Agilent Basics of Measuring the Dielectric Properties of Materials. Application note

Transcription

1 Agilent Basics of Measuing the Dielectic Popeties of Mateials Application note

2 Contents Intoduction...3 Dielectic theoy...4 Dielectic constant...4 Pemeability...7 Electomagnetic popagation...8 Dielectic mechanisms Oientation (dipola) polaization...11 Electonic and atomic polaization...11 Relaxation time...12 Debye elation...12 Cole-Cole diagam...13 Ionic conductivity...13 Intefacial o space chage polaization Measuement systems Netwok analyzes Impedance analyzes and LCR metes Fixtues Softwae Measuement techniques...17 Coaxial pobe...17 Tansmission line Fee space...23 Resonant cavity Paallel plate Inductance measuement method Compaison of methods...31 Agilent solutions...32 Refeences...33 Web esouces

3 Intoduction A wide vaiety of industies need a bette undestanding of the mateials they ae woking with to shoten design cycles, impove incoming inspection, pocess monitoing, and quality assuance. Evey mateial has a unique set of electical chaacteistics that ae dependent on its dielectic popeties. Accuate measuements of these popeties can povide scientists and enginees with valuable infomation to popely incopoate the mateial into its intended application fo moe solid designs o to monito a manufactuing pocess fo impoved quality contol. A dielectic mateials measuement can povide citical design paamete infomation fo many electonics applications. Fo example, the loss of a cable insulato, the impedance of a substate, o the fequency of a dielectic esonato can be elated to its dielectic popeties. The infomation is also useful fo impoving feite, absobe and packaging designs. Moe ecent applications in the aea of aeospace, automotive, food and medical industies have also been found to benefit fom knowledge of dielectic popeties. Agilent Technologies Inc. offes a vaiety of instuments, fixtues, and softwae to measue the dielectic popeties of mateials. Agilent measuement instuments, such as netwok analyzes, impedance analyzes and LCR metes ange in fequency up to 1.1THz. Fixtues to hold the mateial unde test (MUT) ae available that ae based on coaxial pobe, paallel plate, coaxial/waveguide tansmission lines, fee space and esonant cavity methods. The table below shows poduct examples that can be measued by Agilent s mateial test solutions. Table 1. Mateials measuement applications example Industy Applications/Poducts Electonics Aeospace/Defense Industial mateials Food & Agicultue Foesty & Mining Phamaceutical & Medical Capacito, substates, PCB, PCB antenna, feites, magnetic ecoding heads, absobes, SAR phantom mateials, senso Stealth, RAM (Radiation Absobing Mateials), adomes Ceamics and composites: IC package, aeospace and automotive components, cement, coatings, bio-implants Polymes and plastics: fibes, substates, films, insulation mateials Hydogel: disposable diape, soft contact lens Liquid cystal: displays Rubbe, semiconductos and supeconductos Othe poducts containing these mateials: ties, paint, adhesives, etc. Food pesevation (spoilage) eseach, food development fo micowave, packaging, moistue measuements Moistue measuements in wood o pape, oil content analysis Dug eseach and manufactuing, bio-implants, human tissue chaacteization, biomass, chemical concentation, fementation 3

4 Dielectic Theoy The dielectic popeties that will be discussed hee ae pemittivity and pemeability. Resistivity is anothe mateial popety which will not be discussed hee. Infomation about esistivity and its measuement can be found in the Agilent Application Note It is impotant to note that pemittivity and pemeability ae not constant. They can change with fequency, tempeatue, oientation, mixtue, pessue, and molecula stuctue of the mateial. Dielectic constant A mateial is classified as dielectic if it has the ability to stoe enegy when an extenal electic field is applied. If a DC voltage souce is placed acoss a paallel plate capacito, moe chage is stoed when a dielectic mateial is between the plates than if no mateial (a vacuum) is between the plates. The dielectic mateial inceases the stoage capacity of the capacito by neutalizing chages at the electodes, which odinaily would contibute to the extenal field. The capacitance with the dielectic mateial is elated to dielectic constant. If a DC voltage souce v is placed acoss a paallel plate capacito (Figue 1), moe chage is stoed when a dielectic mateial is between the plates than if no mateial (a vacuum) is between the plates. A C = 0. t C= C κ' 0. ' C κ' = ε = C 0. V t A Figue 1. Paallel plate capacito, DC case Whee C and C 0. ae capacitance with and without dielectic, k = e is the eal dielectic constant o pemittivity, and A and t ae the aea of the capacito plates and the distance between them (Figue 1). The dielectic mateial inceases the stoage capacity of the capacito by neutalizing chages at the electodes, which odinaily would contibute to the extenal field. The capacitance of the dielectic mateial is elated to the dielectic constant as indicated in the above equations. If an AC sinusoidal voltage souce V is placed acoss the same capacito (Figue 2), the esulting cuent will be made up of a chaging cuent I c and a loss cuent I l that is elated to the dielectic constant. The losses in the mateial can be epesented as a conductance (G) in paallel with a capacito (C). 4

5 I = I + I = V (jωc κ' + G) c I 0. If G = ωc κ'', then 0. I = V (jωc )( κ' j κ'') = V (jωc ) κ ω = 2πf V I t A C G Figue 2. Paallel plate capacito, AC case The complex dielectic constant k consists of a eal pat k which epesents the stoage and an imaginay pat k which epesents the loss. The following notations ae used fo the complex dielectic constant intechangeably k = k* = e = e*. Fom the point of view of electomagnetic theoy, the definition of electic displacement (electic flux density) D f is: Df = εe whee e = e* = e 0. e is the absolute pemittivity (o pemittivity), e is the elative pemittivity, 1 9. ε 10. F/m is the fee space pemittivity Π and E is the electic field. Pemittivity descibes the inteaction of a mateial with an electic field E and is a complex quantity. ε κ = = ε = ε jε '' ε 0. Dielectic constant (k) is equivalent to elative pemittivity (e ) o the absolute pemittivity (e) elative to the pemittivity of fee space (e 0. ). The eal pat of pemittivity (e ) is a measue of how much enegy fom an extenal electic field is stoed in a mateial. The imaginay pat of pemittivity (e ) is called the loss facto and is a measue of how dissipative o lossy a mateial is to an extenal electic field. The imaginay pat of pemittivity (e ) is always geate than zeo and is usually much smalle than (e ). The loss facto includes the effects of both dielectic loss and conductivity. 5.

