Agilnt Basics of Masuing th Dilctic Poptis of Matials Application Not
Contnts Intoduction...3 Dilctic thoy...4 Dilctic Constant...4 Pmability...7 Elctomagntic popagation...8 Dilctic mchanisms...10 Ointation (dipola) polaization...11 Elctonic and atomic polaization...11 Rlaxation tim...12 Dby Rlation...12 Col-Col diagam...13 Ionic conductivity...13 Intfacial o spac chag polaization... 14 Masumnt Systms...15 Ntwok analyzs...15 Impdanc analyzs and LCR mts...16 Fixtus...16 Softwa...16 Masumnt tchniqus...17 Coaxial pob...17 Tansmission lin...20 F spac...23 Rsonant cavity...25 Paalll plat...27 Compaison of mthods...28 Rfncs...30 Wb Rsoucs...32 2
Intoduction Evy matial has a uniqu st of lctical chaactistics that a dpndnt on its dilctic poptis. Accuat masumnts of ths poptis can povid scintists and ngins with valuabl infomation to poply incopoat th matial into its intndd application fo mo solid dsigns o to monito a manufactuing pocss fo impovd quality contol. A dilctic matials masumnt can povid citical dsign paamt infomation fo many lctonics applications. Fo xampl, th loss of a cabl insulato, th impdanc of a substat, o th fquncy of a dilctic sonato can b latd to its dilctic poptis. Th infomation is also usful fo impoving fit, absob, and packaging dsigns. Mo cnt applications in th aa of industial micowav pocssing of food, ubb, plastic and camics hav also bn found to bnfit fom knowldg of dilctic poptis. Agilnt Tchnologis Inc. offs a vaity of instumnts, fixtus, and softwa to masu th dilctic poptis of matials. Agilnt masumnt instumnts, such as ntwok analyzs, LCR mts, and impdanc analyzs ang in fquncy up to 325 GHz. Fixtus to hold th matial und tst (MUT) a availabl that a basd on coaxial pob, coaxial/wavguid tansmission lin tchniqus, and paalll plat. 3
Dilctic Thoy Th dilctic poptis that will b discussd h a pmittivity and pmability. Rsistivity is anoth matial popty which will not b discussd h. Infomation about sistivity and its masumnt can b found in th Agilnt Application Not 1369-1 1. It is impotant to not that pmittivity and pmability a not constant. Thy can chang with fquncy, tmpatu, ointation, mixtu, pssu, and molcula stuctu of th matial. Dilctic constant A matial is classifid as dilctic if it has th ability to sto ngy whn an xtnal lctic fild is applid. If a DC voltag souc is placd acoss a paalll plat capacito, mo chag is stod whn a dilctic matial is btwn th plats than if no matial (a vacuum) is btwn th plats. Th dilctic matial incass th stoag capacity of th capacito by nutalizing chags at th lctods, which odinaily would contibut to th xtnal fild. Th capacitanc with th dilctic matial is latd to dilctic constant. If a DC voltag souc V is placd acoss a paalll plat capacito (Figu 1), mo chag is stod whn a dilctic matial is btwn th plats than if no matial (a vacuum) is btwn th plats. A C 0 = t C = C k' 0 k' = ' = C C 0 V t - - + - + - + + A - + - + - + + - + Figu 1. Paalll plat capacito, DC cas Wh C and C 0 a capacitanc with and without dilctic, k ' = ' is th al dilctic constant o pmittivity, and A and t a th aa of th capacito plats and th distanc btwn thm (Figu 1). Th dilctic matial incass th stoag capacity of th capacito by nutalizing chags at th lctods, which odinaily would contibut to th xtnal fild. Th capacitanc of th dilctic matial is latd to th dilctic constant as indicatd in th abov quations. If an AC sinusoidal voltag souc V is placd acoss th sam capacito (Figu 2), th sulting cunt will b mad up of a chaging cunt I c and a loss cunt I l that is latd to th dilctic constant. Th losss in th matial can b psntd as a conductanc (G) in paalll with a capacito (C). 4
I = I + I = V ( jwc k' + G ) If c I = V ( jwc )( k' - j k") = V ( jwc ) k w = 2πf G = wc l 0 k", 0 0 thn 0 V I t - - + - + - + + A - + - + - + + - - + C G Figu 2. Paalll plat capacito, AC cas Th complx dilctic constant k consists of a al pat k' which psnts th stoag and an imaginay pat k'' which psnts th loss. Th following notations a usd fo th complx dilctic constant intchangably k = k* = = *. Fom th point of viw of lctomagntic thoy, th dfinition of lctic displacmnt (lctic flux dnsity) D f is: D f = E wh = * = 0 is th absolut pmittivity (o pmittivity), is th lativ pmittivity, 0 1 36π x 10-9 F/m is th f spac pmittivity and E is th lctic fild. Pmittivity dscibs th intaction of a matial with an lctic fild E and is a complx quantity. k = = = j '' 0 Dilctic constant (k) is quivalnt to lativ pmittivity ( ) o th absolut pmittivity () lativ to th pmittivity of f spac ( 0 ). Th al pat of pmittivity ( ') is a masu of how much ngy fom an xtnal lctic fild is stod in a matial. Th imaginay pat of pmittivity ( '') is calld th loss facto and is a masu of how dissipativ o lossy a matial is to an xtnal lctic fild. Th imaginay pat of pmittivity ( ") is always gat than zo and is usually much small than ( '). Th loss facto includs th ffcts of both dilctic loss and conductivity. 5
