Americas TM Contact Center

Americas TM Contact Center
1/10/2006 Materials Measurement Techniques & Applications Dr. Stoyan Ganchev Americas TM Contact Center

Agenda 85070E/85071E Product Overview Fundamentals
1/10/2006 Agenda 85070E/85071E Product Overview Fundamentals Measurement Instruments Considerations in choosing a Technique and Fixture Measurement Techniques Parallel Plate Coaxial Probe Transmission Line Free-Space Resonant Cavity The class starts with a review of fundamentals of making material measurements. Then we will focus on LF/RF and RF/MW material measurements.

1/10/2006 Objectives Introduce the Agilent Technologies dielectric measurements solutions Provide basic education on dielectric measurements Provide guidance in choosing the best measurement technique for a given application Give practical information for improving measurements The objective of the class is to provide a tutorial on dielectric (magnetic) material measurements, to increase awareness of measurement solutions, to recommend guidelines for choosing of the best technique, and to share best measurement practices.

1/10/2006 Agenda 85070E/85071E Product Overview Fundamentals Measurement Instruments Considerations in choosing a Technique and Fixture Measurement Techniques Parallel Plate Coaxial Probe Transmission Line Free-Space Resonant Cavity We will start with short overview of the two products 85070E and 85071E.

When you order only 85070E, this will include:
1/10/2006 Two Products 85070E 85071E When you order only 85070E, this will include: Dielectric Probe Software on CD-Rom mounting bracket to connect probe to Option 001 Probe Stand or similar stand ECal holder to connect to mounting bracket Type-N male to 3.5 mm male adapter, 3.5 mm male to 2.4 mm female adapter 11901D foam lined walnut box Includes: Software IMPORTANT: Depending on the transmission line the customer will need additionally fixture, that may be air coaxial line or waveguide and appropriate calibration kit. For free space measurement the two antennas should be purchased from third parties. The dielectric probe kit when configured correctly will have all necessary parts to start measurements (the probe, software, cable, calibration means, adapters, etc.). Only network analyzer and computer with HP-IB are needed additional. When using PNA, computer is not required. In the case of 85071E, only the software is provided. The slim probe that can be used up to 50 GHz is new addition to 85070E. The GRL (Gated Reflect Line) algorithm is the new option in 85071E. IMPORTANT: The configuration should specify additionally the type of probe, cable and other options (see next slide).

Main Options Model Number Description 85070E 020 030 050
1/10/2006 Main Options Model Number Description 85070E 020 030 050 Dielectric Probe Kit High Temperature Probe Slim Form Probe Performance Probe 85071E 100 200 300 Materials Measurement Software Free Space Calibration Reflectivity Software Resonant Cavity Software

Options for 85070E Options (probes) Options (other)
1/10/2006 Options for 85070E Options (probes) 020 - High Temperature Probe (200 MHz to 20 GHz), includes: High Temperature Probe Calibration Short 030 - Slim Form Probe Kit (500 MHz to 50 GHz), includes: 3 Slim Form probes Calibration short 10 mm diameter sealed probe holder 6 O-rings 050 - Performance Probe Kit (500 MHz to 50 GHz), includes: Performance Probe Mounting accessories Options (other) 001 - Probe Stand 002 - High Temperature Cable GHz Flexible Cable GHz Flexible Cable 033 - Slim form probe replenishment kit, contains 3 extra Slim Form Probes Security Key - (Must choose one) UL7 - Parallel Hardware Key (required for Windows NT® 4.0) UL8 - USB Hardware Key 85070EU-070 Software upgrade from older version There are many new option for 85070E. Now which probe you will chose is optional. The same applies for the cable. Please note that the software upgrade is not an option to the main number, but 85070EU-070.

What is in options 020 and 030 for 85070E?
1/10/2006 What is in options 020 and 030 for 85070E? 020 030 Short Short O-rings Holder Probes Probe This pictures show what exactly you will get if you order the high temperature probe (opt. 020) and the slim probe (opt. 030). 020 High Temperature Probe Kit (200 MHz to 20 GHz) High Temperature Probe Calibration Short 030 - Slim Form Probe Kit (500 MHz to 50 GHz), Includes: 3 Slim Form probes Calibration short 10 mm diameter sealed probe holder 6 O-rings

What is in option 050 for 85070E? 050 Short Probe
1/10/2006 What is in option 050 for 85070E? 050 Short Probe 050 Performance Probe Kit (500 MHz to 50 GHz) Performance Probe Calibration Short

85070E Configurations Chose probe, one, two or all three
1/10/2006 85070E Configurations 85070E Chose probe, one, two or all three High temperature 030 - Slim form probe 050 - Performance probe Chose cable GHz Flexible Cable GHz Flexible Cable 002 - High Temperature Cable This is a convenient flow chart to help you configure 85070E probe kit. Chose security key (one) UL7 - Parallel Security Key UL8 - USB Security Key

1/10/2006 Options for 85071E Options 100 - Free Space Calibration Option. Provides Gated Reflect Line (GRL) calibration technique for free space measurement method. 200 Arch Reflectivity Software automates measurements made with the NRL Arch technique Options 100 and 200 are only compatible with PNA and 8510C network analyzers with Time Domain Option installed. 300 Resonant Cavity Software 071 - Upgrade from any older version of software Security Key - (Must choose one) UL7 - Parallel Software Security Key UL8 - USB Software Security Key This is a list of all of the options for 85070E.

Gated Reflect Line (GRL) features
1/10/2006 Option 100, GRL Gated Reflect Line (GRL) features converts a coaxial/waveguide 2-port calibration into a full 2-port free-space calibration requires a PNA or an 8510 network analyzer with the time domain option, an appropriate free-space fixture and a metal plate for calibration. includes also a gated isolation/response calibration to reduce errors from diffraction effects at the sample edges, and multiple residual reflections between the antennas accurate free space measurements are now possible without expensive spot focusing antennas, micro positioning fixturing or direct receiver access. the software automatically sets up all the free space calibration definitions and network analyzer parameters. for PNA, additional ease and timesaving is provided with ECal. a guided calibration wizard steps the user through the calibration process. Free Space Calibration Option increases ease of use and reduces the costs associated with TRM and TRL calibration methods. The new Gated Reflect Line (GRL) calibration technique converts a coaxial/waveguide 2-port calibration into a full 2-port free space calibration. Use of this option requires an 8510 or a PNA Series network analyzer with the time domain option, an appropriate free space fixture and a metal calibration plate. This option also includes a gated isolation/response calibration, which reduces errors from diffraction effects at the sample edges, and multiple residual reflections between the antennas. Accurate free space measurements are now possible without expensive spot focusing antennas, micro positioning fixturing or direct receiver access. The software automatically sets up all the free space calibration definitions and network analyzer parameters, saving engineering time. In the PNA, additional ease and timesaving is provided with ECal, electronic calibration. A guided calibration wizard steps the user through the easy calibration process.

Reflectivity Software
1/10/2006 New feature for 85071E: Option 200, Reflectivity Software Reflectivity Software Option 200 provides a separate software program that automates NRL (Naval Research Lab) arch measurements. The program guides you through the complete process of setup, calibration and measurement of material absorption. Measurements are displayed in both a graphical and tabular form — with up to four measurements displayed simultaneously for comparison. The software includes markers to aid in measurement analysis, and complete measurement results and setup can be saved and recalled. Also, data can be saved in a spreadsheet compatible file format or copied into other applications for further analysis.