6 When complex pemittivity is dawn as a simple vecto diagam (Figue 3), the eal and imaginay components ae 9.0. out of phase. The vecto sum foms an angle d with the eal axis (e ). The elative lossiness of a mateial is the atio of the enegy lost to the enegy stoed. '' ε 1 tan δ = = D = ε Q = Enegy lost pe cycle Enegy stoed pe cycle Figue 3. Loss tangent vecto diagam The loss tangent o tan d is defined as the atio of the imaginay pat of the dielectic constant to the eal pat. D denotes dissipation facto and Q is quality facto. The loss tangent tan d is called tan delta, tangent loss o dissipation facto. Sometimes the tem quality facto o Q-facto is used with espect to an electonic micowave mateial, which is the ecipocal of the loss tangent. Fo vey low loss mateials, since tan d d, the loss tangent can be expessed in angle units, milliadians o micoadians. 6.

7 Pemeability Pemeability (µ) descibes the inteaction of a mateial with a magnetic field. A simila analysis can be pefomed fo pemeability using an inducto with esistance to epesent coe losses in a magnetic mateial (Figue 4). If a DC cuent souce is placed acoss an inducto, the inductance with the coe mateial can be elated to pemeability. L= L µ ' 0. L µ ' = L 0. R L Figue 4. Inducto In the equations L is the inductance with the mateial, L 0. is fee space inductance of the coil and µ is the eal pemeability. If an AC sinusoidal cuent souce is placed acoss the same inducto, the esulting voltage will be made up of an induced voltage and a loss voltage that is elated to pemeability. The coe loss can be epesented by a esistance (R) in seies with an inducto (L). The complex pemeability (µ* o µ) consists of a eal pat (µ ) that epesents the enegy stoage tem and an imaginay pat (µ ) that epesents the enegy loss tem. Relative pemittivity µ is the pemittivity elative to fee space: µ µ = = µ jµ '' µ 0. µ = π H/m is the fee space pemeability Some mateials such as ion (feites), cobalt, nickel, and thei alloys have appeciable magnetic popeties; howeve, many mateials ae nonmagnetic, making the pemeability vey close to the pemeability of fee space (µ = 1). All mateials, on the othe hand, have dielectic popeties, so the focus of this discussion will mostly be on pemittivity measuements. 7

8 Electomagnetic Wave Popagation In the time-vaying case (i.e., a sinusoid), electic fields and magnetic fields appea togethe. This electomagnetic wave can popagate though fee space (at the speed of light, c = 3 x m/s) o though mateials at slowe speed. Electomagnetic waves of vaious wavelengths exist. The wavelength l of a signal is invesely popotional to its fequency f (λ = c/f), such that as the fequency inceases, the wavelength deceases. Fo example, in fee space a 10. MHz signal has a wavelength of 30. m, while at 10. GHz it is just 3 cm. Many aspects of wave popagation ae dependent on the pemittivity and pemeability of a mateial. Let s use the optical view of dielectic behavio. Conside a flat slab of mateial (MUT) in space, with a TEM wave incident on its suface (Figue 5.). Thee will be incident, eflected and tansmitted waves. Since the impedance of the wave in the mateial Z is diffeent (lowe) fom the fee space impedance η (o Z 0. ) thee will be impedance mismatch and this will ceate the eflected wave. Pat of the enegy will penetate the sample. Once in the slab, the wave velocity v, is slowe than the speed of light c. The wavelength λ d is shote than the wavelength λ 0. in fee space accoding to the equations below. Since the mateial will always have some loss, thee will be attenuation o insetion loss. Fo simplicity the mismatch on the second bode is not consideed. h o Z 0 Z= h e ' 0. Z = η = Z = = 120. ' 0. ε ε 0. λ η λ 0. = v = d ' ε c ε ' µ π TEM Ai e ' 0 MUT e ' Impedance lowe Wavelength shote Velocity slowe Magnitude attenuated Figue 5. Reflected and tansmitted signals 8

9 Figue 6. depicts the elation between the dielectic constant of the Mateial Unde Test (MUT) and the eflection coefficient G fo an infinitely long sample (no eflection fom the back of the sample is consideed). Fo small values of the dielectic constant (appoximately less than 20.), thee is a lot of change of the eflection coefficient fo a small change of the dielectic constant. In this ange dielectic constant measuement using the eflection coefficient will be moe sensitive and hence pecise. Convesely, fo high dielectic constants (fo example between 70. and 9.0.) thee will be little change of the eflection coefficient and the measuement will have moe uncetainty Reflection coefficient Dielectic constant ' Figue 6. Reflection coefficient vesus dielectic constant 9.

10 Dielectic Mechanisms A mateial may have seveal dielectic mechanisms o polaization effects that contibute to its oveall pemittivity (Figue 7). A dielectic mateial has an aangement of electic chage caies that can be displaced by an electic field. The chages become polaized to compensate fo the electic field such that the positive and negative chages move in opposite diections. At the micoscopic level, seveal dielectic mechanisms can contibute to dielectic behavio. Dipole oientation and ionic conduction inteact stongly at micowave fequencies. Wate molecules, fo example, ae pemanent dipoles, which otate to follow an altenating electic field. These mechanisms ae quite lossy which explains why food heats in a micowave oven. Atomic and electonic mechanisms ae elatively weak, and usually constant ove the micowave egion. Each dielectic mechanism has a chaacteistic cutoff fequency. As fequency inceases, the slow mechanisms dop out in tun, leaving the faste ones to contibute to e. The loss facto (e ) will coespondingly peak at each citical fequency. The magnitude and cutoff fequency of each mechanism is unique fo diffeent mateials. Wate has a stong dipola effect at low fequencies but its dielectic constant olls off damatically aound 22 GHz. PTFE, on the othe hand, has no dipola mechanisms and its pemittivity is emakably constant well into the millimete-wave egion. A esonant effect is usually associated with electonic o atomic polaization. A elaxation effect is usually associated with oientation polaization. ' Dipola (Rotational) + - Ionic '' Atomic Electonic f, Hz MW + - IR - V + UV Figue 7. Fequency esponse of dielectic mechanisms 10.