Whn complx pmittivity is dawn as a simpl vcto diagam (Figu 3), th al and imaginay componnts a 90 out of phas. Th vcto sum foms an angl d with th al axis ( '). Th lativ lossinss of a matial is th atio of th ngy lost to th ngy stod. " 1 tan d= = D = ' Q Engy Lost p Cycl = Engy Stod p Cycl '' ' Figu 3. Loss tangnt vcto diagam Th loss tangnt o tan d is dfind as th atio of th imaginay pat of th dilctic constant to th al pat. D dnots dissipation facto and Q is quality facto. Th loss tangnt tan d is calld tan dlta, tangnt loss o dissipation facto. Somtims th tm quality facto o Q-facto is usd with spct to an lctonic micowav matial, which is th cipocal of th loss tangnt. Fo vy low loss matials, sinc tan d d, th loss tangnt can b xpssd in angl units, milliadians o micoadians. 6
Pmability Pmability (µ) dscibs th intaction of a matial with a magntic fild. A simila analysis can b pfomd fo pmability using an inducto with sistanc to psnt co losss in a magntic matial (Figu 4). If a DC cunt souc is placd acoss an inducto, th inductanc with th co matial can b latd to pmability. L = L µ ' 0 L µ ' = L 0 R L Figu 4. Inducto In th quations L is th inductanc with th matial, L 0 is f spac inductanc of th coil and µ' is th al pmability. If an AC sinusoidal cunt souc is placd acoss th sam inducto, th sulting voltag will b mad up of an inducd voltag and a loss voltag that is latd to pmability. Th co loss can b psntd by a sistanc (R) in sis with an inducto (L). Th complx pmability (µ* o µ) consists of a al pat (µ') that psnts th ngy stoag tm and an imaginay pat (µ'') that psnts th ngy loss tm. Rlativ pmittivity µ is th pmittivity lativ to f spac: µ = µ µ0 = µ jµ '' µ 0 = 4π x 10-7 H/m is th f spac pmability Som matials such as ion (fits), cobalt, nickl, and thi alloys hav appciabl magntic poptis; howv, many matials a nonmagntic, making th pmability vy clos to th pmability of f spac (µ = 1). All matials, on th oth hand, hav dilctic poptis, so th focus of this discussion will mostly b on pmittivity masumnts. 7
Elctomagntic Wav Popagation In th tim-vaying cas (i.., a sinusoid), lctic filds and magntic filds appa togth. This lctomagntic wav can popagat though f spac (at th spd of light, c = 3 x 10 8 m/s) o though matials at slow spd. Elctomagntic wavs of vaious wavlngths xist. Th wavlngth l of a signal is invsly popotional to its fquncy f (l = c/f), such that as th fquncy incass, th wavlngth dcass. Fo xampl, in f spac a 10 MHz signal has a wavlngth of 30 m, whil at 10 GHz it is just 3 cm. Many aspcts of wav popagation a dpndnt on th pmittivity and pmability of a matial. Lt s us th optical viw of dilctic bhavio. Consid a flat slab of matial (MUT) in spac, with a TEM wav incidnt on its sufac (Figu 5). Th will b incidnt, flctd and tansmittd wavs. Sinc th impdanc of th wav in th matial Z is diffnt (low) fom th f spac impdanc η (o Z 0 ) th will b impdanc mismatch and this will cat th flctd wav. Pat of th ngy will pntat th sampl. Onc in th slab, th wav vlocity v, is slow than th spd of light c. Th wavlngth l d is shot than th wavlngth l 0 in f spac accoding to th quations blow. Sinc th matial will always hav som loss, th will b attnuation o instion loss. Fo simplicity th mismatch on th scond bod is not considd. Z l d h = h = = l ' 0 ' v = Z 0 c = ' µ 0 0 = 120π TEM h o Z 0 Ai ' 0 Z= h MUT ' Impdanc low Wavlngth shot Vlocity slow Magnitud attnuatd ' Figu 5. Rflctd and tansmittd signals 8
Figu 6 dpicts th lation btwn th dilctic constant of th Matial Und Tst (MUT) and th flction cofficint G fo an infinitly long sampl (no flction fom th back of th sampl is considd). Fo small valus of th dilctic constant (appoximatly lss than 20), th is a lot of chang of th flction cofficint fo a small chang of th dilctic constant. In this ang dilctic constant masumnt using th flction cofficint will b mo snsitiv and hnc pcis. Convsly, fo high dilctic constants (fo xampl btwn 70 and 90) th will b littl chang of th flction cofficint and th masumnt will hav mo unctainty. 1 Rflct ion cofficint G 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 10 20 30 40 50 60 70 80 90 100 Dilctic constant ' Figu 6. Rflction cofficint vsus dilctic constant 9
Dilctic Mchanisms A matial may hav sval dilctic mchanisms o polaization ffcts that contibut to its ovall pmittivity (Figu 7). A dilctic matial has an aangmnt of lctic chag cais that can b displacd by an lctic fild. Th chags bcom polaizd to compnsat fo th lctic fild such that th positiv and ngativ chags mov in opposit dictions. At th micoscopic lvl, sval dilctic mchanisms can contibut to dilctic bhavio. Dipol ointation and ionic conduction intact stongly at micowav fquncis. Wat molculs, fo xampl, a pmannt dipols, which otat to follow an altnating lctic fild. Ths mchanisms a quit lossy which xplains why food hats in a micowav ovn. Atomic and lctonic mchanisms a lativly wak, and usually constant ov th micowav gion. Each dilctic mchanism has a chaactistic cutoff fquncy. As fquncy incass, th slow mchanisms dop out in tun, laving th fast ons to contibut to '. Th loss facto ( '') will cospondingly pak at ach citical fquncy. Th magnitud and cutoff fquncy of ach mchanism is uniqu fo diffnt matials. Wat has a stong dipola ffct at low fquncis but its dilctic constant olls off damatically aound 22 GHz. Tflon, on th oth hand, has no dipola mchanisms and its pmittivity is makably constant wll into th millimt-wav gion. ' Dipola (Rotational) + - Ionic '' Atomic Elctonic 10 3 10 6 10 9 10 12 10 15 f, Hz MW + - IR - + V UV Figu 7. Fquncy spons of dilctic mchanisms A sonant ffct is usually associatd with lctonic o atomic polaization. A laxation ffct is usually associatd with ointation polaization. 10