Resonant Cavity Software
1/10/2006 New feature for 85071E: Option 300, Resonant Cavity Software Resonant Cavity Software Can control and measure dielectric properties with two types of resonators: Waveguide TE10n resonator using perturbation technique as described in ASTM 2520 Split Dielectric Post Resonator (SPDR) for measuring of substrate materials or thin films

What more you will need? 85070E 85071E Network Analyzer
1/10/2006 What more you will need? 85070E 85071E Network Analyzer Computer with IEEE-488 interface card and HP-IB cable (Not required for PNA family) Network Analyzer Computer with IEEE-488 interface card and HP-IB cable (Not required for PNA family) Fixture Coaxial Waveguide Two antennae NRL Arch Resonator(s) For both products additionally is needed network analyzer and computer with HP-IB card and cable. The computer is not required for the PNA family. For 85071E software additionally is needed fixture (coaxial or waveguide) and in the case of free-space measurements, two antennae.

Key features of both 8507xE Software
1/10/2006 Key features of both 8507xE Software Runs internally on the PNA series of network analyzers or on external computer for the other network analyzer families View measurement results in a variety of formats Measurement markers simplify measurement analysis Split screen view shows measurement results simultaneously as a plot and a table Ability to copy/paste measurement results to other applications in either plot or table format. Data is easily shared with other Windows® based programs or through the user programmable Component Object Model (COM) interface Here is a list of the key features of both software.

Key features (continued)
1/10/2006 Key features (continued) Compatible with Windows® 98, 2000, ME, XP, or Windows NT® 4.0 (Windows NT® 4.0 requires Option UL7 Parallel Security Key) Supports both Agilent Technologies and National Instruments GPIB cards (IEEE-488) COM interface allows the measurements to be setup, triggered and read from a user written program. Compatible with a variety of network analyzer families 85070E is compatible with E4991A impedance analyzer Here is a list of the key features of both software. Important new addition is that 85070E dielectric probe is already compatible with two Kobe instruments: E4991A and the obsolete 4291B. This not only improves the low frequency coverage of the probe (starting 10 MHz for the high temperature probe), but also gives the customers more options for dielectric measurement solutions.

New feature 85070E: Cal refresh with ECal
1/10/2006 New feature 85070E: Cal refresh with ECal Calibration Refresh with ECal will reduces drift errors ECal Holder The new automated Electronic Calibration Refresh feature recalibrates the system automatically, in seconds, just before each measurement is made. This virtually eliminates cable instability and system drift errors. Processes can now be monitored over long time periods, including tests that vary MUT temperature and pressure over time. How it works: The Agilent Electronic Calibration module (ECal) microwave ports are connected in line between the probe and the network analyzer test port cable. The ECal module communication port is connected either to the PC or PNA Series network analyzer running the 85070E software. The software guides the user through a normal “three standard” calibration, (usually open, short, water), performed at the end of the probe. This calibration is then transferred to the ECal module. The ECal module remains in line and a complete ECal calibration is automatically performed before each measurement. Errors due to test port cable movement are removed by the new calibration. This measurement shows the effects of system drift and cable instability on a dielectric measurement of water and the improvement with Electronic calibration refresh. Both measurements were made 24 hours after the original calibration. The lighter colored, noisier, trace was made before the Electronic Calibration refresh was turned on. The darker, smoother, trace shows the improvement made after the Electronic Calibration refresh was turned on. For systems without an ECal module, a simpler, "one standard" refresh calibration feature is also available, which can reduce the effects of system drift over time or temperature. After the initial "three standard" probe calibration is performed, the calibration can be refreshed at any time with the connection of a single standard. Any one of the three calibration standards can be defined as the refresh standard. Water measurement with and without ECal calibration refresh.

Software Menus for 85070E File
1/10/2006 Software Menus for 85070E File Save or recall measurement setups or previous measurement results. Print copies of the measurement results in a tabular or graphical format. Edit Copy the measurement results to the clipboard. Either graph or the tabular listing can be copied. This allows your measurement results to be pasted into other applications. View Select the section you want to view. Selections include the toolbar, status bar, table of the measurement data and chart of the measurement data. Calibration Select the frequency range, number of points, linear or log sweep. Guided calibration sequence; choice of calibration materials or user-specified; refresh calibration for single standard or ECal; recalibration versus temperature; automatic refresh on or off.

Software Menus for 85070E (continued)
1/10/2006 Software Menus for 85070E (continued) Measure: Trigger a measurement. Chart: Select the format to be displayed on the chart. Choices include er’, er’’, loss tangent and Cole-Cole. Set Graticule scale factors or “autoscale”. Select from linear, semi-log or log-log representations. Table: Choose between different tabular formatting (er` and er`` or er` and tand) Display: Display current measurement data; save/display up to 3 memory traces; compare data to reference trace with trace math. Turn the marker on or off. Preferences: Select your preference of fonts, colors and annotations used to plot and list the measurement data. Help: On-line help including the product manual. Toolbar: Provides single click access to the most important menu items.

1/10/2006 Visual Basic Example Dim material As AUTOMATION8507XLib.Automation85070 Private Sub Calibrate_Click() Call material.CalibrateProbe End Sub Private Sub Form_Load() Set material = CreateObject("AUTOMATION8507X.Automation85070") Call material.Init Private Sub Measure_Click() Dim num As Long Dim er As Single Dim ei As Single Dim f As Single Call material.TriggerProbe Call material.GetMeasurement(5, f, er, ei) Here is an example of how to trigger measurement. This may be important when the customer needs to take many measurements in short time to investigate fast changing process.

Legacy Network Analyzer Families
1/10/2006 Compatible HP/Agilent Network and Impedance Analyzers PNA, PNA-L MHz to 110 GHz ENA, ENA-L KHz to 8.5 GHz E4991A up to 3 GHz (with 85070E) Legacy Network Analyzer Families 8712/14 , 8719/20/22, 8510B/C Notes: 1. Options 100 and 200 of 85071E work only with PNA or 8510 with time domain option. 2. Out of support instruments “should” work with 85070/1E, but it is not warranted, because the compatibility has not been established. 85070E and 85071E are compatible with nearly all of our network analyzers. Important new addition is that 85070E dielectric probe is already compatible with two Kobe instruments: E4991A and the obsolete 4291B. This not only improves the low frequency coverage of the probe (starting 10 MHz for the high temperature probe), but also gives the customers more options for dielectric measurement solutions.

PC Requirements Windows® 95, 98, Me, NT 4.0 or NT 2000, XP
1/10/2006 PC Requirements Windows® 95, 98, Me, NT 4.0 or NT 2000, XP GPIB interface card with a compatible driver (Agilent SICL or National Instruments 488.2M)* CD drive * Note, the 8507xE can be installed and run on a PNA series analyzer eliminating the need for both a PC and a GPIB card. To install the 8507xE on a PNA analyzer a PC with a CD drive is required to copy the 85070E installation files from the supplied CD to 3.5-inch disks or a USB CD drive to hook to PNA. The PC requirements are very moderate. PC is not needed for PNA.

Customer Downloadable Demos Available on the Web
1/10/2006 Customer Downloadable Demos Available on the Web Demo programs are available on the web. Please start from this URL:

1/10/2006 Agenda 85070E/85071E Product Overview Fundamentals Measurement Instruments Considerations in choosing a Technique and Fixture Measurement Techniques Parallel Plate Coaxial Probe Transmission Line Free-Space Resonant Cavity

Origin of Microwave Dielectric Measurements
1/10/2006 Origin of Microwave Dielectric Measurements Why now, 60 years later, are these measurements still so important?

