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Agilent Basics of Measuring the Dielectric Properties of ...

AgilentBasics of Measuring the Dielectric Properties of MaterialsApplication NoteContents Constant ..4 Permeability ..7 Electromagnetic (dipolar) polarization ..11 Electronic and atomic polarization ..11 Relaxation time ..12 Debye Relation ..12 Cole-Cole conductivity ..13 Interfacial or space charge polarization .. 14 Measurement analyzers ..15 Impedance analyzers and LCR meters ..16 Fixtures ..16 Software ..16 Measurement Coaxial probe ..17 Transmission line ..20 Free space ..23 Resonant cavity ..25 Parallel plate ..27 Comparison of IntroductionEvery material has a unique set of electrical characteristics that are dependent on its Dielectric Properties . Accurate measurements of theseproperties can provide scientists and engineers with valuable information toproperly incorporate the material into its intended application for moresolid designs or to monitor a manufacturing process for improved qualitycontrol. A Dielectric materials measurement can provide critical design parameterinformation for many electronics applications.

From the point of view of electromagnetic theory, the definition of electric displacement (electric flux density) D f is: D f = eE where e= e* = e 0e r is the absolute permittivity (or permittivity), e r is the relative permittivity, e 0 ≈ 1 36π x 10-9 F/m is the free space permittivity and E …

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Transcription of Agilent Basics of Measuring the Dielectric Properties of ...

1 AgilentBasics of Measuring the Dielectric Properties of MaterialsApplication NoteContents Constant ..4 Permeability ..7 Electromagnetic (dipolar) polarization ..11 Electronic and atomic polarization ..11 Relaxation time ..12 Debye Relation ..12 Cole-Cole conductivity ..13 Interfacial or space charge polarization .. 14 Measurement analyzers ..15 Impedance analyzers and LCR meters ..16 Fixtures ..16 Software ..16 Measurement Coaxial probe ..17 Transmission line ..20 Free space ..23 Resonant cavity ..25 Parallel plate ..27 Comparison of IntroductionEvery material has a unique set of electrical characteristics that are dependent on its Dielectric Properties . Accurate measurements of theseproperties can provide scientists and engineers with valuable information toproperly incorporate the material into its intended application for moresolid designs or to monitor a manufacturing process for improved qualitycontrol. A Dielectric materials measurement can provide critical design parameterinformation for many electronics applications.

2 For example, the loss of acable insulator, the impedance of a substrate, or the frequency of a dielectricresonator can be related to its Dielectric Properties . The information is alsouseful for improving ferrite, absorber, and packaging designs. More recentapplications in the area of industrial microwave processing of food, rubber,plastic and ceramics have also been found to benefit from knowledge ofdielectric Properties . Agilent Technologies Inc. offers a variety of instruments, fixtures, and software to measure the Dielectric Properties of materials. Agilent measure-ment instruments, such as network analyzers, LCR meters, and impedanceanalyzers range in frequency up to 325 GHz. Fixtures to hold the materialunder test (MUT) are available that are based on coaxial probe,coaxial/waveguide transmission line techniques, and parallel TheoryThe Dielectric Properties that will be discussed here are permittivity andpermeability. Resistivity is another material property which will not be discussed here.

3 Information about resistivity and its measurement can befound in the Agilent Application Note 1369-11. It is important to note thatpermittivity and permeability are not constant. They can change with frequency, temperature, orientation, mixture, pressure, and molecular structure of the constantA material is classified as Dielectric if it has the ability to store energywhen an external electric field is applied. If a DC voltage source is placedacross a parallel plate capacitor, more charge is stored when a dielectricmaterial is between the plates than if no material (a vacuum) is between theplates. The Dielectric material increases the storage capacity of the capacitorby neutralizing charges at the electrodes, which ordinarily would contributeto the external field. The capacitance with the Dielectric material is relatedto Dielectric constant. If a DC voltage source Vis placed across a parallelplate capacitor (Figure 1), more charge is stored when a Dielectric materialis between the plates than if no material (a vacuum) is between the 1.

4 Parallel plate capacitor, DC caseWhere Cand C0are capacitance with and without Dielectric , k'= e'ris thereal Dielectric constant or permittivity, and Aand tare the area of thecapacitor plates and the distance between them (Figure 1). The dielectricmaterial increases the storage capacity of the capacitor by neutralizingcharges at the electrodes, which ordinarily would contribute to the externalfield. The capacitance of the Dielectric material is related to the dielectricconstant as indicated in the above equations. If an AC sinusoidal voltagesource V is placed across the same capacitor (Figure 2), the resulting current will be made up of a charging current Icand a loss current Ilthat isrelated to the Dielectric constant. The losses in the material can be represented as a conductance (G) in parallel with a capacitor (C).4tA-+-+-+-+-+-+-+-++ V0'00k''CCCCtACr====keFigure 2. Parallel plate capacitor, AC caseThe complex Dielectric constant k consists of a real part k' which representsthe storage and an imaginary part k'' which represents the loss.