Ointation (dipola) polaization A molcul is fomd whn atoms combin to sha on o mo of this lctons. This aangmnt of lctons may caus an imbalanc in chag distibution cating a pmannt dipol momnt. Ths momnts a ointd in a andom mann in th absnc of an lctic fild so that no polaization xists. Th lctic fild E will xcis toqu T on th lctic dipol, and th dipol will otat to align with th lctic fild causing ointation polaization to occu (Figu 8). If th fild changs th diction, th toqu will also chang. T E F + F Figu 8. Dipol otation in lctic fild Th fiction accompanying th ointation of th dipol will contibut to th dilctic losss. Th dipol otation causs a vaiation in both ' and '' at th laxation fquncy which usually occus in th micowav gion. As mntiond, wat is an xampl of a substanc that xhibits a stong ointation polaization. Elctonic and atomic polaization Elctonic polaization occus in nutal atoms whn an lctic fild displacs th nuclus with spct to th lctons that suound it. Atomic polaization occus whn adjacnt positiv and ngativ ions sttch und an applid lctic fild. Fo many dy solids, ths a th dominant polaization mchanisms at micowav fquncis, although th actual sonanc occus at a much high fquncy. In th infad and visibl light gions th intia of th obiting lctons must b takn into account. Atoms can b modld as oscillatos with a damping ffct simila to a mchanical sping and mass systm (Figu 7). Th amplitud of th oscillations will b small fo any fquncy oth than th sonant fquncy. Fa blow sonanc, th lctonic and atomic mchanisms contibut only a small constant amount to ' and a almost losslss. Th sonant fquncy is idntifid by a sonant spons in ' and a pak of maximum absoption in ''. Abov th sonanc, th contibution fom ths mchanisms disappas. 11
Rlaxation tim Rlaxation tim τ is a masu of th mobility of th molculs (dipols) that xist in a matial. It is th tim quid fo a displacd systm alignd in an lctic fild to tun to 1/ of its andom quilibium valu (o th tim quid fo dipols to bcom ointd in an lctic fild). Liquid and solid matials hav molculs that a in a condnsd stat with limitd fdom to mov whn an lctic fild is applid. Constant collisions caus intnal fiction so that th molculs tun slowly and xponntially appoach th final stat of ointation polaization with laxation tim constant τ. Whn th fild is switchd off, th squnc is vsd and andom distibution is stod with th sam tim constant. Th laxation fquncy f c is invsly latd to laxation tim: τ 1 = = w 1 2π c fc At fquncis blow laxation th altnating lctic fild is slow nough that th dipols a abl to kp pac with th fild vaiations. Bcaus th polaization is abl to dvlop fully, th loss ( '') is dictly popotional to th fquncy (Figu 9). As th fquncy incass, '' continus to incas but th stoag ( ') bgins to dcas du to th phas lag btwn th dipol alignmnt and th lctic fild. Abov th laxation fquncy both '' and ' dop off as th lctic fild is too fast to influnc th dipol otation and th ointation polaization disappas. Dby lation Matials that xhibit a singl laxation tim constant can b modld by th Dby lation, which appas as a chaactistic spons in pmittivity as a function of fquncy (Figu 9). ' is constant abov and blow th laxation with th tansition occuing na th laxation fquncy (22 GHz). Additionally, '' is small abov and blow laxation and paks in th tansition gion at th laxation fquncy. Dby quation : s ( w) = + 1 + j τ w ', '' 60 40 ' Fo Fo w= 0, w=, (0) = ( ) = s 20 " 0.1 1 10 100 f, GHz Figu 9. Dby laxation of wat at 30º C In calculating th abov cuvs th static (DC) valu of th dilctic constant is s = 76.47, th optical (infinit fquncy) valu of th dilctic constant is = 4.9 and th laxation tim τ = 7.2 ps. 12
Col-Col diagam Th complx pmittivity may also b shown on a Col-Col diagam by plotting th imaginay pat ( '') on th vtical axis and th al pat ( ') on th hoizontal axis with fquncy as th indpndnt paamt (Figu 10). A Col-Col diagam is, to som xtnt, simila to th Smith chat. A matial that has a singl laxation fquncy as xhibitd by th Dby lation will appa as a smicicl with its cnt lying on th hoizontal '' = 0 axis and th pak of th loss facto occuing at 1/τ. A matial with multipl laxation fquncis will b a smicicl (symmtic distibution) o an ac (nonsymmtical distibution) with its cnt lying blow th hoizontal ''= 0 axis. Th cuv in Figu 10 is a half cicl with its cnt on th x-axis and its adius s. Th maximum imaginay pat of th dilctic constant 2 ' max will b qual to th adius. Th fquncy movs count clockwis on th cuv. " 30 20 - " s max = = 2 35.8 Incasing f (GHz) 10 Cnt 0 10 20 30 40 50 60 70 = 4.9 s = 76. 