Why make measurements? Development of new materials Controlling a
1/10/2006 Why make measurements? Development of new materials Controlling a manufacturing process Every material has a unique set of electrical characteristics that are dependent on its dielectric properties. Accurate measurements of these properties can provide scientists and engineers with valuable information to properly incorporate the material into its intended application for more solid designs or to monitor a manufacturing process for improved quality control. A dielectric materials measurement can provide critical design parameter information for many electronics applications. For example, the loss of a cable insulator, the impedance of a substrate for microwave integrated circuit, or the frequency of a dielectric resonator can be related to its dielectric properties. The information is also useful for improving ferrite, absorber, and packaging designs. More recent applications in the area of industrial microwave processing of food, rubber, cement, plastic and ceramics have also been found to benefit from a knowledge of dielectric properties. Shorter design cycles Higher performance Reduced scrap Incoming inspection of materials

Extremely Diverse Applications
1/10/2006 Extremely Diverse Applications “Materials” can mean just about anything. They are produced or used by many diverse industries. For example, customers use network analyzers to measure: radar-absorbing “stealth” coatings disposable diapers cookie dough moisture in asphalt roads ceramics for microwave sintering/annealing washed coal cement biological tissues (including blood, brain tissue simulation) many, many others What can these people have in common??? Only one thing: Need to measure the dielectric properties!!! Extremely Diverse "Materials" can mean just about anything. They are produced or used by many diverse industries. Our customers use Agilent network analyzers to measure very “unexpected” for us things. What can these people have in common??? Only one thing: Electro-magnetic measurements, from 20 Hz to 100 GHz, provided useful information about their material - better, faster, and more accurately than other methods.

Industries, Products, Measurement Needs
1/10/2006 Industries, Products, Measurement Needs Market Segments -- Let's segment these customers in terms of their experience with microwave equipment in general and network analysis in particular. India Presnetation, SIG, Americas TM Contact Center

1/10/2006 List of Applications

List of Applications (continued)
1/10/2006 List of Applications (continued) Here are some Trade Groups and Professional Societies Related to Materials Measurements: MRS -- Materials Research Society IMPI – International Microwave Power Institute IFT – Institute of Food Technologists BEMS – Bioelectromagnetics Society ACS – American Chemical Society ASTM – American Society of Testing of Materials ASNT – American Society of Nondestructive Testing QNDE -- Quantitative Nondestructive Evaluation

Parallel Plate Capacitor (DC)
1/10/2006 Parallel Plate Capacitor (DC) t A - + V A material is classified as “dielectric” if it has the ability to store energy when an external electric field is applied. If a DC voltage source is placed across a parallel plate capacitor, more charge is stored when a dielectric material is between the plates than if no material (a vacuum) is between the plates. The dielectric material increases the storage capacity of the capacitor by neutralizing charges at the electrodes which ordinarily would contribute to the external field. The capacitance with the dielectric material is related to dielectric constant. Capacitance with no dielectric (vacuum) Dielectric constant or permittivity (real)

Parallel Plate Capacitor (AC)
1/10/2006 Parallel Plate Capacitor (AC) I + A V t - + - + - + - + - + C G - + - + - + - if If an AC sinusoidal voltage source is placed across the same capacitor, the resulting current will be made up of a charging current and a loss current that are related to the real and imaginary dielectric constant. The losses in the material can be represented as a conductance (G) in parallel with a capacitor (C). The complex dielectric constant k consists of a real part k’ which represents the storage and an imaginary part k’’ which represents the loss. The following notations are used for the complex dielectric constant interchangeably k = k* = er = er*. then

Permittivity (electromagnetic fields)
1/10/2006 Permittivity (electromagnetic fields) Definition of electric displacement (electric flux density) Absolute permittivity or permittivity Relative permittivity or dielectric constant Considerations from point of view of electromagnetic theory. Permittivity (e) describes the interaction of a material with an electric field. Dielectric constant (k) is equivalent to relative permittivity (e r ) or the absolute permittivity (e) relative to the permittivity of free space (e0). The real part of permittivity (er’) is a measure of how much energy from an external electric field is stored in a material. The imaginary part of permittivity (er”) is called the loss factor and is a measure of how dissipative or lossy a material is to an external electric field. Free space permittivity

Permittivity is complex
1/10/2006 Permittivity is complex The permittivity is often called dielectric constant, but is changing with frequency and temperature. storage loss Permittivity Measure of how much energy from an external electric field is stored in the material Permittivity (e) describes the interaction of a material with an electric field. Dielectric constant (k) is equivalent to relative permittivity (er = e/ e0), or the permittivity relative to free space. The real part of permittivity (er’) is a measure of how much energy from an external electric field is stored in a material. The imaginary part of permittivity (er") is called the loss factor. It is a measure of how dissipative or lossy a material is to an external electric field. The imaginary part of permittivity (er") is always > 0 and is usually much smaller than (er’). The loss factor includes the effects of both dielectric loss and conductivity. Although it is called dielectric constant, (er) changes with frequency. Loss factor Measure of how much dissipative or lossy a material is to an external field

Loss Tangent Dissipation Factor Quality Factor 1/10/2006
When complex permittivity is drawn as a simple vector diagram, the real and imaginary components are 90o out of phase. The vector sum forms an angle d with the real axis (er’). The relative “lossiness” of a material is the ratio of the energy lost to the energy stored. Here tand = loss tangent = tan delta = tangent loss = dissipation factor In some cases is used the term “quality factor or Q-factor” with respect to an electronic microwave material. Quality Factor Dissipation Factor

Optical Dielectric Parameters
1/10/2006 Optical Dielectric Parameters n* - complex index of refraction n – (real) index of refraction k – index of absorption Light is electromagnetic wave at very high frequencies, so microwaves will follow the same laws of geometrical optics. The index of refraction is often used at optical wavelengths and relates to the dielectric constant e. The dielectric constant can change significantly with the frequency. For example for water at 3 GHz er’ = 77, but at optical frequencies er’ = 1.75. g - complex propagation factor a – attenuation coefficient (factor) b – phase coefficient

Snell’s Law and Critical Angle for Total Internal Reflection
1/10/2006 Snell’s Law and Critical Angle for Total Internal Reflection Snell’s Law Critical angle for total reflection The optical properties hold for the entire electromagnetic spectrum. An example is the Snell’s law of refraction. Another example is the critical angle for total internal reflection – it is basis for not only optical fibers, but also for dielectric waveguides that are used in the millimeter wave region.

1/10/2006 Propagation Factor The electromagnetic fields of a plane wave, propagating through a material are function of time t and distance x. Angular frequency w forms relation to time. There is a relation between the complex propagation factor and the material properties (both dielectric and magnetic). The complex propagation factor g describes relation to distance and depends on the material properties. Attenuation Factor Phase Factor

Attenuation Factor Derivation
1/10/2006 Attenuation Factor Derivation For non magnetic dielectric After taking a square of both sides of the above equation It is possible to find direct relation between the attenuation factor a and the phase factor b with the dielectric constant (real and imaginary). Next step is to equate the real and imaginary parts of both sides. We can find expression for the attenuation and phase factor with respect to the real and imaginary dielectric constant or expression of the real and imaginary dielectric constant with respect of attenuation and phase factor.

Attenuation Factor and Phase Factor
1/10/2006 Attenuation Factor and Phase Factor When you split the complex equation from the previous page to real and imaginary equations, the system can be solved with respect to a and b or real and imaginary dielectric constant.

Attenuation Factor Calculation
1/10/2006 Attenuation Factor Calculation Normally we would measure attenuation in dB/m, not in Neper/m. Here are several convenient equation to calculate the attenuation factor in dB/m. The last equation is the simplest, but presumes that the tand << 1. The frequency is in GHz for convenience.