5 The follow-ing notations are used for the complex Dielectric constant interchangeably k = k* = er = e*r . From the point of view of electromagnetic theory , the definition of electricdisplacement (electric flux density) Dfis:Df =eEwhere e= e* = e0er is the absolute permittivity (or permittivity), er is the relative permittivity, e0 136 x 10-9 F/m is the free space permittivity and Eis the electric field. Permittivity describes the interaction of a material with an electric field Eand is a complex quantity. k = ee0 = er = er jer'' Dielectric constant (k) is equivalent to relative permittivity (er) or theabsolute permittivity (e) relative to the permittivity of free space (e0). Thereal part of permittivity (er') is a measure of how much energy from anexternal electric field is stored in a material. The imaginary part of permit-tivity (er'') is called the loss factor and is a measure of how dissipative orlossy a material is to an external electric field.

6 The imaginary part of permit-tivity (er") is always greater than zero and is usually much smaller than (er').The loss factor includes the effects of both Dielectric loss and conductivity. 5 CGtA-+-+-+-+-+-+-+-++-VIfCjVjCjVIthenCGI fGCjVIIIlc 2)()"')((,")'(0000====+=+=kkkkkwwwww-Whe n complex permittivity is drawn as a simple vector diagram (Figure 3),the real and imaginary components are 90 out of phase. The vector sumforms an angle dwith the real axis (er'). The relative lossiness of a material isthe ratio of the energy lost to the energy stored. Figure 3. Loss tangent vector diagramThe loss tangent or tan d is defined as the ratio of the imaginary part of thedielectric constant to the real part. Ddenotes dissipation factor and Qisquality factor. The loss tangent tan d is called tan delta, tangent loss or dissipation factor. Sometimes the term quality factor or Q-factor is usedwith respect to an electronic microwave material, which is the reciprocal of the loss tangent.

7 For very low loss materials, since tan d d, the loss tangent can be expressed in angle units, milliradians or 'r''reeeEnergy Stored per CycleEnergy Lost per CycleQDrr====1tan'"eedPermeabilityPermea bility ( ) describes the interaction of a material with a magneticfield. A similar analysis can be performed for permeability using an inductorwith resistance to represent core losses in a magnetic material (Figure 4). Ifa DC current source is placed across an inductor, the inductance with thecore material can be related to 4. InductorIn the equations Lis the inductance with the material, L0is free spaceinductance of the coil and ' is the real permeability. If an AC sinusoidal current source is placed across the same inductor, the resulting voltage willbe made up of an induced voltage and a loss voltage that is related to permeability. The core loss can be represented by a resistance (R) in serieswith an inductor (L). The complex permeability ( * or ) consists of a realpart ( ') that represents the energy storage term and an imaginary part ( '')that represents the energy loss term.

8 Relative permittivity ris the permittivity relative to free space: r= 0= r j r'' 0 = 4 x 10-7 H/mis the free space permeabilitySome materials such as iron (ferrites), cobalt, nickel, and their alloys haveappreciable magnetic Properties ; however, many materials are nonmagnetic,making the permeability very close to the permeability of free space ( r= 1).All materials, on the other hand, have Dielectric Properties , so the focus ofthis discussion will mostly be on permittivity measurements. 7RL00''LLLL== Electromagnetic Wave PropagationIn the time-varying case ( , a sinusoid), electric fields and magnetic fieldsappear together. This electromagnetic wave can propagate through freespace (at the speed of light, c = 3 x 108m/s) or through materials at slowerspeed. Electromagnetic waves of various wavelengths exist. The wavelengthlof a signal is inversely proportional to its frequency f (l = c/f), such that asthe frequency increases, the wavelength decreases.

9 For example, in freespace a 10 MHz signal has a wavelength of 30 m, while at 10 GHz it is just 3 cm. Many aspects of wave propagation are dependent on the permittivityand permeability of a material. Let s use the optical view of dielectricbehavior. Consider a flat slab of material (MUT) in space, with a TEM waveincident on its surface (Figure 5). There will be incident, reflected and transmitted waves. Since the impedance of the wave in the material Z is different (lower) from the free space impedance (or Z0) there will beimpedance mismatch and this will create the reflected wave. Part of theenergy will penetrate the sample. Once in the slab, the wave velocity v, isslower than the speed of light c. The wavelength ldis shorter than the wavelength l0in free space according to the equations below. Since thematerial will always have some loss, there will be attenuation or insertionloss. For simplicity the mismatch on the second border is not considered.

10 Figure 5. Reflected and transmitted signals8 MUTI mpedance lowerWavelength shorterVelocity slowerMagnitude attenuatedTEMor Z0'rZ='rAir'0eeehh''0000'120rrdrcvZZ ======hhlleeeeFigure 6 depicts the relation between the Dielectric constant of the MaterialUnder Test (MUT) and the reflection coefficient |G| for an infinitely longsample (no reflection from the back of the sample is considered). For smallvalues of the Dielectric constant (approximately less than 20), there is a lotof change of the reflection coefficient for a small change of the dielectricconstant. In this range Dielectric constant measurement using the reflectioncoefficient will be more sensitive and hence precise. Conversely, for highdielectric constants (for example between 70 and 90) there will be littlechange of the reflection coefficient and the measurement will have 6. Reflection coefficient versus Dielectric constant constantReflect ion coefficient G||'reDielectric MechanismsA material may have several Dielectric mechanisms or polarization effectsthat contribute to its overall permittivity (Figure 7).


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