Materials Measurement Phil Bartley Shelley Begley

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Problems with N-R Model• This set of equations become unstable when M11 isequal to zero. One equation, two unknowns.• The derivation involves taking the log of a complexnumber. The log of a complex number is not a singlevalued function.The major flaw in this technique is when the value of S 11 is equal to zero (or theuncertainty in the measurement is as large as the measurement value) When thishappens we have only one independent equation and two unknowns. One way thiscan happen is when the reflection off the back surface of the material cancels out thereflection off the front surface. Fortunately this seldom happens with magneticmaterials. This is because these materials are usually lossey. Non-magneticmaterials can be better analyzed by using other models. These models will bediscussed later.Another problem occurs because the derivation proposed by Nicolson and Rossinvolves taking the log of a complex quantity. The log of a complex number is not asingle valued function. This can usually be accounted for by knowing how many 360degree phase transitions S 21 makes. You need to know if the -30 degree phase of S21is really -30 degrees or -30 -360=-390 degrees. This is easy to do if the phase shift atthe first frequency point is less than -360 degrees. If not an estimate of u and e isneeded. These estimates only need to be accurate enough to correctly predict thenumber of -360 degree phase shifts. Another possibility is to estimate the number ofphase shifts by calculating the group delay.38
Example of N-R <strong>Measurement</strong>sThese two plots show measurements made on a sample of Teflon. In the first casethe measured value of S 11 never approaches zero. In the second case, because of thelonger length of the sample, the measured value of S11 approaches zero at severalfrequencies. Since the equations used to solve for u and e are ill-conditioned thecomputed results are in error.39
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 24 and 25: Other Empirical ModelsταβOnly fe
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 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

Materials Measurement Phil Bartley Shelley Begley

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