Attenuation Factor Calculation
1/10/2006 Attenuation Factor Calculation 0.03 Teflon Example 0.02 0.01 The attenuation is in dB/cm. This means that attenuation of 1 cm thick sample is calculated for different frequencies. The graph shows the attenuation of a 1 cm of Teflon for different frequencies. It is obvious that 1 cm is not enough thickness for a good measurement in the whole frequency range. There are two ways to get measurable attenuation: use longer sample measure at higher frequency if possible 10 20 30 40 50

Attenuation Factor Calculation (continued)
1/10/2006 Attenuation Factor Calculation (continued) Water Example In the previous example for Teflon we did calculate the attenuation versus frequency using one and the same value of the complex dielectric constant, because the dielectric constant of Teflon will not change with the frequency like most of the low loss materials. The dielectric properties of water though will change substantially with frequency like most of the lossy materials. For this reason the frequency dependence of the attenuation of water is not calculated. This an example of the attenuation of a lossy material – water. The calculation is for specific frequency, because the dielectric properties will change with frequency.

Attenuation Factor Calculation (continued)
1/10/2006 Attenuation Factor Calculation (continued) How the attenuation depends on the dielectric constant and loss tangent? 10 20 0.02 0.04 0.05 0.1 0.15 0.2 1 2 3 Till now we considered the frequency dependence of the attenuation factor. Here is demonstrated how it will depend on the dielectric constant and loss tangent.

Penetration (or Skin) Depth
1/10/2006 Penetration (or Skin) Depth Field strength decays exponentially over distance d Power is square of the field strength The field penetration depth or skin depth D is the distance through homogeneous material over which the electric field strength falls to 1/e or or 36.8% of initial value. E0 In many cases is important to know how the field will attenuate when it penetrated the dielectric. The measure of this is the penetration or skin depth which is the distance at which the electric field strength becomes 1/e of the initial value (the value of the field strength when entering the dielectric).

Power Penetration Depth
1/10/2006 Power Penetration Depth The power penetration depth Dp is two times less than the field penetration depth D. Half-power depth It is important to understand about what penetration depth the customer talks. The power penetration depth is different from the field penetration depth (it is twice less). Half-power penetration depth is in turn different than the power penetration depth. Using the above examples any power penetration depth can be calculated.

Inductance of coil in free space
1/10/2006 Inductor Core material R L Real permeability Permeability (m) describes the interaction of a material with a magnetic field. A similar analysis can be performed for permeability using an inductor with resistance to represent core losses in a magnetic material. If a DC current source is placed across an inductor, the inductance with the core material can be related to permeability. Inductance of coil in free space

Permeability is complex
1/10/2006 Permeability is complex storage loss Free space permeability Absolute permeability The complex permeability (m) consists of a real part (m’) that represents the energy storage and a an imaginary part (m“) that represents the energy loss term. Relative permeability (mr) is the absolute permeability (m) relative to the permeability of free space (m0). Some materials such as iron (ferrites), cobalt, nickel and their alloys have appreciable magnetic properties; however, many materials are non-magnetic. All materials, on the other hand, have dielectric properties. Relative permeability

Electromagnetic Field Interaction
1/10/2006 Electromagnetic Field Interaction STORAGE Electric Magnetic Fields Fields LOSS Permittivity Permeability MUT When electric and magnetic fields pass through a material, each can interact with that material in two ways: Storage: Energy may be exchanged between the field and the material, in a bi-directional (lossless) manner Loss: Energy may be permanently lost from the field, and absorbed in the material (usually as heat) The electric interactions are quantified by permittivity (er), also called dielectric constant (k). The magnetic properties are described by permeability (mr). These are complex numbers with real and imaginary parts: Real Part: Represents storage term; denoted with ‘ Imaginary Part: represents loss term; denoted with “. This presentation focuses on permittivity, since most of the common materials are completely non-magnetic. STORAGE LOSS Dielectric Constant

Electromagnetic Field Interaction
1/10/2006 Electromagnetic Field Interaction h or Z0 TEM h or Z0 is the free-space impedance which is 120p = 367 W. MUT Air Impedance lower Wavelength shorter Velocity slower Magnitude attenuated Let’s use the “optical view” of dielectric behavior. Consider a flat slab of material in space, with a wave incident on its surface. We will have incident, reflected and transmitted waves. Since the impedance of the wave in the material is different (lower) from the free space impedance, there will be impedance mismatch and this will create the reflected wave. Part of the energy will penetrate the sample. Once in the slab, the wave velocity is slower and the wavelength is shorter according the equations above. Since the material will always have some loss, there will be attenuation or insertion loss. For simplicity the mismatch on the second border is not considered.

Reflection Coefficient versus Dielectric Constant
1/10/2006 Reflection Coefficient versus Dielectric Constant 10 20 30 40 50 60 70 80 90 100 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Dielectric Constant Reflection coefficient G air MUT For nonmagnetic lossless dielectric On the graph is depicted the relation between the dielectric constant of the MUT (Material Under Test) and the reflection coefficient. It is important to note that for small dielectric constant (less than 20, approximately), there is a lot of change of the reflection coefficient for a small change of the dielectric constant. From this follows that the dielectric measurement using the reflection coefficient will be more sensitive and hence precise. Conversely, for high dielectric constants (for example between 70 and 90) there will be little change of the reflection coefficient and the measurement will have more uncertainty. All of the above simple modeling presumes infinite thickness of the MUT.

Measuring of Infinitely Long Sample in Waveguide
1/10/2006 Measuring of Infinitely Long Sample in Waveguide air sample No reflection here Waveguide flange G air MUT Previous simple considerations for “infinitely long sample” can be applied in a simple measurement method for liquid or powder material. The test fixture is a waveguide matched load and we fill it with the MUT. There will be no reflection from the back of the sample, so the condition for infinite sample will hold. - complex reflection coefficient (s11) l - free-space wavelength a - broad waveguide dimension Waveguide matched load

Dielectric Properties (at 3 GHz)
1/10/2006 Dielectric Properties (at 3 GHz) Low Loss Lossy 100 Water Salt TiO Water 2 50 Steak 20 Alumina 10 Alcohol PC Board 5 Quartz 20% Wood This graph has er’ (storage) along the vertical axis, and tand (loss) on the horizontal axis (both logarithmic). The values for several common materials are shown as dots (at a single frequency and temperature). “Low-loss” materials, such as Teflon, have small values of tan d. They are commonly used in electronic applications such as: insulators (e.g. for cables), substrates, and dielectric resonators. “High-loss” materials include water, food, and many natural materials. These materials quickly absorb microwave energy, and so are not used for electronic components. However, they are important to: understanding microwave radiation in the “real world” material analysis (e.g. moisture content) high-power microwave processing (heating and drying) Mylar Ice 10% 2 Teflon 0% Air 1 .00001 .0001 .001 .01 .1 1

Dielectric Mechanisms vs. Frequency
1/10/2006 Dielectric Mechanisms vs. Frequency Dipolar (Rotational) Atomic Electronic 10 3 6 9 12 15 f, Hz + - V IR MW UV Ionic Electric Polarization Conductivity At the microscopic level, several dielectric mechanisms can contribute to dielectric behavior: Dipole orientation (and ionic conduction) interact strongly at microwave frequencies. Water molecules, for example, are permanent dipoles, which rotate to follow an alternating. electric field. These mechanisms are quite lossy – which explains why food heats in a microwave oven. Atomic and electronic mechanisms are relatively weak, and usually constant over the microwave region. Each dielectric mechanism has a characteristic “cutoff frequency.” As frequency increases, the slow mechanisms drop out in turn, leaving the faster ones to contribute to e’. The magnitude and “cutoff frequency” of each mechanism is unique for different materials. Water has a strong dipolar effect at low frequencies - but its dielectric constant rolls off dramatically around 22 GHz. Teflon, on the other hand, has no dipolar mechanisms -so its permittivity is remarkably constant well into the millimeter-wave region.