11 Oientation (dipola) polaization A molecule is fomed when atoms combine to shae one o moe of theis electons. This eaangement of electons may cause an imbalance in chage distibution ceating a pemanent dipole moment. These moments ae oiented in a andom manne in the absence of an electic field so that no polaization exists. The electic field E will execise toque T on the electic dipole, and the dipole will otate to align with the electic field causing oientation polaization to occu (Figue 8). If the field changes the diection, the toque will also change. T E F + F Figue 8. Dipole otation in electic field The fiction accompanying the oientation of the dipole will contibute to the dielectic losses. The dipole otation causes a vaiation in both e and e at the elaxation fequency which usually occus in the micowave egion. As mentioned, wate is an example of a substance that exhibits a stong oientation polaization. Electonic and atomic polaization Electonic polaization occus in neutal atoms when an electic field displaces the nucleus with espect to the electons that suound it. Atomic polaization occus when adjacent positive and negative ions stetch unde an applied electic field. Fo many dy solids, these ae the dominant polaization mechanisms at micowave fequencies, although the actual esonance occus at a much highe fequency. In the infaed and visible light egions the inetia of the obiting electons must be taken into account. Atoms can be modeled as oscillatos with a damping effect simila to a mechanical sping and mass system (Figue 7). The amplitude of the oscillations will be small fo any fequency othe than the esonant fequency. Fa below esonance, the electonic and atomic mechanisms contibute only a small constant amount to e and ae almost lossless. The esonant fequency is identified by a esonant esponse in e and a peak of maximum absoption in e. Above the esonance, the contibution fom these mechanisms disappeas. 11

12 Relaxation time Relaxation time t is a measue of the mobility of the molecules (dipoles) that exist in a mateial. It is the time equied fo a displaced system aligned in an electic field to etun to 1/e of its andom equilibium value (o the time equied fo dipoles to become oiented in an electic field). Liquid and solid mateials have molecules that ae in a condensed state with limited feedom to move when an electic field is applied. Constant collisions cause intenal fiction so that the molecules tun slowly and exponentially appoach the final state of oientation polaization with elaxation time constant t. When the field is switched off, the sequence is evesed and andom distibution is estoed with the same time constant. The elaxation fequency f c is invesely elated to elaxation time: 1 1 τ = = ω 2π f c c At fequencies below elaxation the altenating electic field is slow enough that the dipoles ae able to keep pace with the field vaiations. Because the polaization is able to develop fully, the loss (e ) is diectly popotional to the fequency (Figue 9.). As the fequency inceases, e continues to incease but the stoage (e ) begins to decease due to the phase lag between the dipole alignment and the electic field. Above the elaxation fequency both e and e dop off as the electic field is too fast to influence the dipole otation and the oientation polaization disappeas. ε ε s Debye equation: εω ( ) = ε jωτ Fo ω = 0., ε(0.) = ε Fo ω =, ε( = ) ε s '' ', ' " f, GHz Figue 9. Debye elaxation of wate at 30º C Debye elation Mateials that exhibit a single elaxation time constant can be modeled by the Debye elation, which appeas as a chaacteistic esponse in pemittivity as a function of fequency (Figue 9.). e is constant above and below the elaxation with the tansition occuing nea the elaxation fequency (22 GHz). Additionally, e is small above and below elaxation and peaks in the tansition egion at the elaxation fequency. In calculating the above cuves the static (DC) value of the dielectic constant is e s = , the optical (infinite fequency) value of the dielectic constant is e = 4.9. and the elaxation time t = 7.2 ps. 12

13 Cole-Cole diagam The complex pemittivity may also be shown on a Cole-Cole diagam by plotting the imaginay pat (e ) on the vetical axis and the eal pat (e ) on the hoizontal axis with fequency as the independent paamete (Figue 10.). A Cole-Cole diagam is, to some extent, simila to the Smith chat. A mateial that has a single elaxation fequency as exhibited by the Debye elation will appea as a semicicle with its cente lying on the hoizontal e = 0. axis and the peak of the loss facto occuing at 1/τ. A mateial with multiple elaxation fequencies will be a semicicle (symmetic distibution) o an ac (nonsymmetical distibution) with its cente lying below the hoizontal e = 0. axis. The cuve in Figue 10. is a half cicle with its cente on the x-axis and its adius ε ε s. The maximum imaginay pat of the dielectic constant e max 2 will be equal to the adius. The fequency moves counte clockwise on the cuve. " " max = s = Inceasing f (GHz) 10 Cente e ' = 4.9 = s Figue 10. Cole-Cole diagam of Figue 9 Ionic conductivity The measued loss of mateial can actually be expessed as a function of both dielectic loss (e d ) and conductivity (s). '' '' σ ε = ε + d ωε 0. At low fequencies, the oveall conductivity can be made up of many diffeent conduction mechanisms, but ionic conductivity is the most pevalent in moist mateials. e is dominated by the influence of electolytic conduction caused by fee ions which exist in the pesence of a solvent (usually wate). Ionic conductivity only intoduces losses into a mateial. At low fequencies the effect of ionic conductivity is invesely popotional to fequency and appeas as a 1/f slope of the e cuve. 13

14 Intefacial o space chage polaization Electonic, atomic, and oientation polaization occu when chages ae locally bound in atoms, molecules, o stuctues of solids o liquids. Chage caies also exist that can migate ove a distance though the mateial when a low fequency electic field is applied. Intefacial o space chage polaization occus when the motion of these migating chages is impeded. The chages can become tapped within the intefaces of a mateial. Motion may also be impeded when chages cannot be feely dischaged o eplaced at the electodes. The field distotion caused by the accumulation of these chages inceases the oveall capacitance of a mateial which appeas as an incease in e. Mixtues of mateials with electically conducting egions that ae not in contact with each othe (sepaated by non-conducting egions) exhibit the Maxwell-Wagne effect at low fequencies. If the chage layes ae thin and much smalle than the paticle dimensions, the chage esponds independently of the chage on neaby paticles. At low fequencies the chages have time to accumulate at the bodes of the conducting egions causing e to incease. At highe fequencies the chages do not have time to accumulate and polaization does not occu since the chage displacement is small compaed to the dimensions of the conducting egion. As the fequency inceases, e deceases and the losses exhibit the same 1/f slope as nomal ionic conductivity. Many othe dielectic mechanisms can occu in this low fequency egion causing a significant vaiation in pemittivity. Fo example, colloidal suspension occus if the chage laye is on the same ode of thickness o lage than the paticle dimensions. The Maxwell-Wagne effect is no longe applicable since the esponse is now affected by the chage distibution of adjacent paticles. 14