47 ' Figu 10. Col-Col diagam of Figu 9 Ionic conductivity Th masud loss of matial can actually b xpssd as a function of both dilctic loss ( d '') and conductivity (s). s '' = d '' + w 0 At low fquncis, th ovall conductivity can b mad up of many diffnt conduction mchanisms, but ionic conductivity is th most pvalnt in moist matials. '' is dominatd by th influnc of lctolytic conduction causd by f ions which xist in th psnc of a solvnt (usually wat). Ionic conductivity only intoducs losss into a matial. At low fquncis th ffct of ionic conductivity is invsly popotional to fquncy and appas as a 1/f slop of th '' cuv. 13
Intfacial o spac chag polaization Elctonic, atomic, and ointation polaization occu whn chags a locally bound in atoms, molculs, o stuctus of solids o liquids. Chag cais also xist that can migat ov a distanc though th matial whn a low fquncy lctic fild is applid. Intfacial o spac chag polaization occus whn th motion of ths migating chags is impdd. Th chags can bcom tappd within th intfacs of a matial. Motion may also b impdd whn chags cannot b fly dischagd o placd at th lctods. Th fild distotion causd by th accumulation of ths chags incass th ovall capacitanc of a matial which appas as an incas in '. Mixtus of matials with lctically conducting gions that a not in contact with ach oth (spaatd by non-conducting gions) xhibit th Maxwll-Wagn ffct at low fquncis. If th chag lays a thin and much small than th paticl dimnsions, th chag sponds indpndntly of th chag on naby paticls. At low fquncis th chags hav tim to accumulat at th bods of th conducting gions causing ' to incas. At high fquncis th chags do not hav tim to accumulat and polaization dos not occu sinc th chag displacmnt is small compad to th dimnsions of th conducting gion. As th fquncy incass, ' dcass and th losss xhibit th sam 1/f slop as nomal ionic conductivity. Many oth dilctic mchanisms can occu in this low fquncy gion causing a significant vaiation in pmittivity. Fo xampl, colloidal suspnsion occus if th chag lay is on th sam od of thicknss o lag than th paticl dimnsions. Th Maxwll-Wagn ffct is no long applicabl sinc th spons is now affctd by th chag distibution of adjacnt paticls. 14
Masuing Systms Ntwok analyzs A masumnt of th flction fom and/o tansmission though a matial along with knowldg of its physical dimnsions povids th infomation to chaactiz th pmittivity and pmability of th matial. Vcto ntwok analyzs such as th PNA, PNA-L, ENA, and ENA-L mak swpt high fquncy stimulus-spons masumnts fom 300 khz to 110 GHz o vn 325 GHz (Figu 12). A vcto ntwok analyz consists of a signal souc, a civ and a display (Figu 11). Th souc launchs a signal at a singl fquncy to th matial und tst. Th civ is tund to that fquncy to dtct th flctd and tansmittd signals fom th matial. Th masud spons poducs th magnitud and phas data at that fquncy. Th souc is thn stppd to th nxt fquncy and th masumnt is patd to display th flction and tansmission masumnt spons as a function of fquncy. Mo infomation on th ntwok analyz functioning and achitctu is availabl in th Application Nots 1287-1 2 and 1287-2 3. Simpl componnts and conncting wis that pfom wll at low fquncis bhav diffntly at high fquncis. At micowav fquncis wavlngths bcom small compad to th physical dimnsions of th dvics such that two closly spacd points can hav a significant phas diffnc. Low fquncy lumpd-cicuit lmnt tchniqus must b placd by tansmission lin thoy to analyz th bhavio of dvics at high fquncis. Additional high fquncy ffcts such as adiation loss, dilctic loss and capacitiv coupling mak micowav cicuits mo complx and xpnsiv. It is tim consuming and costly to ty to dsign a pfct micowav ntwok analyz. Incidnt Fixtu MUT Tansmittd Souc Rflctd Signal spaation Incidnt (R) Rflctd (A) Tansmittd (B) Rciv/dtcto Pocsso/display Figu 11. Ntwok analyz Instad, a masumnt calibation is usd to liminat th systmatic (stabl and patabl) masumnt os causd by th impfctions of th systm. Random os du to nois, dift, o th nvionmnt (tmpatu, humidity, pssu) cannot b movd with a masumnt calibation. This maks a micowav masumnt suscptibl to os fom small changs in th masumnt systm. Ths os can b minimizd by adopting good masumnt pactics, such as visually inspcting all connctos fo dit o damag and by minimizing any physical movmnt of th tst pot cabls aft a calibation. Mo infomation on th ntwok analyz calibation is availabl in th Application Not 1287-3 4. 15