Dipole and Hydrogen Atom in Electric Field
1/10/2006 Dipole and Hydrogen Atom in Electric Field - + E F T The static electric field will exercise torque on the electric dipole which will tend to align this dipole in the direction of the field. If the field changes the direction, so will the torque. The friction accompanying the orientation of the dipole will contribute to the dielectric losses. Here is an example of how a dipole (like water) will interact with electric field. The dipole will rotate to align in the direction of the field. The rotation is accompanied with friction that will account for the attenuation. The other example is of electronic polarization of the simplest atom, the Hydrogen. In this case the electric field will just distort the orbit. This loss mechanism is much weaker. + - H E Electronic polarization causes distortion of the electron orbit in the presence of electric field.

Debye Relaxation for Water at 30oC
1/10/2006 Debye Relaxation for Water at 30oC 0.1 1 10 100 20 40 60 f, GHz The static (DC) value of dielectric constant or e for f = 0 the optical (infinite frequency) dielectric constant or e for f = These are theoretical curves calculated using the Debye relaxation model for water at 30 degrees C. This model works very well for water. At low frequencies, the dipoles can “follow” the field and e’ will be high. At high frequencies, the dipoles can not follow the rapidly changing field - and e’ falls off. The resonance character of the attenuation (the imaginary part of the dielectric constant) can be explained in a similar way. Before the resonance the loss is increasing because the dipoles still can totally orient when the electric field changes direction, so the loss is proportional to the frequency. After resonance the frequency is so high that the dipoles do not have enough time to orient, so there is less friction and less losses. the angular frequency the relaxation time

Cole-Cole Plots (Water)
1/10/2006 Cole-Cole Plots (Water) o 20 C Increasing f (GHz) 40 23.7 9.14 34.9 30 34.9 o 23.7 4.63 60 C 20 3.25 The complex permittivity may also be shown on a Cole-Cole diagram by plotting the imaginary part (er”) on the vertical axis and the real part (er‘) on the horizontal axis with frequency as the independent parameter. Above are Cole-Cole plots for water for two temperatures. The curves are theoretical, but show also measurement points. A material that has a single relaxation frequency as exhibited by the Debye relation will appear as a semicircle with it center lying on the horizontal er” = 0 axis and the peak of the loss factor occurring at l/t. A material with multiple relaxation frequencies will be a semicircle (symmetric distribution) or an arc (nonsymmetrical distribution) with its center lying below the horizontal er” = 0 axis. For high-loss materials, both er‘ and er” change dramatically with frequency. A Cole-Cole plot (similar to a Smith chart) is often used to plot the “frequency response” of materials. Simple lossy materials (e.g. water) scribe a semi-circle on a Cole-Cole plot. More complex materials may form an ellipse, or an arc with bumps on it. The two traces demonstrate that er‘ (for water) changes dramatically with temperature. as well as frequency. 9.14 10 1.74 4.63 0.58 10

Cole-Cole Plot Explanation
1/10/2006 Cole-Cole Plot Explanation 10 20 30 40 50 60 70 Increasing f (GHz) Center Let’s study some important properties of the Cole-Cole plot of Debye model. From the Debye equation we can calculate the er’ for frequency 0 and infinity. The curve is half circle with center on the x axis and radius The maximum imaginary part of the dielectric constant will be equal to the radius The frequency moves counter clock wise on the curve.

Relaxation Time t Dipolar (orientation polarization) Water at 20o C
1/10/2006 Relaxation Time t 1 10 100 Water at 20o C f, GHz fc = 22 GHz (t = 7.2 psec) Time t required for 1/e of a perturbed (aligned) system to return to equilibrium (random state). Dipolar (orientation polarization) + - For dipolar dielectrics (such as water), a “relaxation constant” t describes the time required for dipoles to become oriented in an electric field. (Or the time needed for thermal agitation to disorient the dipoles after the electric field is removed.) At low frequencies, the dipoles can “follow” the field and e’ will be high. At high frequencies, the dipoles can not follow the rapidly changing field - and e’ falls off. The loss factor e” peaks at the frequency 1/t. Here, energy is transferred into the material at the fastest possible rate.

Other Empirical Models
1/10/2006 Other Empirical Models Only few materials exhibit pure relaxation properties with single relaxation time that are described with the Debye equation. The Cole-Cole model is used in determination of user defined standard for coaxial dielectric probe. Cole-Davidson model Only few materials exhibit pure relaxation properties with single relaxation time that are described with the Debye equation. There are many other empirical expressions that will describe better the frequency dependent behavior of materials with more than one relaxation times or distribution of relaxation times. Such are the Cole-Cole equation and Cole-Davidson equation. Based on the above equation the Cole-Cole model is used for determining of a user-defined standards for coaxial probes. the relaxation time constant the relaxation width (distribution parameter) distribution parameter that leads to asymmetric distribution of t

Comparison Between the Different Models
1/10/2006 Comparison Between the Different Models Debye Cole-Davidson b = 0.5 Cole-Cole a = 0.2 10 20 30 40 50 60 70 This is theoretical calculation of the different models, represented with equations on the previous slide. The values of a and b are chosen to show the difference between the models and necessarily does not represent

Measurement Instruments
1/10/2006 Measurement Instruments LCR Meters and Impedance Analyzers Impedance/Material Analyzer Network Analyzers

4294A Precision Impedance Analyzer
1/10/2006 4294A Precision Impedance Analyzer 16451B 16452B and 16454A Fixtures Frequency Range: 40 Hz to 110 MHz. Allows highly accurate measurements of various materials such as printed circuit boards, ceramic and insulating materials (16451B Dielectric Test Fixture), liquids (16452A Liquid Test Fixture) and magnetic materials (16454A Magnetic Material Test Fixture).

Permittivity Measurements using the 4294A
1/10/2006 Permittivity Measurements using the 4294A System Configuration 4294A Precision Impedance Analyzer 16451B Dielectric Test Fixture Characteristics of Measurement System Frequency: 40 Hz - 30 MHz Operating Temperature: 0o C to +55o C Applicable Material Shape: A solid which is flat and smooth. Applicable Material Size: Depends on the characteristics of the test material (MUT) and the measurement method. Type of Electrodes: 4 electrodes are furnished for different types of materials. The contacting and non-contacting electrode methods are applicable. For more information please refer to Product Note (or old AN , 380-1).

4294A Electrode Considerations
1/10/2006 4294A Electrode Considerations When using the electrodes A and B, caution must be taken when measuring a material which is not smooth or changes thickness when pressure is applied. If such a material is to be tested, the non-contacting method can be used, but the material must be at least a few millimeters thick. When testing material which has thickness of less than a few hundred micrometers, it is recommended to apply a thin film electrode to the surface of the material and measure with electrodes C and D. If this method is employed, make sure that the resistance of the thin film electrode is small.

Permittivity and Loss Tangent
1/10/2006 Characteristics of PCB measured using 4294A and 16451B Permittivity and Loss Tangent of Glass Epoxy Settings of 4294A OSC LEVEL: 500mV Frequency: 1kHz-30MHz Parameters: εr´ and tan δ BW: 5 Compensation: OPEN/SHORT/LOAD LOAD STD: Air (3pF) Settings of 16451B Electrode: Type B Measurement Method: Contacting

Cole-Cole Plot of Ceramic Material
1/10/2006 Characteristics of PCB measured using 4294A and 16451B Cole-Cole Plot of Ceramic Material Settings of 4294A OSC LEVEL: 500mV Frequency: 300Hz-30MHz BW: 5 Compensation: OPEN&SHORT&LOAD LOAD STD: Air (1pF) Settings of B Electrode: Type C Measurement Method: Contacting

Permeability Measurements using
1/10/2006 Permeability Measurements using 4294A and 16454A System Configuration 4294A Precision Impedance Analyzer 42942A Terminal Adapter 16454A Magnetic Material Test Fixture 16454A Magnetic Material Test Fixture Characteristics of Measurement System Frequency: 40 Hz MHz Operating Temperature: 0o C to +55o C Applicable Material Shape: next slide Applicable Material Size: next slide For more information please refer to AN

Applicable MUT sizes for 16454A Test Fixture
1/10/2006 Applicable MUT sizes for 16454A Test Fixture < 8mm <20mm 3.1mm 5mm 8.5mm 3mm Small size Large size

Characteristics of a magnetic material measured using 4294A and 16454A
1/10/2006 Characteristics of a magnetic material measured using 4294A and 16454A Permeability and Loss Tangent of Ferrite Core Settings of 4294A OSC LEVEL: 500mV Frequency: 10kHz-110MHz Parameters: μr´and tandm BW: 5 Compensation: SHORT Settings of 16454A Electrode: LARGE

E4991A Impedance/Material Analyzer
1/10/2006 E4991A Impedance/Material Analyzer 16453A 16454A fixtures 16453A Operating temperature: -55o C to +200o C Frequency Range: 1 MHz to 3 GHz (E4991A) but fixtures are 1 MHz to 1 GHz only. Provides a total solution for high-accuracy and easy measurement of surface-mount components and dielectric materials.

