NAT'L INST. OF STAND & TECH NIST PUBLICATIONS AlllDb MSMMM3NET National Institute of Standards and Technology Technology Administration, U.S. Department of Commerce NIST Technical Note 1536 Measuring the Permittivity and Permeability of Lossy Materials: Solids, Liquids, Metals, Building Materials, and Negative-Index Materials James Baker-Jarvis Michael D. Janezic Bill F. Riddle Robert T. Johnk Pavel Kabos Christopher L. Holloway Richard G. Geyer Chriss A. Grosvenor too NIST Technical Note 1536 Measuring the Permittivity and Permeabiiity of Lossy Materials: Solids, Liquids, Metals, Building Materials, and Negative-Index Materials James Baker Jarvis Michael D. Janezic Bill F. Riddle Robert T. Johnk Pavel Kabos Christopher L. Holloway Richard G. Geyer Chriss A. Grosvenor Electromagnetics Division National Institute of Standards and Technology Boulder, CO 80305 February 2005 o % U.S. Department of Commerce Carlos M. Gutierrez, Secretary Technology Administration Phillip J. Bond, Under Secretary for Technology National Institute of Standards and Technology Hratch G. Semerjian, Acting Director Certain commercial entities, equipment, or materials may be identified in this document in order to describe an experimental procedure or concept adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the entities, materials, or equipment are necessarily the best available for the purpose. National Institute of Standards and Technology Technical Note 1536 Natl. Inst. Stand. Techno!. Tech. Note 1536, 172 pages (February 2005) CODEN: NTNOEF U.S. Government Printing Office Washington: 2005 For sale by the Superintendent of Documents, U.S. Government Printing Office Internet bookstore: gpo.gov Phone:202-512-1800 Fax:202-512-2250 Mail: Stop SSOP, Washington, DC 20402-0001 Contents 1 Introduction 2 2 Electrical Properties of Lossy Materials 4 2.1 Electromagnetic Concepts for Lossy Materials 4 2.2 Overview of Relevant Circuit Theory 7 2.3 DC and AC Conductivity 11 3 Applied, Macroscopic, Evanescent, £ind Local Fields 14 3.1 Microscopic, Local, Evanescent, and Macroscopic Fields 14 3.2 Averaging 19 3.3 Constitutive Relations 20 3.4 Local Electromagnetic Fields in Materials 22 3.5 Effective Electrical Properties and Mixture Equations 23 3.6 Structures that Exhibit Effective Negative Permittivity and Permeability 23 4 Instrumentation, Specimen Holders, and Specimen Preparation 27 4.1 Network Analyzers 27 4.2 ANA Calibration 28 4.2.1 Coaxial Line Calibration 28 4.2.2 The Waveguide Calibration Kit 28 4.2.3 On-Wafer Calibration, Measurement, and Measurement Verification 29 4.3 Specimen- Holder Specifications 30 4.3.1 Specimen Holder 30 4.3.2 Specimen Preparation 31 5 Overview of Measurement Methods for Solids 33 6 Transmission-Line Techniques 40 6.1 Coaxial Line, Rectangular, and Cylindrical Waveguides 41 6.1.1 Overview of Waveguides Used in Transmission/Reflection Dielectric Measurements 41 6.1.2 sections of Waveguides Used as Specimen Holders 43 6.2 Slots in Waveguide 45 6.3 Microstrip, Striphnes, and Coplanar Waveguide . 45 6.4 Ground- Penetrating Radar 50 6.5 Free-Space Measurements 50 m 7 Coaxial Line and Waveguide Measurement Algorithms for Permittivity and Permeability 51 7.1 Specimen Geometry and Modal Expansions 52 7.2 Completely Filled Waveguide 55 7.2.1 Materials with Positive Permittivity and Permeability 55 7.2.2 Negative-Index Materials 57 7.3 Methods for the Numerical Determination of Permittivity 59 7.3.1 Iterative Solutions 59 7.3.2 Exphcit Method for Nonmagnetic Materials 60 7.4 Corrections to Data 60 7.4.1 Influence of Gaps Between Specimen and Holder 60 7.4.2 Attenuation Due to Imperfect Conductivity of Specimen Holders ... 61 7.4.3 Appearance of Higher Order Modes 62 7.4.4 Mode Suppression in Waveguides 62 7.4.5 Uncertainty Sources and Analysis 62 7.4.6 Systematic Uncertainties in Permittivity Data Related to Air Gaps . 65 7.5 Permeability and Permittivity Calculation 66 7.5.1 Nicolson-Ross-Weir Solutions (NRW) 66 7.5.2 Modified Nicolson-Ross: Reference-Plane Invariant Algorithm .... 68 7.5.3 Iterative Solution 69 7.5.4 Exphcit Solution 70 7.5.5 NIM Parameter Extraction 70 7.5.6 Measurement Results 71 7.5.7 Measurements of Magnetic Materials 72 7.5.8 Effects of Air Gaps Between the Specimen and the Waveguide for Magnetic Materials 72 7.6 Uncertainty Determination of Combined Permittivity and Permeability Measurements in Waveguide 75 7.6.1 Independent Sources of Uncertainty for Magnetic Measurements ... 75 7.6.2 Measurement Uncertainty for a Specimen in a Transmission Line ... 76 7.7 Uncertainty in the Gap Correction 76 7.7.1 Waveguide Air-Gap Uncertainty for Dielectrics 78 7.7.2 Coaxial Air-Gap Correction for Dielectrics 78 8 Short-Circuited Line Methods 78 8.1 Theory 78 8.2 Measurements 80 IV 9 Permeameters for Ferrites and Metals 81 9.1 Overview of Permeameters 81 9.2 Permeability of Metals 82 9.3 Ferrites and Resistive Materials 83 10 Other Transmission-Line Methods 84 10.1 Two-Port for Thin Materials and Thin Films 84 10.1.1 Overview 84 10.1.2 Scattering Parameters 85 10.2 Short-Circuited Open-ended Probes . 