15 Measuement System Netwok Analyzes A measuement of the eflection fom and/o tansmission though a mateial along with knowledge of its physical dimensions povides the infomation to chaacteize the pemittivity and pemeability of the mateial. Vecto netwok analyzes such as the PNA family, ENA seies and FieldFox make swept high fequency stimulusesponse measuements fom 9. khz to 1.1 THz. (Figue 12). A vecto netwok analyze consists of a signal souce, a eceive and a display (Figue 11). The souce launches a signal at a single fequency to the mateial unde test. The eceive is tuned to that fequency to detect the eflected and tansmitted signals fom the mateial. The measued esponse poduces the magnitude and phase data at that fequency. The souce is then stepped to the next fequency and the measuement is epeated to display the eflection and tansmission measuement esponse as a function of fequency. Moe infomation on the netwok analyze functioning and achitectue is available in the application notes and Simple components and connecting wies that pefom well at low fequencies behave diffeently at high fequencies. At micowave fequencies wavelengths become small compaed to the physical dimensions of the devices such that two closely spaced points can have a significant phase diffeence. Low fequency lumped-cicuit element techniques must be eplaced by tansmission line theoy to analyze the behavio of devices at highe fequencies. Additional high fequency effects such as adiation loss, dielectic loss and capacitive coupling make micowave cicuits moe complex and expensive. It is time consuming and costly to ty to design a pefect micowave netwok analyze. Incident Fixtue MUT Tansmitted Souce Reflected Signal sepaation Incident (R) Reflected (A) Tansmitted (B) Receive/detecto Pocesso/display Figue 11. Netwok analyze Instead, a measuement calibation is used to eliminate the systematic (stable and epeatable) measuement eos caused by the impefections of the system. Random eos due to noise, dift, o the envionment (tempeatue, humidity, pessue) cannot be emoved with a measuement calibation. This makes a micowave measuement susceptible to eos fom small changes in the measuement system. These eos can be minimized by adopting good measuement pactices, such as visually inspecting all connectos fo dit o damage and by minimizing any physical movement of the test pot cables afte a calibation. Moe infomation on the netwok analyze calibation is available in the Application Note

16 Impedance analyzes and LCR metes Impedance analyzes and LCR metes such as the ones listed in Figue 12 ae used to measue the mateial popeties at lowe fequencies. The mateial is stimulated with an AC souce and the actual voltage acoss the mateial is monitoed. Mateial test paametes ae deived by knowing the dimensions of the mateial and by measuing its capacitance and dissipation facto. PNA family Netwok analyzes ENA seies FieldFox Handheld VNA E4991B Impedance/Mateial Analyze E4990A E4980A, 4285A Impedance Analyze LCR metes DC f (Hz) Figue 12. Fequency coveage of Agilent Technologies instuments used fo dielectic measuements Fixtues Befoe the dielectic popeties of a mateial can be measued with netwok analyze, impedance analyze, o LCR mete, a measuement fixtue (o sample holde) is equied to apply the electomagnetic fields in a pedictable way and to allow connection to the measuement instument. The type of fixtue equied will depend on the chosen measuement technique and the physical popeties of the mateial (solid, liquid, powde, gas). Softwae The measued data fom the instument is not always pesented in the most convenient teminology o fomat. In this case, softwae is equied to convet the measued data to pemittivity o pemeability. Softwae may also be equied to model any inteaction between the fixtue and MUT to allow the extaction of the bulk mateial popeties. 16.

17 Measuement Techniques Coaxial pobe Method featues Boadband Simple and convenient (non-destuctive) Limited e accuacy and tan d low loss esolution Best fo liquids o semi-solids Mateial assumptions Semi-infinite thickness Non-magnetic Isotopic and homogeneous Flat suface No ai gaps The open-ended coaxial pobe is a cut off section of tansmission line. The mateial is measued by immesing the pobe into a liquid o touching it to the flat face of a solid (o powde) mateial. The fields at the pobe end finge into the mateial and change as they come into contact with the MUT (Figue 13). The eflected signal 5. (S 11 ) can be measued and elated to e *. A typical measuement system using a coaxial pobe method consists of a netwok o impedance analyze, a coaxial pobe and softwae. Both the softwae and the pobe ae included in the E dielectic pobe kit. An extenal compute is needed in many cases to contol the netwok analyze though GP-IB. The A USB to GPIB inteface povides a convenient and flexible way to ealize this connection. Fo the PNA family and the ENA seies of netwok analyzes, the softwae can be installed diectly in the analyze and thee is no need fo an extenal compute. Solids Semisolids (powde) Reflection (S ) 11 Liquids S11 Figue 13. Coaxial pobe method 17