85070E Dielectric Probe with E4991A
1/10/2006 85070E Dielectric Probe with E4991A Recommended option for E4991A is option 010 Frequency range High temperature probe 10 MHz – 3 GHz Slim probe 500 MHz – 3 GHz For ion liquids is possible electrode polarization for low frequencies Calibration is performed in the following way Configure probe calibration from the software Calibrate at the APC7 port of the option 010 using E4991A From 85070E software, calibrate the end of the probe

MW Frequency Concerns MW frequency Low frequency vs. Large wavelength
1/10/2006 MW Frequency Concerns MW frequency Low frequency vs. Large wavelength Small wavelength Lumped element Transmission line Simple components and connecting wires that perform well at low frequencies behave differently at high frequencies. At microwave frequencies wavelengths become small compared to the physical dimensions of the devices such that two closely spaced points can have a significant phase difference. Low frequency lumped-circuit element techniques must be replaced by transmission line theory to analyze the behavior of devices at higher frequencies. Additional high frequency effects make microwave circuits more complex and expensive. Simple Complex Expensive (high MW frequencies) Low cost (compared to high MW frequencies)

1/10/2006 Network Analyzers Agilent Technologies PNA, PNA-L, ENA, ENA-L family of network analyzers (Legacy 8712/4, 8753, 8720, and 8510) 30 kHz to 110 GHz (and above up to 325 GHz) Measures reflection/transmission (magnitude and phase) vs. frequency High accuracy 50 ohm measurement environment

Generalized Network Analyzer Block Diagram
1/10/2006 Generalized Network Analyzer Block Diagram Fixture Incident Transmitted MUT Reflected SOURCE SIGNAL SEPARATION INCIDENT (R) REFLECTED (A) TRANSMITTED (B) A measurement of the reflection from and/or the transmission through a material along with knowledge of its physical dimensions provides the information to characterize the permittivity and permeability of the material. A vector network analyzer consists of a signal source, a receiver and a display. The source launches a signal at a single frequency to the MUT. The receiver is tuned to that frequency to detect the reflected and transmitted signals from the material. The source is then stepped to the next frequency and the measurement is repeated to display the reflection and transmission measurement response as a function of frequency. RECEIVER / DETECTOR PROCESSOR / DISPLAY

T/R Versus S-Parameter Test Sets
1/10/2006 T/R Versus S-Parameter Test Sets Transmission/Reflection Test Set S-Parameter Test Set Source Source Transfer switch R R A B A B Port 1 Port 2 Port 1 Port 2 The ET models will work well with the dielectric probe 85070E since we measure only the reflection. Part of the models of the 85071E software will not work with the ET models, because measurement of s22 and s12 is required. When consider which model to recommend, ask also the question: what measurements in the future you plan to perform? Fwd Rev Fwd MUT MUT Source applies only to port 1 port 2 is always receiver response, one-port calibrations available Source can be applied to port 1 or port 2 forward and reverse measurements two-port calibration possible

Three Versus Four-Receiver Analyzers
1/10/2006 Three Versus Four-Receiver Analyzers 3 Receivers 4 Receivers Source Source Transfer switch Transfer switch R1 R A A B B R2 Port 1 Port 2 Port 1 Port 2 The TRL calibration is the most precise one and is recommended for accurate dielectric measurements. Fwd Rev Fwd Rev MUT MUT TRL*, LRM* cal true TRL, LRM cal

Network Analyzer Calibration and Measurement Accuracy
1/10/2006 Network Analyzer Calibration and Measurement Accuracy Provides insight into the sensitivity and limitations of various materials measurement techniques. Vector error correction estimates then mathematically removes systematic errors. Estimate systematic errors from measurements of known calibration standards. Residual systematic errors a function of how well calibration standards are known.

Network Analyzer Calibration and Measurement Accuracy (continued)
1/10/2006 Network Analyzer Calibration and Measurement Accuracy (continued) Calibration is always important, but at high frequencies measurement errors can be more significant Calibration eliminates systematic (stable, repeatable) errors, but not random or drift errors noise, drift, or environment temperature, humidity, pressure Minimize errors with good measurement practices visually inspect connectors for dirt/damage minimize physical movement of test port cables both during calibration and measurement It is too time consuming and costly to try to design a perfect microwave network analyzer. Instead a measurement calibration is used to eliminate the systematic (stable and repeatable) measurement errors caused by the imperfections of the system. Random errors due to noise, drift or the environment cannot be removed with a measurement calibration. This makes a microwave measurement susceptible to errors from small changes in the measurement system. These errors can be minimized by adopting good measurement practices such as visually inspecting all connectors for dirt or damage, and by minimizing any physical movement of the test port cables after a calibration.

Agilent Technologies Instrument Summary
1/10/2006 Agilent Technologies Instrument Summary ENA, ENA-L Network PNA, PNA-L analyzers Legacy – 8712, 8753, 8720, 8510 Impedance/Material Analyzer E4991A 4192A, 4194A, 4263B, LCR meters 4294A, 4285A, 4278A Impedance analyzers f (Hz) 1 2 3 4 5 6 7 8 9 10 11 DC 10 10 10 10 10 10 10 10 10 10 10

Considerations in choosing a Technique and Fixture
1/10/2006 Considerations in choosing a Technique and Fixture Consider form of material sample (liquid, solid, sheet, etc.) General knowledge of desired measurement Destructive versus non-destructive Desired frequency range Expected range of permittivity and permeability Isotropic versus non-isotropic Mathematical model relating measured s-parameters and material characteristics Limitations of model, for example perturbation theory assumes small variation in field pattern. Electric field necessary in material to sense permittivity Magnetic field necessary in material to sense permeability

Parallel Plate Liquids < 10 mm 10-50 mm 1/10/2006
The parallel plate method involves sandwiching a thin sheet of material or liquid between two electrodes to form a capacitor. An LCR meter or impedance analyzer is used to measure the loaded fixture. e’ is computed from the measurement of capacitance and e” is computed from the measurement of dissipation factor (D). < 10 mm 10-50 mm Liquids

LF Parallel Plate Summary
1/10/2006 LF Parallel Plate Summary Relatively simple computation of er from C and D Frequency limited to < 100 MHz Does not provide mr Inexpensive Works well for thin sheets, PC boards, films, etc. The parallel plate method works best for accurate, low frequency measurements of thin sheets or liquids. It does not measure materials with magnetic properties. Accurate: typically 1% for er’ , and 5%  for tand