Impdanc analyzs and LCR mts Impdanc analyzs and LCR mts such as th ons listd in Figu 12 a usd to masu th matial poptis at low fquncis. Th matial is stimulatd with an AC souc and th actual voltag acoss th matial is monitod. Matial tst paamts a divd by knowing th dimnsions of th matial and by masuing its capacitanc and dissipation facto. Ntwok analyzs ENA, ENA-L PNA, PNA-L Lgacy 8712, 8753, 8720, 8510 E4991A Impdanc/matial analyz 4192A, 4194A, 4263B, LCR mts 4294A, 4285A, 4278A Impdanc analyzs DC 101 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 11 f (Hz) Figu 12. Fquncy covag of Agilnt Tchnologis instumnts usd fo dilctic masumnts Fixtus Bfo th dilctic poptis of a matial can b masud with ntwok analyz, impdanc analyz, o LCR mt, a masumnt fixtu (o sampl hold) is quid to apply th lctomagntic filds in a pdictabl way and to allow connction to th masumnt instumnt. Th typ of fixtu quid will dpnd on th chosn masumnt tchniqu and th physical poptis of th matial (solid, liquid, powd, gas). Softwa Th masud data fom th instumnt is not always psntd in th most convnint tminology o fomat. In this cas, softwa is quid to convt th masud data to pmittivity o pmability. Softwa may also b quid to modl any intaction btwn th fixtu and MUT to allow th xtaction of th bulk matial poptis. 16
Masumnt Tchniqus Coaxial pob Mthod fatus Boadband Simpl and convnint (non-dstuctiv) Limitd accuacy and tan d low loss solution Bst fo liquids o smi-solids Matial assumptions Smi-infinit thicknss Non-magntic Isotopic and homognous Flat sufac No ai gaps Th opn-ndd coaxial pob is a cut off sction of tansmission lin. Th matial is masud by immsing th pob into a liquid o touching it to th flat fac of a solid (o powd) matial. Th filds at th pob nd fing into th matial and chang as thy com into contact with th MUT (Figu 13). Th flctd signal 5 (S 11 ) can b masud and latd to *. A typical masumnt systm using a coaxial pob mthod consists of a ntwok o impdanc analyz, a coaxial pob and softwa. Both th softwa and th pob a includd in th 85070E dilctic pob kit. An xtnal comput is ndd in many cass to contol th ntwok analyz though GP-IB. Th 82357A USB to GPIB intfac povids a convnint and flxibl way to aliz this connction. Fo th PNA family of ntwok analyzs th softwa can b installd dictly in th analyz and th is no nd fo an xtnal comput. Solids Smisolids (powd) Rflction (S ) 11 Liquids S11 Figu 13. Coaxial pob mthod 17
Figu 14 shows th two pobs that a availabl in th 85070E kit; th high tmpatu pob (a) and th slim fom pob (b). Th high tmpatu pob (a) is shown with th shoting block to th ight. Th slim pobs a shown at th bottom of (b) with th shot on th top and a coupl of oth accssois. Shot (a) (b) Shot Flang Aptu High tmpatu pob Slim pobs Figu 14. Two dilctic pob configuations Ruggd in dsign, th high tmpatu pob fatus a hmtic glass-tomtal sal, which maks it sistant to coosiv o abasiv chmicals. Th pob withstands a wid 40 to +200 C tmpatu ang, which allows masumnts vsus fquncy and tmpatu. Th lag flang allows masumnts of flat sufacd solid matials, in addition to liquids and smi-solids. Th slim fom pob fatus a slim dsign, which allows it to fit asily in fmntation tanks, chmical action chambs, o oth quipmnt with small aptus. Th slim dsign also allows it to b usd with small sampl sizs. This pob is bst usd fo liquids and soft smi-solids. Fo castabl solids, th pob is conomical nough to b cast into th matial and lft in plac. Bcaus of th consumabl natu of this dsign, ths pobs a offd in sts of th. Th Slim Fom pob kit coms with a sald Slim Fom hold that adapts a 2.2 mm out diamt to 10 mm inn diamt backt includd in th kit as wll as commcially availabl Midi sizd adapts and bushings. Additional dtaild infomation is availabl in th Dilctic Pob Tchnical Ovviw 6 and Softwa Onlin Hlp 7. Th dilctic pobs a compatibl with th Agilnt ntwok analyzs and th E4991A impdanc analyz. With th impdanc analyz th high tmpatu pob is spcifid fom 10 MHz. Bfo masuing, calibation at th tip of th pob must b pfomd. A th-tm calibation cocts fo th dictivity, tacking, and souc match os that can b psnt in a flction masumnt. In od to solv fo ths th o tms, th wll-known standads a masud. Th diffnc btwn th pdictd and actual valus is usd to mov th systmatic (patabl) os fom th masumnt. Th th known standads a ai, a shot cicuit, and distillat and d-ionizd wat. Evn aft calibating th pob, th a additional soucs of o that can affct th accuacy of a masumnt. Th a th main soucs of os: Cabl stability Ai Gaps Sampl thicknss 18
It is impotant to allow nough tim fo th cabl (that conncts th pob to th ntwok analyz) to stabiliz bfo making a masumnt and to b su that th cabl is not flxd btwn calibation and masumnt. Th automatd Elctonic Calibation Rfsh fatu calibats th systm automatically, in sconds, just bfo ach masumnt is mad. This vitually liminats cabl instability and systm dift os. Fo solid matials, an ai gap btwn th pob and sampl can b a significant souc of o unlss th sampl fac is machind to b at last as flat as th pob fac. Fo liquid sampls ai bubbls on th tip of th pob can act in th sam way as an ai gap on a solid sampl. Th sampl must also b thick nough to appa infinit to th pob. Th is a simpl quation 6 to calculat th appoximat thicknss of th sampl fo th high tmpatu pob sampl and suggstd thicknss fo th slim pob sampl. A simpl pactical appoach is to put a shot bhind th sampl and chck to s if it affcts th masumnt sults. Figu 15 shows a compaison of masumnts of dilctic constant and loss facto of mthanol at oom tmpatu (25 C) using th high tmpatu pob, with thotical calculations using th Col-Col modl. Th following paamts a usd in th Col-Col calculations: s = 33.7, = 4.45, τ = 4.95 x 10-11, α = 0.036. ' " 30 Thoy Masumnt 20 10 10 5 Thoy Masumnt 0.1 1 10 f, GHz 0.1 1 10 f, GHz (a) (b) Figu 15. Masud dilctic constant (a) and loss facto (b) of mthanol at 25º C compad with Col-Col modl A disadvantag of th dilctic pob mthod is th limitd accuacy, und som conditions, whn compad to oth mthods lik th tansmission lin mthod using th 85071E and sonato mthod. 19