18 Figue 14 shows the thee pobes that ae available in the E kit; the high tempeatue pobe (a), the slim fom pobe (b), and the pefomance pobe (c). The high tempeatue pobe (a) is shown with the shoting block to the ight. Thee slim pobes ae shown at the bottom of (b) with the shot on the top and a couple of othe accessoies. The pefomance pobe (c) is shown with the shoting block to the top. (a) (b) Shot (c) Shot Flange Apetue High tempeatue pobe Shot Slim pobes Pefomance Pobe Figue 14. Thee dielectic pobe configuations Rugged in design, the high tempeatue pobe (a) featues a hemetic glass-tometal seal, which makes it esistant to coosive o abasive chemicals. The pobe withstands a wide 40. to C tempeatue ange, which allows measuements vesus fequency and tempeatue. The lage flange allows measuements of flat sufaced solid mateials, in addition to liquids and semisolids. The slim fom pobe (b) featues a slim design, which allows it to fit easily in fementation tanks, chemical eaction chambes, o othe equipment with small apetues. The slim design also allows it to be used with smalle sample sizes. This pobe is best used fo liquids and soft semi-solids. Fo castable solids, the pobe is economical enough to be cast into the mateial and left in place. Because of the consumable natue of this design, these pobes ae offeed in sets of thee. The slim fom pobe kit comes with a sealed slim fom holde that adapts a 2.2 mm oute diamete to 10. mm inne diamete backet included in the kit as well as commecially available Midi sized adaptes and bushings. The pefomance pobe (c) combines ugged, high tempeatue and fequency pefomance in a slim design, pefect fo you most demanding applications. The pobe is sealed on both the pobe tip and the connecto end, which makes it ou most ugged pobe. The pobe withstands a wide 40. ºC to ºC tempeatue ange, which allows measuements vesus fequency and tempeatue. The pobe can be autoclaved, so it is pefect fo applications in the food, medical, and chemical industies whee steilization is a must. The slim design allows it to fit easily in fementation tanks, chemical eaction chambes, o othe equipment with small apetues. The small diamete also allows it to be used with the smallest sample sizes of all Agilent s pobes. It is useful fo measuing liquid, semi-solid, as well as flat sufaced solid mateials. Additional detailed infomation is available in the Dielectic Pobe Technical Oveview 6. and Softwae Online Help 7. 18

19 The dielectic pobes ae compatible with the Agilent netwok analyzes and the E49.9.1B impedance analyze. With the impedance analyze the high tempeatue pobe is specified fom 10. MHz. Befoe measuing, calibation at the tip of the pobe must be pefomed. A thee-tem calibation coects fo the diectivity, tacking, and souce match eos that can be pesent in a eflection measuement. In ode to solve fo these thee eo tems, thee well-known standads ae measued. The diffeence between the pedicted and actual values is used to emove the systematic (epeatable) eos fom the measuement. The thee known standads ae ai, a shot cicuit, and distillate and de-ionized wate. Even afte calibating the pobe, thee ae additional souces of eo that can affect the accuacy of a measuement. Thee ae thee main souces of eos: Cable stability Ai Gaps Sample thickness It is impotant to allow enough time fo the cable (that connects the pobe to the netwok analyze) to stabilize befoe making a measuement and to be sue that the cable is not flexed between calibation and measuement. The automated Electonic Calibation Refesh featue ecalibates the system automatically, in seconds, just befoe each measuement is made. This vitually eliminates cable instability and system dift eos. Fo solid mateials, an ai gap between the pobe and sample can be a significant souce of eo unless the sample face is machined to be at least as flat as the pobe face. Fo liquid samples ai bubbles on the tip of the pobe can act in the same way as an ai gap on a solid sample. The sample must also be thick enough to appea infinite to the pobe. Thee is a simple equation 6. to calculate the appoximate thickness of the sample fo the high tempeatue pobe sample and suggested thickness fo the slim pobe sample. A simple pactical appoach is to put a shot behind the sample and check to see if it affects the measuement esults. Figue 15. shows a compaison of measuements of dielectic constant and loss facto of methanol at oom tempeatue (25. C) using the high tempeatue pobe, with theoetical calculations using the Cole-Cole model. The following paametes ae used in the Cole-Cole calculations: ε = ε = τ = α = s , 4.45., ,

20 ' " 30 Theoy Measuement Theoy Measuement f, GHz f, GHz (a) (b) Figue 15. Measued dielectic constant (a) and loss facto (b) of methanol at 25 ºC compaed with Cole-Cole model A disadvantage of the dielectic pobe method is the limited accuacy, unde some conditions, when compaed to othe methods like the tansmission line method using the E and esonato method. Tansmission line Tansmission line methods involve placing the mateial inside a potion of an enclosed tansmission line. The line is usually a section of ectangula waveguide o coaxial ailine (Figue 16.). e* and µ* ae computed fom the measuement of the eflected signal (S 11 ) and tansmitted signal (S 21 ). Mateial assumptions Sample fills fixtue coss section No ai gaps at fixtue walls Smooth, flat faces, pependicula to long axis Homogeneous Method featues Boadband low end limited by pactical sample length Limited low loss esolution (depends on sample length) Measues magnetic mateials Anisotopic mateials can be measued in waveguide 20.

21 Waveguide l Reflection (S 11) Tansmission (S ) 21 Coax S 11 S 21 µ Figue 16. Tansmission line method; waveguide and coaxial line case Coaxial tansmission lines cove a boad fequency ange, but a tooid shaped sample is moe difficult to manufactue (Figue 17(a)). Waveguide fixtues extend to the mm-wave fequencies and the samples ae simple to machine, but thei fequency coveage is banded (Figue 17(b)). A typical measuement system using a tansmission line technique consists of a vecto netwok analyze, a coaxial ailine o waveguide section, softwae such as the E to pefom the convesion to e* and μ*. An extenal compute can be used to contol the netwok analyze, intefacing ove LAN, USB o though GP-IB. The B USB to GPIB inteface povides a convenient and flexible way to ealize this connection. Fo the PNA family and the ENA seies of netwok analyzes, the softwae can be installed diectly in the analyze and thee is no need fo an extenal compute. Additional infomation about the E Mateials Measuement softwae can be found in the Technical Oveview 8 and Softwae Online Help 9.. (a) (b) Figue 17. Coaxial 7 mm ai line with samples (a) and X-band waveguide staight section with samples (b) The 5.0. Ohm ailine fom Agilent veification kits (Figue 17(a)) is the ecommended coaxial sample holde. Evey waveguide calibation kit in the A family contains a pecision waveguide section (Figue 17(b)), ecommended fo a waveguide sample holde. 21