RF Parallel Plate Summary
1/10/2006 RF Parallel Plate Summary Automatic computation of er from C and D Frequency limited to 1MHz to 1.8GHz Provides automatic mr Sample must be flat, smooth sheet Works well for thin sheets, PC boards, films, etc. RF Parallel Plate provides ease of use and good accuracy for both dielectric and magnetic materials (use “inductance” measurement method to measure permeability). Accurate: typically 8% for er’ < 10 , and  for tand

Coaxial Probe Technique
1/10/2006 Coaxial Probe Technique High temperature probe Slim form and Performance probes Method features Broadband Simple and convenient (Nondestructive) Limited er accuracy and tan d low loss resolution Best for liquids or semi-solids Material assumptions: "semi-infinite" thickness non-magnetic isotropic and homogeneous flat surface no air gaps The coaxial probe technique is best for liquids and semi-solid (powder) materials. For solid materials one flat surface is required. Special precautions should be taken to avoid air gaps between the sample and the probe (this may be air bubble in the case of liquid). Since only the s11 parameter is measured, only the dielectric properties can be calculated, and the MUT should be non magnetic. The underlying theory presumes infinite sample. In reality the sample should be “thick enough” and the thickness can be calculated from a simple equation that will be discussed later. The method is simple, convenient, nondestructive (no special sample is needed in most of the cases) and with one measurement we can sweep up to 20 GHz. The disadvantages of the method are the limited accuracy compared with other methods (transmission method 85071E, resonator methods) and the limitation of the thickness of the sample.

High Temperature Coaxial Probe
1/10/2006 High Temperature Coaxial Probe Flange Measuring Aperture The high temperature probe has a flange that will align correctly the probe when measuring solid material. The material measurement is very localized, because the measuring aperture is pretty small – 3 mm diameter. This reinforces the requirement that the material is homogeneous. The probe may be attractive also for measuring of materials that should be homogeneous, but because of manufacturing or other reasons have local variations in their properties. Generally speaking the probe can be applied for nondestructive testing to discover local defects in the materials. 200 MHz – 20 GHz

Slim Coaxial Probe 500 MHz – 50 GHz 1/10/2006
Since the slim probe does not have flange it is not convenient to measure solid materials. The slim probe would be best for liquids. It’s measuring aperture is even smaller that the high temperature probe. The slim probe can bend easily and render unusable. For this reason we call it disposable and recommend that it is handled with care.

1/10/2006 Slim Coaxial Probe This picture shows how to use the probe with the probe holder that is part of the kit. Using the probe with the 10 mm diameter sealed probe holder

Performance Coaxial Probe
1/10/2006 Performance Coaxial Probe Combines rugged, high temperature, and frequency performance in a slim design. This probe features rugged, high temperature and frequency performance in a slim design, perfect for your most demanding applications. The probe is sealed on both the probe tip and the connector end, which make it our most rugged probe. The probe withstands a wide –40 ºC to +200 ºC temperature range, which allows measurements versus frequency and temperature.

Performance Probe Features
1/10/2006 Performance Probe Features Combines rugged high temperature performance with high frequency performance, all in one slim design. 0.500 – 50 GHz Withstands -40 to 200 degrees C Hermetically sealed on both ends, and can be put in autoclave Food grade stainless steel The probe can be autoclaved, so it is perfect for applications in the food, medical, and chemical industries where sterilization is a must. The slim design allows it to fit easily in fermentation tanks, chemical reaction chambers, or other equipment with small apertures. The small diameter also allows it to be used with smallest sample sizes of all Agilent’s probes. It is useful for measuring liquid, semi-solid, as well as flat surfaced solid materials. The Performance Form Probe Kit comes complete with a calibration short.

Curing and other consumable applications, and When cost is an issue
1/10/2006 Probes Comparison Probes Capabilities High Temp Slim Form Performance Frequency 200MHz – 20GHz 500MHz – 50GHz Probe Diameter Fat Super slim Slim Withstands Extreme Temperatures x Complete Hermetic Seal Low Cost, Consumable Suggested Applications Quick check for hard flat solids, low frequency liquids when big diameter is not a problem. Curing and other consumable applications, and When cost is an issue Medical, Chemical, Food, Extreme Temp, Sterile, and other applications that need a sealed probe.

Coaxial Probe Solids Semisolids (Powder) Reflection (S ) Liquids 11
1/10/2006 Coaxial Probe Solids Semisolids (Powder) Reflection (S ) The open-ended coaxial probe is a cut off section of transmission line. The material is measured by touching the probe to a flat face of a pliable solid (plastic) or immersing it into a liquid or semisolid. The fields at the probe end “fringe” into the material and change as they come into contact with the MUT. The reflected signal (S11) can be measured and related to er. 11 Liquids

Open-Ended Coax Formulation
1/10/2006 Open-Ended Coax Formulation 2b 2a Metal plane erc - the dielectric constant of the dielectric filling the coaxial line, a and b - the inner and outer radii of the coaxial line, and Here are the challenges when calculating the dielectric constant from the measured reflection coefficient (S11). The normalized aperture admittance which is in the left hand part of the equation can be calculated from S11. The main problem is that the dielectric constant is under the triple integral (and in the exponent) and there is no analytical solution for it. A Taylor series expansion of the exponential expression yields an equation where the integrals are independent of the medium characteristics. Once the integrals are computed for a given probe geometry, the resulting polynomial expression provides fast computation of the YL. _________________________ D. V. Blackham, R. D. Pollard, “An Improved Technique for Permittivity Measurements Using a Coaxial Probe,” IEEE Trans. on Instr. Meas., vol. 46, No 5, Oct. 1997, pp D. V. Blackham, R. D. Pollard, “An Improved Technique for Permittivity Measurements Using a Coaxial Probe,” IEEE Trans. on Instr. Meas., vol. 46, No 5, Oct. 1997, pp

Fringe Field for the Slim Coaxial Probe
1/10/2006 Fringe Field for the Slim Coaxial Probe The theory of the probe is based on radiation from a coaxial aperture in an infinite metal plane. It is difficult to model the fringe fields for the slim probe. The “genetic algorithm” is used to model the probe. To derive the model the only information needed is uncorrected reflection coefficient measurements of a variety materials with known dielectric constant. Different model for finding the dielectric constant will be used for the slim probe.

Dielectric Probe System
1/10/2006 Dielectric Probe System Computer (not required for PNA) Network Analyzer PNA, PNA-L, ENA, ENA-L, E4991A, 4294A Legacy 8712/14, 8752, 8753, 8719, 8720, 8722, or 8510 LOG MAG PHASE DELAY SMITH CHART POLAR LIN MAG SWR MORE START N MHZ CH1 S11 1 U FS Cor Hid HP-IB 85070E Dielectric Probe A typical coaxial probe system consists of a vector network analyzer, a coaxial probe, an external computer with HP-IB card and software. For the PNA family computer is not required. 85070E Software (Included with probe kit)

Coaxial Probe Calibration
1/10/2006 Coaxial Probe Calibration Directivity Three term calibration (1-port) corrects Tracking Source match Measure three known standards Open Short User-defined standard (usually water) A three term calibration corrects for the directivity, tracking and source match errors that can be present in a reflection measurement. In order to solve for these three error terms, three well known standards are measured and the difference between the predicted and actual values are used to remove the systematic (repeatable) errors from the measurement. The three known standards are air, a short circuit and distillate (de ionized) water. Difference in predicted and actual value is used to correct measurement

1/10/2006 Coaxial Probe Errors Allow time for cable to stabilize Minimize cable flexing Cable stability Machine a flat sample face Probe flatness ~ 100 m inches (sample flatness should be similar) Air gaps Even after calibrating the probe, there are additional sources of error that can affect the accuracy of a measurement. It is important to allow enough time for the cable (that connects the probe to the network analyzer) to stabilize before making a measurement and to be sure that the cable is not flexed between calibration and measurement. For solid materials, air gap between the probe and sample can be a significant source of error unless the sample face is machined to be at least as flat as the probe face. The sample must also be thick enough to appear “infinite” to the probe. Recommended minimum thickness for high temperature probe Sample thickness Powder measurements results depend on packing Uniform packing and mixing theory

