slots ad electically the patch of the micostip atea looks geate tha its physical dimesios. The dimesios of the patch alog its legth have ow bee exteded o each ed by a distace L, which is give empiically by Hammestad [3] as: L = 0.4h ( ε + 0.3) eff W h W ( ε 0.58) eff h (3.) 4

12 The effective legth of the patch L eff ow becomes: L eff = L + L (3.3) Fo a give esoace fequecy f o, the effective legth is give by [9] as: L eff c = (3.4) f ε o eff Fo a ectagula Micostip patch atea, the esoace fequecy fo ay give by James ad Hall [4] as: TM m mode is f o = c m + ε L W eff (3.5) Whee m ad ae modes alog L ad W espectively. Fo efficiet adiatio, the width W is give by Bahl ad Bhatia [5] as: W = f o c ( ε + ) (3.6) 3.4. Cavity Model Although the tasmissio lie model discussed i the pevious sectio is easy to use, it has some iheet disadvatages. Specifically, it is useful fo patches of ectagula desig ad it igoes field vaiatios alog the adiatig edges. These disadvatages ca be ovecome by usig the cavity model. A bief oveview of this model is give below. I this model, the iteio egio of the dielectic substate is modeled as a cavity bouded by electic walls o the top ad bottom. The basis fo this assumptio is the followig obsevatios fo thi substates ( h << λ) [0]. Sice the substate is thi, the fields i the iteio egio do ot vay much i the z diectio, i.e. omal to the patch. The electic field is z diected oly, ad the magetic field has oly the tasvese compoets H x ad H y i the egio bouded by the patch metallizatio ad the goud plae. This obsevatio povides fo the electic walls at the top ad the bottom. 4

13 W J t h J b Figue 3. Chage distibutio ad cuet desity ceatio o the micostip patch Coside Figue 3. show above. Whe the micostip patch is povided powe, a chage distibutio is see o the uppe ad lowe sufaces of the patch ad at the bottom of the goud plae. This chage distibutio is cotolled by two mechaisms-a attactive mechaism ad a epulsive mechaism as discussed by Richads [6]. The attactive mechaism is betwee the opposite chages o the bottom side of the patch ad the goud plae, which helps i keepig the chage cocetatio itact at the bottom of the patch. The epulsive mechaism is betwee the like chages o the bottom suface of the patch, which causes pushig of some chages fom the bottom, to the top of the patch. As a esult of this chage movemet, cuets flow at the top ad bottom suface of the patch. The cavity model assumes that the height to width atio (i.e. height of substate ad width of the patch) is vey small ad as a esult of this the attactive mechaism domiates ad causes most of the chage cocetatio ad the cuet to be below the patch suface. Much less cuet would flow o the top suface of the patch ad as the height to width atio futhe deceases, the cuet o the top suface of the patch would be almost equal to zeo, which would ot allow the ceatio of ay tagetial magetic field compoets to the patch edges. Hece, the fou sidewalls could be modeled as pefectly magetic coductig sufaces. This implies that the magetic fields ad the electic field distibutio beeath the patch would ot be distubed. Howeve, i pactice, a fiite width to height atio would be thee ad this would ot make the tagetial magetic fields to be completely zeo, but they beig vey small, the side walls could be appoximated to be pefectly magetic coductig [5]. 43

14 Sice the walls of the cavity, as well as the mateial withi it ae lossless, the cavity would ot adiate ad its iput impedace would be puely eactive. Hece, i ode to accout fo adiatio ad a loss mechaism, oe must itoduce a adiatio esistace R ad a loss esistace R. A lossy cavity would ow epeset a atea ad the loss is take ito accout L by the effective loss taget δ eff which is give as: δ eff = / Q T (3.7) Q T is the total atea quality facto ad has bee expessed by [4] i the fom: Q T = + + (3.8) Q Q Q Q d epesets the quality facto of the dielectic ad is give as : whee d c ωwt Q d = = (3.9) P taδ ω is the agula esoat fequecy. d W T is the total eegy stoed i the patch at esoace. P d is the dielectic loss. ta δ is the loss taget of the dielectic. Q c epesets the quality facto of the coducto ad is give as : Q c ωw = P c T = h (3.0) whee P c is the coducto loss. is the ski depth of the coducto. h is the height of the substate. Q epesets the quality facto fo adiatio ad is give as: Q ω W P T = (3.) whee P is the powe adiated fom the patch. Substitutig equatios (3.8), (3.9), (3.0) ad (3.) i equatio (3.7), we get δ + P eff = ta δ + (3.) h ωwt 44