22 Figue 18 shows measuement esults of pemittivity (a) and loss tangent (b) of two Plexiglas samples with lengths of 25. mm and 31 mm espectively, in an X-band waveguide. The sample holde is the pecise waveguide section of 140. mm length that is povided with the X116.44A calibation kit (Figue 17(b)). The netwok analyze is a PNA, the calibation type is TRL and the pecision NIST algoithm 9. is used fo calculation. In both gaphs below thee ae two pais of taces fo two diffeent measuements of the same samples. The top two measuements of each gaph ae pefomed fo the case when the sample holde is not calibated out. ' mm 31 mm tan mm 31 mm mm 31 mm calibated out sample holde f, GHz mm 31 mm calibated out sample holde f, GHz (a) (b) Figue 18. Measuement of two Plexiglas samples, 25 mm and 31 mm long in a X-band waveguide In this case based on the sample length and sample holde length, the E softwae will otate the calibation plane coectly to the sample face, but will not compensate fo the losses of the waveguide. The bottom two measuements of the same samples ae pefomed fo the case when the sample holde is pat of the calibation and the waveguide losses and electical length ae calibated out. As expected, the loss tangent cuves (b) show lowe values when the sample holde is calibated out and they ae moe constant with espect to fequency. This is due to the fact that the waveguide losses ae no longe added to the sample s losses. With the PNA netwok analyze, besides calibating out the sample holde, it is possible to pefom fixtue de-embedding, which will lead to the same esults. This appoach equies measuing the empty sample holde afte the calibation. 22

23 Fee space Mateial assumptions Lage, flat, paallel-faced samples Homogeneous Method featues Non-contacting, non-destuctive High fequency low end limited by pactical sample size Useful fo high tempeatue Antenna polaization may be vaied fo anisotopic mateials Measues magnetic mateials Fee-space methods use antennas to focus micowave enegy at o though a slab o sheet of mateial (Figue 19.). This method is non-contacting and can be applied to mateials to be tested unde high tempeatues and hostile envionments. Figue 19. shows two typical feespace measuement setups: an S-paamete configuation (uppe) and the NRL ach (lowe). A typical measuement system using a fee-space method consists of a vecto netwok analyze, a fee space fixtue (antennas, tunnels, aches, etc.), and E softwae. An extenal compute can be used to contol the netwok analyze, intefacing ove LAN, USB o though GP-IB. The B USB to GPIB inteface povides a convenient and flexible way to ealize this connection. Fo the PNA family and the ENA seies of netwok analyzes, the softwae can be installed diectly in the analyze and thee is no need fo an extenal compute. Mateial Sample To Pot 1 of netwok analyze To Pot 2 of netwok analyze To Pot 1 of netwok analyze To Pot 2 of netwok analyze Figue 19. Fee space measuement setups 23

24 High tempeatue measuements ae easy to pefom in fee space since the sample is neve touched o contacted (Figue 20.). The sample can be heated by placing it within a funace that has windows of insulation mateial that ae tanspaent to micowaves. Agilent Technologies does not povide the funace needed fo such a type of measuement. Figue 20. illustates the basic set up. Heating panels Funace Themal insulation Sample Themocouple Figue 20. High tempeatue measuement in fee space Calibating the netwok analyze fo a fee space measuement is challenging. Fee space calibation standads pesent special poblems since they ae connecto-less. A calibation can be as simple as a esponse calibation o as complex as a full two-pot calibation depending on the convenience and accuacy desied. The E softwae offes an optional fee space calibation method called GRL (Gated match, Reflect, Line). This calibation outine inceases the ease of use and educes the costs associated with some othe calibation methods, such as TRM (Thu, Reflect, Match) and TRL (Thu, Reflect, Line). Use of this option equies a netwok analyze with the time domain option, an appopiate fee space fixtue, and a metal calibation plate. This option also includes a gated isolation/esponse calibation, which educes eos fom diffaction effects at the sample edges and multiple esidual eflections between the antennas. The E softwae automatically sets up all the fee space calibation definitions and netwok analyze paametes, saving engineeing time. A guided calibation wizad steps the use though the easy calibation pocess. 24

25 2.6 ' f, GHz Figue 21. Measuement of Rexolite sample in a U-band (40 60 GHz) Figue 21 depicts the esult of a GRL calibation measuing Rexolite mateial in U-band ( GHz) with a PNA netwok analyze and E softwae. The fixtue was made with standad gain hons and a eadily available, domestic use, shelving unit to demonstate that when doing a GRL calibation, even with the simplest set up, it is still possible to pefom easonable measuements. Fo pecise measuements, moe igid fixtues with focused hons ae ecommended. Figue GHz Thomas Keating Ltd. Quasi-Optical Table with Gaussian beam hons, focusing mios and sample holde. At mm-wave and submm-wave fequencies, Quasi-Optical Tables ae ideal. They can be puchased fom Thomas Keating Ltd, o though Agilent Special Handling Engineeing. Agilent model numbes: GHz GHz GHz GHz GHz GHz E E E E E E E E E E E E24 Additional fequencies, as well as tables coveing multiple fequency bands may be available on equest. 25.

26 Resonant Cavity Resonant vesus boadband techniques Resonant techniques High impedance envionment Reasonable measuements possible with small samples Measuements at only one o a few fequencies Well suited fo low loss mateials Boadband techniques Low impedance envionment Requies lage samples to obtain easonable measuements Measuement at any fequency Resonant cavities ae high Q stuctues that esonate at specific fequencies. A piece of sample mateial inseted into the cavity affects the esonant fequency (f) and quality facto (Q) of the cavity. Fom these paametes, the complex pemittivity of the mateial can be calculated at a single fequency. A typical measuement system consists of a netwok analyze, a esonant cavity fixtue and softwae to make the calculations. Thee ae many diffeent methods and types of fixtues. Agilent E option Resonant Cavity Softwae automates thee methods: Split Cylinde method, Split Post Dielectic Resonato method and ASTM D Cavity Petubation method. An extenal compute can be used to contol the netwok analyze, intefacing ove LAN, USB o though GP-IB. Fo the PNA family and the ENA seies of netwok analyzes, the softwae can be installed diectly in the analyze and thee is no need fo an extenal compute. Agilent also offes high Q esonant cavity fixtues fo the Split Cylinde 13 and Split Post 14 methods. Split cylinde esonato Figue 23. Agilent 85072A 10 GHz split cylinde esonato 26.