Tansmission lin Tansmission lin mthods involv placing th matial insid a potion of an nclosd tansmission lin. Th lin is usually a sction of ctangula wavguid o coaxial ailin (Figu 16). * and µ * a computd fom th masumnt of th flctd signal (S 11 ) and tansmittd signal (S 21 ). Matial assumptions Sampl fills fixtu coss sction No ai gaps at fixtu walls Smooth, flat facs, ppndicula to long axis Homognous Mthod fatus Boadband low nd limitd by pactical sampl lngth Limitd low loss solution (dpnds on sampl lngth) Masus magntic matials Anisotopic matials can b masud in wavguid Wavguid l Rflction (S ) 11 Tansmission (S ) 21 Coax S 11 S 21 µ Figu 16. Tansmission lin mthod; wavguid and coaxial lin cas 20
Coaxial tansmission lins cov a boad fquncy ang, but a tooidshapd sampl is mo difficult to manufactu (Figu 17(a)). Wavguid fixtus xtnd to th mm-wav fquncis and th sampls a simpl to machin, but thi fquncy covag is bandd (Figu 17(b)). A typical masumnt systm using a tansmission lin tchniqu consists of a vcto ntwok analyz, a coaxial ailin o wavguid sction, softwa such as th 85071E to pfom th convsion to * and µ *, and an xtnal comput. Fo th PNA family of ntwok analyzs th softwa can b installd insid th ntwok analyz so th is no nd fo an xtnal comput. Additional infomation about th 85071E softwa can b found in th Tchnical Ovviw 8 and Softwa Onlin Hlp 9. (a) (b) Figu 17. Coaxial 7 mm ai lin with sampls (a) and X-band wavguid staight sction with sampls (b) Th 50 Ohm ailin fom Agilnt vification kits (Figu 17(a)) is th commndd coaxial sampl hold. Evy wavguid calibation kit in th 11644A family contains a pcision wavguid sction (Figu 17(b)), commndd fo a wavguid sampl hold. 21
Figu 18 shows masumnt sults of pmittivity (a) and loss tangnt (b) of two Plxiglas sampls with lngths of 25 mm and 31 mm spctivly, in an X-band wavguid. Th sampl hold is th pcis wavguid sction of 140 mm lngth that is povidd with th X11644A calibation kit (Figu 17(b)). Th ntwok analyz is a PNA, th calibation typ is TRL and th pcision NIST algoithm 9 is usd fo calculation. In both gaphs blow th a two pais of tacs fo two diffnt masumnts of th sam sampls. Th top two masumnts of ach gaph a pfomd fo th cas whn th sampl hold is not calibatd out. ' tan d 2.58 25 mm 31 mm 0.005 25 mm 31 mm 2.56 2.54 25 mm 31 mm calibatd out sampl hold 9 10 11 12 f, GHz 0.004 0.003 25 mm 31 mm calibatd out sampl hold 9 10 11 12 f, GHz (a) (b) Figu 18. Masumnt of two Plxiglas sampls, 25 mm and 31 mm long in a X-band wavguid In this cas basd on th sampl lngth and sampl hold lngth, th 85071E softwa will otat th calibation plan coctly to th sampl fac, but will not compnsat fo th losss of th wavguid. Th bottom two masumnts of th sam sampls a pfomd fo th cas whn th sampl hold is pat of th calibation and th wavguid losss and lctical lngth a calibatd out. As xpctd, th loss tangnt cuvs (b) show low valus whn th sampl hold is calibatd out and thy a mo constant with spct to fquncy. This is du to th fact that th wavguid losss a no long addd to th sampl s losss. With th PNA ntwok analyz, bsids calibating out th sampl hold, it is possibl to pfom fixtu d-mbdding, which will lad to th sam sults. This appoach quis masuing th mpty sampl hold aft th calibation. 22
F spac Matial assumptions Lag, flat, paalll-facd sampls Homognous Mthod fatus Non-contacting, non-dstuctiv High fquncy low nd limitd by pactical sampl siz Usful fo high tmpatu Antnna polaization may b vaid fo anisotopic matials Masus magntic matials F-spac mthods us antnnas to focus micowav ngy at o though a slab of matial without th nd fo a tst fixtu (Figu 19). This mthod is non-contacting and can b applid to matials to b tstd und high tmpatus and hostil nvionmnts. Figu 19 shows two typical fspac masumnt stups: an S-paamt configuation (upp) and th NRL ach (low). An xmplay masumnt systm using a f-spac mthod consists of a vcto ntwok analyz, a fixtu (antnnas, tunnls, achs, tc.), softwa lik th 85071, and a comput (not ncssay if th PNA family is usd). Calibating th ntwok analyz fo a f spac masumnt is challnging. F spac calibation standads psnt spcial poblms sinc thy a conncto-lss. A calibation can b as simpl as a spons calibation o as complx as a full two-pot calibation dpnding on th convninc and accuacy dsid. A TRL (Thu-Rflct-Lin) o TRM (Thu-Rflct-Match) calibation may actually b asi than oth calibation tchniqus in f spac. Figu 19. F spac masumnt stups Tim domain gating is oftn usd to tak th plac of o supplmnt an xisting calibation. Th 85071E softwa offs an optional f spac calibation outin calld GRL (Gatd Rflct Lin). This calibation outin incass th as of us and ducs th costs associatd with TRM and TRL calibation mthods. Th Gatd Rflct Lin calibation tchniqu convts a coaxial o wavguid 2-pot calibation into a full 2-pot f spac calibation. Us of this option quis a PNA Sis ntwok analyz o an 8510 with th tim domain option, an appopiat f spac fixtu, and a mtal calibation plat. This option also includs a gatd isolation/ spons calibation, which ducs os fom diffaction ffcts at th sampl dgs and multipl sidual flctions btwn th antnnas. 23