15 Thus, equatio (3.) descibes the total effective loss taget fo the micostip patch atea Full Wave Solutios-Method of Momets Oe of the methods, that povide the full wave aalysis fo the micostip patch atea, is the Method of Momets. I this method, the suface cuets ae used to model the micostip patch ad the volume polaizatio cuets ae used to model the fields i the dielectic slab. It has bee show by Newma ad Tulyatha [7] how a itegal equatio is obtaied fo these ukow cuets ad usig the Method of Momets, these electic field itegal equatios ae coveted ito matix equatios which ca the be solved by vaious techiques of algeba to povide the esult. A bief oveview of the Momet Method descibed by Haigto [8] ad [5] is give below. The basic fom of the equatio to be solved by the Method of Momet is: F ( g) = h (3.3) whee F is a kow liea opeato, g is a ukow fuctio, ad h is the souce o excitatio fuctio. The aim hee is to fid g, whe F ad h ae kow. The ukow fuctio g ca be expaded as a liea combiatio of N tems to give: g = N = a g = a g + a g a g (3.4) N N whee a is a ukow costat ad g is a kow fuctio usually called a basis o expasio fuctio. Substitutig equatio (3.4) i (3.3) ad usig the lieaity popety of the opeato F, we ca wite: N = a F( g ) = h (3.5) The basis fuctios g must be selected i such a way, that each F g ) i the above ( equatio ca be calculated. The ukow costats a caot be detemied diectly because thee ae N ukows, but oly oe equatio. Oe method of fidig these costats is the method of weighted esiduals. I this method, a set of tial solutios is established with oe o moe vaiable paametes. The esiduals ae a measue of the diffeece betwee the tial solutio ad the tue solutio. The vaiable paametes ae selected i a way which guaatees a best fit of the tial fuctios based o the miimizatio of the esiduals. This is doe by defiig 45

16 a set of N weightig (o testig) fuctios { w m} = w, w,... wn i the domai of the opeato F. Takig the ie poduct of these fuctios, equatio (3.5) becomes: whee m =,,... N N = a w m, F( g ) = w, h (3.6) m Witig i Matix fom as show i [5], we get: whee w, F( g) w, F( g )... w, F( g ) w, F( g )... M M [ ][ a ] [ h ] [ ] F = m [ a ] The ukow costats F = (3.7) m m a a = a M a 3 N [ h ] m w, h w, h = w 3, h M wn, h a ca ow be foud usig algebaic techiques such as LU decompositio o Gaussia elimiatio. It must be emembeed that the weightig fuctios must be selected appopiately so that elemets of { w } ae ot oly liealy idepedet but they also miimize the computatios equied to evaluate the ie poduct. Oe such choice of the weightig fuctios may be to let the weightig ad the basis fuctio be the same, that is, w = g. This is called as the Galeki s Method as descibed by Katoovich ad Akilov [9]. Fom the atea theoy poit of view, we ca wite the Electic field itegal equatio as: whee E is the kow icidet electic field. J is the ukow iduced cuet. f e is the liea opeato. E = f (J ) (3.8) e The fist step i the momet method solutio pocess would be to expad J as a fiite sum of basis fuctio give as: J = M i= J i b i (3.9) 46

17 whee b i is the ith basis fuctio ad J i is a ukow coefficiet. The secod step ivolves the defiig of a set of M liealy idepedet weightig fuctios, w. Takig the ie poduct o both sides ad substitutig equatio (3.9) i equatio (3.8) we get: j whee j =,,... M w j M, E = w, f ( J, b ) (3.0) i= j e i i Witig i Matix fom as, [ ][ J ] [ ] Z = (3.) ij E j whee Z = w f ( b ) ij E j, e i = w H j j, J is the cuet vecto cotaiig the ukow quatities. The vecto E cotais the kow icidet field quatities ad the tems of the Z matix ae fuctios of geomety. The ukow coefficiets of the iduced cuet ae the tems of the J vecto. Usig ay of the algebaic schemes metioed ealie, these equatios ca be solved to give the cuet ad the the othe paametes such as the scatteed electic ad magetic fields ca be calculated diectly fom the iduced cuets. Thus, the Momet Method has bee biefly explaied fo use i atea poblems. The softwae used i this thesis, Zelad Ic s IE3D [0] is a Momet Method simulato. Futhe details about the softwae will be povided i the ext chapte. 47