27 The split cylinde esonato is a cylindical esonant cavity sepaated into two halves. The sample is loaded in a gap between the two cylinde halves. One cylinde half is fixed, and the othe adjusts allowing the gap to accommodate vaying sample thicknesses. The eal pat of pemittivity, e, and loss tangent o tan delta, tand, ae calculated fom the sample thickness, cylinde length, and S-paamete measuements of the split cylinde esonato, both empty and loaded with the sample. Using a mode matching model developed at NIST in Boulde, Coloado 14 pemittivity and loss tangent can be calculated at the 10. GHz TE 0.11 mode. It may also be possible to measue at some highe ode TE 0.np modes 2 whee no intefeing modes exist. This method was adopted by the IPC as TM standad test method. 15. Split post dielectic esonato Figue 24. QWED 5 GHz split post dielectic esonato, available fom Agilent as 85071E-E04 Split Post Dielectic Resonatos fom QWED, use low loss dielectic mateials which make it possible to build esonatos having highe Q-factos and bette themal stability than taditional all-metal cavities. This method is one of the easiest and highest accuacy methods fo measuing complex pemittivity and loss tangent of low loss and thin sheet mateials 16.. The elatively inexpensive fixtues can be puchased fom QWED o though Agilent Special Handling Engineeing in single fequencies fom 1 to 22GHz. Agilent model numbes: 1.1 GHz E E GHz E E GHz E E GHz E E GHz E E0.7 Additional fequencies may be available on equest. 27

28 Cavity petubation (ASTM D25.20.) ' V (f f ) c c s ε = + 1 2V f s s '' V 1 1 c ε = 4V Q Q s s c Iis-coupled end plates Sample Q S Q 0 f V is the volume index c is fo the empty cavity, index s is fo the sample loaded f Q o µ f S f C Figue 25. Resonant cavity measuement The ASTM cavity petubation method uses a ectangula waveguide with iis-coupled end plates, opeating in TE10.n mode (Figue 25.). Fo a dielectic measuement, the sample should be placed in a maximum electic field. Although Agilent Technologies does not povide a eady-made esonato fixtue fo the cavity petubation method, it is not difficult to adapt a pecision waveguide staight section, such as those available in the116.44a seies waveguide calibation Kits. A hole needs to be dilled exactly in the middle of the waveguide length and the two iis-coupled end plates need to be manufactued. The dimension of the iis hole is b/2.2, whee b is the naow dimension of the waveguide coss section. If the sample is inseted though a hole in the middle of the waveguide length, then an odd numbe of half wavelengths will bing the maximum electic field to the sample location, so that the dielectic popeties of the sample can be measued. (An even numbe of half wavelengths will bing the maximum magnetic field to the sample location so that magnetic popeties of the sample can also be measued.) The cavity petubation method equies a vey small sample such that the fields in the cavity ae only slightly distubed to shift the measued esonant fequency and cavity Q. This assumption allows simplifying the theoy to use the equations above to calculate the dielectic popeties of the mateial. 28

29 Paallel plate The paallel plate method, also called the thee teminal method in ASTM standad D , involves sandwiching a thin sheet of mateial o liquid between two electodes to fom a capacito. The measued capacitance is then used to calculate pemittivity. In an actual test setup, two electodes ae configued with a test fixtue sandwiching dielectic mateial. The impedancemeasuing instument would measue vecto components of capacitance (C) and dissipation (D) and a softwae pogam would calculate pemittivity and loss tangent. The method woks best fo accuate, low fequency measuements of thin sheets o liquids. A typical measuement system using the paallel plate method consists of an impedance analyze o LCR mete and a fixtue such as the B and A dielectic test fixtue, which opeates up to 1 GHz. The A test fixtue is offeed fo measuing liquids. Moe infomation about the paallel plate method and othe Agilent Technologies low fequency mateials measuement solutions ae available in Application Note (P/N EN) 1 and Electodes (Aea=A) Solid Thickness = t Figue 26. Paallel plate method Liquid Cp Equivalent Cicuit G Y = G + j C C p G = j C 0 j C 0 C 0 Co : Ai Capacitance * = = 0 p C p j C t C = A p 0 R p G C 0 t A 0 Figue 27. Agilent 16451B and 16453A dielectic test fixtue with impedance analyze 29.

30 Inductance measuement method Relative pemeability of magnetic mateial deived fom the self-inductance of a coed inducto that has a closed loop (such as the tooidal coe) is often called effective pemeability. The conventional method of measuing effective pemeability is to wind some wie aound the coe and evaluate the inductance with espect to the ends of the wie. This type of measuement is usually pefomed with an impedance analyze. Effective pemeability is deived fom the inductance measuement esult. The Agilent A magnetic mateial test fixtue povides an ideal stuctue fo single-tun inducto, with no flux leakage when a tooidal coe is inseted in it. Moe infomation about the inductance measuement method is available in the Application Note (P/N EN) A h No magnetic flux leakage c b whee, elative pemeability measued inductance with MUT measued inductance without MUT pemeability of fee space height of MUT (Mateial Unde Test) oute diamete of MUT inne diamete of MUT Figue 28. Inductance measuement method 30.

31 Compaison of Methods Many factos such as accuacy, convenience, and the mateial shape and fom ae impotant in selecting the most appopiate measuement technique. Some of the significant factos to conside ae summaized hee: Fequency ange Expected values of e and μ Requied measuement accuacy Mateial popeties (i.e., homogeneous, isotopic) Fom of mateial (i.e., liquid, powde, solid, sheet) Sample size estictions Destuctive o nondestuctive Contacting o non-contacting Tempeatue Cost Figue 29. povides a quick compaison between the measuement methods that have been discussed aleady. Coaxial Pobe Tansmission Line and µ Fee Space and µ Resonant Cavity Boadband, convenient, non-destuctive Best fo lossy MUTs; liquids and semi-solids Boadband Best fp lossy to low loss MUTs; machineable solids Boadband; Non-contacting Best fo flats sheets, powdes, high tempeatues Single fequency; Accuate Best fo low loss MUTs; small samples Paallel Plate Accuate Best fo low fequencies; thin, flat sheets Inductance measuement Accuate, simple measuement, a tooidal coe µ stuctue is equied Figue 29. Summay of the measuement techniques 31

