Materials Measurement Phil Bartley Shelley Begley

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Other Empirical ModelsταβOnly few materials exhibit pure relaxation properties with singlerelaxation time that are described with the Debye equation.εε( ω)( ω)εs−ε∞ε∞+1+j=1−( ωτ ) αεs−ε∞= ε +∞( 1+jωτ) βthe relaxation time constantthe relaxation width (distribution parameter)The Cole-Cole model isused in determination ofuser defined standard forcoaxial dielectric probe.Cole-Davidson modeldistribution parameter that leads to asymmetric distribution of τOnly few materials exhibit pure relaxation properties with single relaxationtime that are described with the Debye equation. There are many otherempirical expressions that will describe better the frequency dependentbehavior of materials with more than one relaxation times or distribution ofrelaxation times. Such are the Cole-Cole equation and Cole-Davidsonequation.Based on the above equation the Cole-Cole model is used for determining ofa user-defined standards for coaxial probes.24
Comparison Between the Different Models"ε r3020Cole-Cole α = 0.2Debye10Cole-Davidsonβ = 0.510 20 30 40 50 60 70'ε rThis is theoretical calculation of the different models, represented withequations on the previous slide. The values of a and b are chosen to showthe difference between the models and necessarily does not represent25
Page 3: Extremely Diverse Applications“Ma
Page 6 and 7: Maxwell’s Equations∇× E=−∂
Page 8 and 9: Permittivity and Permeability Defin
Page 10 and 11: Definition of Dielectric Constant o
Page 12 and 13: Dielectric MechanismsIonic Polariza
Page 14 and 15: Consider Dipole RotationRandom Orie
Page 16 and 17: Electric Field Changed DirectionEDi
Page 18 and 19: Small and Large MoleculesMany mater
Page 20 and 21: ε rε' '',r6040Debye Relaxation fo
Page 22 and 23: Cole-Cole Plot Explanation"ε r3020
Page 26 and 27: Dielectric Properties (at 3 GHz)100
Page 28 and 29: Which Technique is Best? Frequency
Page 30 and 31: Impedance Analyzers and FixturesHer
Page 32 and 33: Measurement Techniques that use a V
Page 34 and 35: Transmission LineMaterial assumptio
Page 36 and 37: Transmission Algorithms in 85071EOp
Page 38 and 39: Problems with N-R Model• This set
Page 40 and 41: NIST Model• Technique uses all fo
Page 42 and 43: Transmission (Fast) Model• This t
Page 44 and 45: Weakness of both the NIST and Trans
Page 46 and 47: Transmission Line Measurement Error
Page 48 and 49: Typical Errors Caused By Air GapsPe
Page 50 and 51: Transmission Line Technique Summary
Page 52 and 53: Non-Contacting method for High or L
Page 54 and 55: 40 - 60GHz Free Space System54
Page 56 and 57: Free Space W-band SystemHere is a p
Page 58 and 59: Free Space Quasi-Optical SystemHere
Page 60 and 61: Before a Measurement Can be Made…
Page 62 and 63: TRL CalibrationThruReflectMove the
Page 64 and 65: Gated Reflect Line (GRL) Calibratio
Page 66 and 67: MUT and GRL Error AdaptersAfter 2-P
Page 68 and 69: MUT and GRL Error AdaptersAfter O11
Page 70 and 71: GRL Thru Standard (Air)A 11 =A 22 =
Page 72 and 73: QO System SchematicAdditional infor
Page 74 and 75:
Measurement Results0.03Imaginary pa
Page 76 and 77:
Measurement with NRL Arch andoption
Page 78:
Free Space LabWith u-band calibrati
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Materials Measurement Phil Bartley Shelley Begley

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