86 10.2.1 Overview of Short-Circuited Probes 86 10.2.2 Mode-Match Derivation for the Reflection Coefficient for the Short-Circuited Probe 87 11 Measurement Methods for Liquids 89 11.1 Liquid Measurements Using Resonant Methods 89 11.2 Open-Circuited Holders 89 11.2.1 Overview 89 11.2.2 Model 1: TEM Model with Correction to Inner Conductor Length . 92 11.2.3 Model 2: Full-Mode Model Theoretical Formulation 93 11.2.4 Uncertainty Analysis for Shielded Open- Circuited Holder 97 11.3 Open-ended Coaxial Probe 99 11.3.1 Theory of the Open-ended Probe 99 11.3.2 Uncertainty Analysis for Coaxial Open-ended Probe 101 12 Dielectric Measurements on Biological Materials 102 12.1 Methods for Biological Measurements 102 12.2 Conductivity of High-Loss Materials Used as Phantoms 103 13 Capacitive Techniques 106 13.1 Overview of Capacitive Techniques 106 13.2 Capacitance Uncertainty 107 13.3 Electrode Polarization and Permittivity Measurements 108 13.3.1 Overview 108 13.3.2 Four-Probe Technique 109 14 Discussion 110 15 Acknowledgments 110 16 References 111 A Review of the Literature on Dielectric Measurements of Lossy Materials 136 B Gap Correction in Dielectric Materials 141 B.l CoELxial Capacitor Model for Dielectric Materials 141 B.2 Rectangular Waveguide Model 144 C Gap Correction for Magnetic Materials 145 C.l Coaxial Capacitor Model for Magnetic Materials 145 C.2 Waveguide Model for Magnetic Materials 147 C.3 Magnetic Corrections for Gaps in the X-Z and Y-Z Planes 148 C.4 Magnetic Corrections for Gaps Across the X-Y Plane 148 C.4.1 Mitigation of the Effects of Air Gaps 148 D Permittivity and Permeability Mixture Equations 148 VI Measuring the Permittivity and Permeability of Lossy Materials: Solids, Liquids, Metals, Building Materials, and Negative-Index Materials James Baker- Jarvis, Michael D. Janezic, Bill Riddle Robert T. Johnk, Pavel Kabos, Christopher L. Holloway Richard G. Geyer, Chriss A. Grosvenor National Institute of Standards and Technology, Electromagnetics Division, MS 818.01, Boulder, CO e-mail:[email protected] Abstract The goal of this report is to provide a comprehensive guide for researchers in the area of measurements of lossy dielectric and magnetic materials with the intent of assembhng the relevant information needed to perform and interpret dielectric measurements on lossy ma- terials in one place. The report should aid in the selection of the most relevant methods for particular applications. We emphasize the metrology aspects of the measurement of lossy dielectrics and the associated uncertainty analysis. We present measurement methods, algo- rithms, and procedures for measuring both commonly used dielectric and magnetic materials, and in addition we present the fundamentals for measuring negative-index materials. Key Words: CaUbration; coaxial line; loss factor; metamaterials; microwave measurements; NIM; permeabihty; permittivity; uncertainty; waveguide. 1. Introduction Many materials used in electromagnetic applications are lossy. The accurate measurement of lossy dielectric materials is challenging since many resonant techniques lose sensitivity when applied to such materials and transmission-line methods are strongly influenced by metal losses. Our goal is to assemble the relevant information needed to perform and interpret dielectric measurements on lossy materials in a single report. Therefore we include sections on the underlying electromagnetics, circuit theory, related physics, measurement algorithms, and uncertainty analysis. We also have included a section on dielectric measurement data we have collected on a wide selection of lossy materials, including building materials, hquids, and substrates. This report should aid in the selection of the most relevant methods for particular applications. With emphasis on metrology, we will introduce the relevant electromagnetic quantities, overview a suite of measurements and methods, develop the relevant equations from first principles, and finally include the uncertainties in the measurement processes. There is a continual demand for accurate measurements of the dielectric and magnetic properties of lossy solids and liquids [1]. T5rpical applications range from dielectric measure- ments of biological tissues for cancer research, building materials, negative index materials, electromagnetic shielding, to propagation of wireless signals. In this report, the term loss will refer to materials with loss tangents greater than approximately 0.05. Measurements without well-characterized uncertainties are of dubious value. Variations in the repeatability of the measurement are not sufficient to characterize the total uncertainty in the measmement. Therefore, in this report, we pay particular attention to uncertainty analysis. Over the years, there has been an abundance of methods developed for measuring elec- tromagnetic permeability and permittivity. These techniques include free-space methods, open-ended coaxial-probe techniques, cavity resonators, dielectric-resonator techniques, and transmission-Une techniques.