32 Agilent solutions Agilent Technologies offes a wide vaiety of test fixtues to measue the dielectic popeties of mateials which coves most mateial types. Figue 30. shows the coveage of Agilent test fixtues depending on mateial types and fequency anges. Mateial types Mateials measuement softwae 85071E Liquid 16452A Gel Liquid test fixtue 85070E Dielectic pobe Semi-solids (Powde) Solid Substate Tooidal coe 16453A 16451B Dielectic test fixtue 16454A 85072A 85071E -Exx Split post dielectic esonatos (SPDR) Magnetic mateial test fixtue 10 GHz split cylinde esonato DC 1 khz 1 MHz 1 GHz 10 GHz 20 GHz 50 GHz 100 GHz Fequency Figue 30. Mateials measuement fixtues Agilent also offes poweful softwae to help customes automate complex pemittivity and pemeability measuement analysis. The E mateials measuement softwae steamlines the pocess of measuing complex pemittivity and pemeability with an Agilent netwok analyze. The easy-to-use softwae guides the use though setup and measuement, instantly conveting S-paamete netwok analyze data into the data fomat of you choice and displaying the esults within seconds. Results can be chated in a vaiety of fomats: e, e, tan δ, μ, μ, tan δ m and Cole-Cole A vaiety of measuement methods and mathematical models ae povided to meet most application needs. A fee space calibation option povides Agilent s exclusive gated eflect line (GRL) calibation fo measuing mateials in fee space. The ach eflectivity option automates popula NRL ach method fo measuing eflections off the suface of a sample. The esonant cavity option offes the highest loss tangent accuacy and esolution. Figue 31 summaizes Agilent fixtues and compatible measuement instuments. 32

33 PNA ENA FieldFox E49.9.1B E A E49.80.A 4285.A Method E Dielectic pobe kit Coaxial pobe E Exx Split post dielectic esonatos (SPDR) Resonant cavity A 10. GHz split cylinde esonato Resonant cavity B Dielectic mateial test fixtue Paallel plate A Liquid test fixtue Paallel plate A Dielectic mateial test fixtue Paallel plate A Magnetic mateial test fixtue Inductance Figue 31. Agilent Technologies instuments and fixtues 1 1. Refe to "Agilent LCR Metes, Impedance Analyzes and Test Fixtues, Selection guide" ( E) and "8507x seies suppoted analyzes" ( SuppotedVNAs.pdf) fo moe detail Refeences 1. Application Note , Solutions fo Measuing Pemittivity and Pemeability with LCR Metes and Impedance Analyzes, Agilent Liteatue Numbe EN 2. Application note , Undestanding the Fundamental Pinciples of Vecto Netwok Analysis, Agilent liteatue numbe E 3. Application note , Exploing the Achitectues of Netwok Analyzes, Agilent liteatue numbe E 4. Application note , Applying Eo Coection to Netwok Analyze Measuements, Agilent liteatue numbe E 5. D. V. Blackham, R. D. Pollad, An Impoved Technique fo Pemittivity Measuements Using a Coaxial Pobe, IEEE Tans. on Inst. Meas., vol. 46, No 5, Oct. 1997, pp Technical Oveview, Agilent 85070E Dielectic Pobe Kit, Agilent liteatue numbe EN 7. Online Help fo softwae, 8. Technical Oveview, Agilent 85071E Mateials Measuement Softwae, Agilent liteatue numbe EN 9. Online Help fo softwae, ASTM Test methods fo complex pemittivity (Dielectic Constant) of solid electical insulating mateials at micowave fequencies and tempeatues to 1650, ASTM Standad D2520, Ameican Society fo Testing and Mateials 11. Application Note 380-1, Dielectic constant measuement of solid mateials using the 16451B dielectic test fixtue, Agilent liteatue numbe ASTM, Test methods fo A-C loss chaacteistics and pemittivity (dielectic constant) of solid electical insulating mateials, ASTM Standad D 150, Ameican Society fo Testing and Mateials 13. Technical Oveview, Agilent 85072A 10GHz Split Cylinde Resonato. Agilent liteatue numbe EN 14. M.D. Janezic, Nondestuctive Relative Pemittivity and Loss Tangent Measuements using a Split-Cylinde Resonato, Ph.D. Thesis, Univesity of Coloado at Boulde, IPC TM Relative Pemittivity and Loss Tangent Using a Split-Cylinde Resonato 16. Application Note Split Post Dielectic Resonatos fo Dielectic Measuements of Substates. Agilent liteatue numbe EN 17. Agilent LCR Metes, Impedance Analyzes and Test Fixtues, Selection guide, Agilent liteatue numbe E 33

34 Web Resouces Visit ou web sites fo additional poduct infomation and liteatue. Mateials Test Equipment: Netwok Analyzes: Impedance Analyzes & LCR metes: Electonic Calibation (ECal) modules: myagilent A pesonalized view into the infomation most elevant to you. Thee-Yea Waanty Beyond poduct specification, changing the owneship expeience. Agilent is the only test and measuement company that offes thee-yea waanty on all instuments, woldwide Agilent Electonic Measuement Goup DEKRA Cetified ISO : Quality Management System Agilent Channel Patnes Get the best of both wolds: Agilent s measuement expetise and poduct beadth, combined with channel patne convenience. Fo moe infomation on Agilent Technologies poducts, applications o sevices, please contact you local Agilent office. The complete list is available at: Ameicas Canada (877) Bazil (11) Mexico United States (80.0.) Asia Pacific Austalia China Hong Kong India Japan (421) 345. Koea Malaysia Singapoe Taiwan Othe AP Counties (6.5.) Euope & Middle East Belgium 32 (0.) Denmak Finland 35.8 (0.) Fance * * /minute Gemany 49. (0.) Ieland Isael /5.44 Italy Nethelands 31 (0.) Spain 34 (9.1) Sweden United Kingdom 44 (0.) Fo othe unlisted counties: (BP ) Poduct specifications and desciptions in this document subject to change without notice. Agilent Technologies, Inc Published in USA, May 16., EN