Accuat f spac masumnts a now possibl without xpnsiv spot focusing antnnas, mico positioning fixtus, o dict civ accss. Th 85070E softwa automatically sts up all th f spac calibation dfinitions and ntwok analyz paamts, saving ngining tim. With th PNA, additional as and tim savings is povidd with ECal, lctonic calibation. A guidd calibation wizad stps th us though th asy calibation pocss. Figu 20 dpicts th sult of a GRL calibation masuing Rxolit matial in U-band (40-60 GHz) with a PNA ntwok analyz and 85071E softwa. Th fixtu is mad fom a adily availabl, domstic us, shlving unit to dmonstat that whn doing a GRL calibation, vn with th simplst st up, it is still possibl to pfom pcis masumnts. 2.6 ' 2.5 2.4 45 50 55 f, GHz Figu 20. Masumnt of Rxolit sampl in a U-band (40 60 GHz) High tmpatu masumnts a asy to pfom in f spac sinc th sampl is nv touchd o contactd (Figu 21). Th sampl can b hatd by placing it within a funac that has windows of insulation matial that a tanspant to micowavs. Agilnt Tchnologis dos not povid th funac ndd fo such a typ of masumnt. Figu 21 illustats th basic st up. Hating panls Funac Thmal insulation Sampl Thmocoupl Figu 21. High tmpatu masumnt in f spac 24
Rsonant cavity Rsonant vsus boadband tchniqus Rsonant tchniqus High impdanc nvionmnt Rasonabl masumnts possibl with small sampls Masumnts at only on o a fw fquncis Wll suitd fo low loss matials Boadband tchniqus Low impdanc nvionmnt Rquis lag sampls to obtain asonabl masumnts Masumnt at any fquncy Rsonant cavitis a high Q stuctus that sonat at ctain fquncis. A pic of sampl matial affcts th cnt fquncy (f) and quality facto (Q) of th cavity. Fom ths paamts, th complx pmittivity ( ) o pmability (µ ) of th matial can b calculatd at a singl fquncy. Th a many diffnt typs of cavitis and mthods. H, th most widly usd cavity ptubation mthod, as dscibd in ASTM 2520 10, is considd. This mthod uss a ctangula wavguid with iis-coupld nd plats, opating in TE 10n mod (Figu 22). Fo a dilctic masumnt th sampl should b placd in a maximum lctic fild and fo a magntic masumnt, in a maximum magntic fild. If th sampl is instd though a hol in th middl of th wavguid lngth, thn an odd numb of half wavlngths (n = 2k + 1) will bing th maximum lctic fild to th sampl location, so that th dilctic poptis of th sampl can b masud. An vn numb of half wavlngths (n = 2k) will bing th maximum magntic fild to th sampl location and th magntic poptis of th sampl can b masud. ( f f ) Vc c ' = 2V f " = Vc 4V s +1 s s 1 1 ( s Q s Q ) c Iis-coupld nd plats V is th volum indx c is fo th mpty cavity, indx s is fo th sampl loadd Sampl f Q S f S o µ f C Q 0 f Q Figu 22. Rsonant cavity masumnt 25
Th cavity ptubation mthod quis a vy small sampl such that th filds in th cavity a only slightly distubd to shift th masud sonant fquncy and cavity Q. This assumption allows simplifying th thoy to us th quations abov to calculat th dilctic poptis of th matial. Although Agilnt Tchnologis dos not povid a ady-mad sonato (i.. iis-coupld nd plats), this mthod is pat of th 85071E softwa, which allows fo automatic masumnt of all ncssay paamts and calculation of th complx dilctic constant. It is asy to adapt th 140 mm long pcision wavguid sction availabl in th X11644A wavguid calibation kit fo sonato masumnts (Figu 23). A hol nds to b dilld xactly in th middl of th wavguid lngth and th two iis-coupld nd plats nd to b manufactud. Th dimnsion of th iis hol is b/2.2, wh b is th naow dimnsion of th wavguid coss sction 10. Figu 23. X-band cavity sonato pats and instd sampl 26
Figu 24 shows masumnts of th diffnt sampls with this cavity. Th th masumnts a psntd on th sam gaph fo compaison puposs. f c = 9.9375 GHz 3 V c = 32.516 cm Q c = 2105 S 21 0.0035 Sampl 1 Sampl 2 9.9375 Empty cavity f s = 9.901 GHz 0.0025 V s = 0.046 cm Q s = 2029 3 0.0015 Sampl 3 ' = 2.30 " = 0.003 9.8 9.9 f, GHz Figu 24. Gaphs of th mpty cavity and th diffnt sampls Th sonant fquncy of th mpty cavity is f c = 9.9375 GHz (fo TE 107 mod) and it shifts to a low fquncy whn th sampl is instd in th cavity. Whn th sonato is loadd with a sampl, th sonanc cuv boadns, which sults in a low quality facto Q. On th y-axis of Figu 23 is th magnitud of th lina tansmission cofficint S 21. Th 8720ES ntwok analyz is usd fo ths masumnts. On th lft of th figu is a calculation fo th Sampl 2, which has a coss sction of 0.29 by 0.157 cm. A typical masumnt systm using th sonant cavity mthod consists of a ntwok analyz, a cavity, softwa, and an xtnal comput (xcpt whn using a PNA Sis). Th is no nd to calibat th ntwok analyz fo this typ of masumnt. Although th sonant cavity tchniqu is xtmly accuat, it is still subjct to os. Th ntwok analyz must hav xcllnt fquncy solution (1 Hz) to masu vy small changs in th Q facto. Th sampl coss-sction dimnsions must b known pcisly. Th is also additional o du to th appoximation in th analysis (ptubation thoy). This mthod has limitations fo low-loss sampls du to th compaativly low Q-facto of th mpty ctangula wavguid cavity. A cylindical typ of cavity offs much high Q-factos, but it has its own disadvantags, th biggst of which is th difficulty to manufactu it. Paalll plat Th paalll plat capacito mthod involvs sandwiching a thin sht of matial btwn two lctods to fom a capacito. A typical masumnt systm using th paalll plat mthod consists of an LCR mt o impdanc analyz and a fixtu such as th 16451B dilctic tst fixtu, which opats up to 30 MHz. Mo infomation about oth Agilnt Tchnologis low fquncy matials masumnt solutions is availabl in Application Not 1369-1 1 and 380-1 11. 27
Compaison of Mthods Many factos such as accuacy, convninc, and th matial shap and fom a impotant in slcting th most appopiat masumnt tchniqu. Som of th significant factos to consid a summaizd h: Fquncy ang Expctd valus of and µ Rquid masumnt accuacy Matial poptis (i.., homognous, isotopic) Fom of matial (i.., liquid, powd, solid, sht) Sampl siz stictions Dstuctiv o nondstuctiv Contacting o noncontacting Tmpatu Cost Figu 25 povids a quick compaison btwn th masumnt mthods that hav bn discussd alady and, in Figu 26, a summaizd th availabl fixtus and instumnts fo matials masumnts. Coaxial pob Boadband, convnint, non-dstuctiv Bst fo lossy MUTs; liquids o smi-solids Tansmission lin and µ Boadband Bst fo lossy to low loss MUTs; machinabl solids F spac Rsonant cavity and µ and µ Non-contacting Bst fo high tmpatus; lag, flat sampls Accuat Bst fo low loss MUTs; small sampls Paalll plat Accuat Bst fo low fquncis; thin, flat shts Figu 25. Summay of th masumnt tchniqus 28
16451B 16452A Tansmission lin softwa 85071E Dilctic pob 85070E 16453A Dilctic matial tst fixtu Dilctic tst fixtu Liquid tst fixtu 16454A Magntic tst fixtu DC 10Hz 100Hz 1kHz 10kHz 100kHz 1MHz 10MHz 100MHz 1GHz 10GHz 100GHz 4263B, 4284A, 4285A, 4294A Ntwok analyzs LCR mts/impdanc analyzs E4991A Impdanc/matial analyz PNA, PNA-L ENA, ENA-L Lgacy 8712, 8753, 8720, 8510 Figu 26. Agilnt Tchnologis instumnts and fixtus 29
Rfncs 1. Application Not 1369-1, Solutions fo Masuing Pmittivity and Pmability with LCR Mts and Impdanc Analyzs, Agilnt Litatu Numb 5980-2862EN, May 6, 2003 2. Application not 1287-1, Undstanding th Fundamntal Pincipls of Vcto Ntwok Analysis, Agilnt litatu numb 5965-7707E, 2000 3. Application not 1287-2, Exploing th Achitctus of Ntwok Analyzs, Agilnt litatu numb 5965-7708E, Dcmb 6, August 2000 4. Application not 1287-3, Applying Eo Coction to Ntwok Analyz Masumnts, Agilnt litatu numb 5965-7709E, Mach 27, 2002 5. D. V. Blackham, R. D. Pollad, An Impovd Tchniqu fo Pmittivity Masumnts Using a Coaxial Pob, IEEE Tans. on Inst. Mas., vol. 46, No 5, Oct. 1997, pp. 1093-1099 6. Tchnical Ovviw, Agilnt 85071E Matials Masumnt Softwa, Agilnt litatu numb 5989-0222EN, Novmb 6, 2003 7. Onlin Hlp fo 85070 softwa 8. Tchnical Ovviw, Agilnt 85070E Dilctic Pob Kit 200 MHz to 50 GHz, Agilnt litatu numb 5988-9472EN, May 9, 2003 9. Onlin Hlp fo 85071 softwa 10. ASTM Tst mthods fo complx pmittivity (Dilctic Constant) of solid lctical insulating matials at micowav fquncis and tmpatus to 1650, ASTM Standad D2520, Amican Socity fo Tsting and Matials 11. Application Not 380-1, Dilctic constant masumnt of solid matials using th 16451B dilctic tst fixtu, Agilnt litatu numb 5950-2390, Sptmb 1998 30
Additional Rfncs Altschul H.M., Dilctic Constant, Chapt IX of Handbook of Micowav Masumnts, M. Such and J. Fox d., Wily 1963 Athu von Hippl (d), Dilctic Matials and Applications, Cambidg, Massachustts: MIT Pss, 3d pinting, Januay 1961 J. Bak-Javis, M. D. Janzic, J. S. Gosvno, R. G. Gy, Tansmission/ Rflction and Shot-Cicuit Mthods fo Masuing Pmitivity and Pmability, NIST Tchnical Not 1355-R, Dcmb 1993 H. E. Bussy, Masumnt of RF poptis of matials-a suvy, Poc. IEEE, vol. 55, No. 6, pp. 1046-1053, Jun 1967. A. C. Lynch, Pcis masumnts on dilctic and magntic matials, IEEE Tans. on Instum. Mas., vol. IM-23, No. 4, Dc. 1974, pp. 425-43 M. Afsa, J.B. Bich, R.N. Clak, Ed. G.W. Chanty; Masumnt of th Poptis of Matials, Poc. IEEE, vol. 74, No 1, pp. 183-199. Jan 1986 A. M. Nicolson, G. F. Ross, Masumnt of th intinsic poptis of matials by tim-domain tchniqus, IEEE Tans. on Instum. Mas., vol. IM-19, Nov 1970, pp. 377-82 W. B. Wi, Automatic masumnt of complx dilctic constant and pmability at micowav fquncis, Poc. IEEE, vol. 62, no. 1, pp. 33-36, Jan. 1974. 31
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