Remeasuring Air at Various Cable Positions
1/10/2006 Cable Phase Stability Remeasuring Air at Various Cable Positions 1.4 1.2 1.0 If the cable is moved or flexed after a calibration, the resulting measurement can vary significantly, causing measurement repeatability to be sacrificed. Instead of moving the probe to the sample, it is best to fix the probe and cable in one position while bringing the sample to the probe. The same result would be seen if a change in temperature occurred after a calibration. This problem can be alleviated by using simple refresh with one standard or ECal refresh as it will be explained in the next slides. 0.8 0.6 5 10 15 20

Refresh Calibration (Single Standard)
1/10/2006 Refresh Calibration (Single Standard) If the perturbation is small, the change can be characterized by the measurement of a single calibration standard = Measured S 11 = Actual S 11 = Directivity error = Source match error = Reflection tracking error If the change in the measurement (due to cable movement or temperature change) is small enough, it may be possible to characterize that small change by measuring a single calibration standard, rather than the three standards required for a normal calibration. A refresh calibration modifies an existing calibration by remeasuring just one standard. This simplifies measurements that must be made at several different temperatures or measurements where the cable must be moved. = Perturbation term

Refresh Calibration for Water
1/10/2006 Refresh Calibration for Water Experimental result with refresh calibration for the real dielectric constant of water. Original calibration is at 25o C and the measurement is at 50o C. The calibration at 50o C and the air refresh at 50o C are very close.

Refresh Calibration for Water
1/10/2006 Refresh Calibration for Water Experimental result with refresh calibration for the loss factor of water. Original calibration is at 25o C and the measurement is at 50o C. The calibration at 50o C and the air refresh at 50o C are very close.

Refresh Calibration with ECal
1/10/2006 Refresh Calibration with ECal How it works: Perform cal at the tip of the probe After the cal, with cal on, characterize three ECal standards and store the values If the cable flexes or temperature changes measure the three standards raw and use the newly calculated error vectors. The new automated Electronic Calibration Refresh feature recalibrates the system automatically, in seconds, just before each measurement is made. This virtually eliminates cable instability and system drift errors. Processes can now be monitored over long time periods, including tests that vary MUT temperature and pressure over time. How it works: The Agilent Electronic Calibration module (ECal) microwave ports are connected in line between the probe and the network analyzer test port cable. The ECal module communication port is connected either to the PC or PNA Series network analyzer running the 85070E software. The software guides the user through a normal “three standard” calibration, (usually open, short, water), performed at the end of the probe. This calibration is then transferred to the ECal module. The ECal module remains in line and a complete ECal calibration is automatically performed before each measurement. Errors due to test port cable movement are removed by the new calibration.

Measurements of Stacks of Paper
1/10/2006 Errors for Thin Materials Measurements of Stacks of Paper Metal-Backed +20% +10% +5% %-Error NOM -5% -10% -20% The sample size must be chosen such that any reflections from boundaries are not detected by the probe. The effects of sample thickness are shown by the measurement of paper that has been stacked to various thicknesses. In one case the paper is backed by metal and in the other case by foam. At the recommended minimum sample thickness (tmin) the error from nominal is less than 5%. Foam-Backed 5 10 13 15 20 Thickness (mm)

Relative Measurements
1/10/2006 Relative Measurements Although the absolute accuracy of a probe measurement may be limited, it does exhibit good measurement repeatability. Therefore, it can make very good relative measurements provided a known reference can be found. In this example kynar is measured with the probe and with a more accurate transmission line (T/R) technique. Rexolite, which is known to have a permittivity of 2.54, is then measured with the probe. A more accurate measurement of kynar is produced by making a measurement relative to rexolite and then adding a value of 2.54 to the difference.

Relative Measurements
1/10/2006 Relative Measurements See the explanation from the previous slide. This results are for the loss factor of the same material.

Coaxial Probe Measurement of Methanol
1/10/2006 Coaxial Probe Measurement of Methanol Comparison between the Cole-Cole theoretical model and a measurement of the dielectric constant of methanol at 25o C.

Coaxial Probe Measurement of Methanol
1/10/2006 Coaxial Probe Measurement of Methanol Comparison between the Cole-Cole theoretical model and a measurement of the loss factor of methanol at 25o C.

Reflection Coefficients at Probe Aperture for Air, Water, and Methanol
1/10/2006 Reflection Coefficients at Probe Aperture for Air, Water, and Methanol A polar plot of the measured reflection coefficient at the probe aperture for air, water and methanol.

Coaxial Probe Summary Convenient, easy to use Requires sample
1/10/2006 Coaxial Probe Summary Convenient, easy to use Requires sample thickness of > 1 cm (typical Little or no sample preparation Solids must have a flat surface Nondestructive for many materials Limited accuracy in e’r ( + 5%) and low loss resolution ( in tand) Not suited to high e’r low e”r materials The coaxial probe method is convenient and operates over a wide 200 MHz to 20 GHz frequency range. It is not well suited to low loss materials, magnetic materials or where high accuracy is desired. Ideal for liquids or semisolids Broad frequency range ( GHz depending on er) Does not provide mr

Agenda 85070D/85071D Product Overview Fundamentals
1/10/2006 Agenda 85070D/85071D Product Overview Fundamentals Measurement Instruments Considerations in choosing a Technique and Fixture Measurement Techniques Parallel Plate Coaxial Probe Transmission Line Free-Space Resonant Cavity

Transmission Line Technique
1/10/2006 Transmission Line Technique Waveguide Material assumptions: sample fills fixture cross section no air gaps at fixture walls smooth, flat faces, perpendicular to long axis homogeneous Coax Method features: Broadband - low end limited by practical sample length Limited low loss resolution Measures magnetic materials Anisotropic materials can be measured in waveguide Coaxial line supports planar TEM mode (free space) The transmission line is a broadband technique for machineable solids. The MUT is assumed to completely fill the cross section of the fixture with no air gaps, have smooth flat faces and to be uniform throughout. Coaxial airline fixtures are broadband, but the samples are more difficult to machine. Waveguide fixtures extend to the mm-wave frequencies and the samples are simpler to machine, but their frequency coverage is banded. A transmission line fixture connects to a vector network analyzer that measures the reflection and transmission from the MUT which are then converted to permittivity and permeability.

Transmission Line Waveguide l Coax Transmission Reflection (S ) (S )
1/10/2006 Transmission Line Waveguide l Transmission Reflection (S ) (S ) 21 11 Transmission-line methods involve putting the MUT inside a portion of an enclosed transmission line. The line is usually rectangular waveguide or a coaxial airline. Coaxial airlines are broadband, but the toroid shaped samples are more difficult to manufacture. Waveguide sections are banded, but the brick shaped samples are simpler to machine and measurements can be extended to the mm-wave bands. The measurement can be based on the reflection coefficient (S11) determination, transmission coefficient determination (S21) , or both. The popular “S parameter” approach (Nicolson-Ross or Weir) uses both S11 and S21 to calculate both e’ and e”. HP described this technique, adapted for the HP 8510, in Product Note (Aug 85). Note that S11 and S21 are composed of multiple-reflections from both boundaries. Coax

Waveguide Section with Samples
1/10/2006 Waveguide Section with Samples On the picture is shown the straight waveguide section for X-band and several brick shaped samples.

Air Coaxial Section with Samples
1/10/2006 Air Coaxial Section with Samples On the picture is shown the 7 mm air coaxial line and toroid samples.

Transmission Line System
1/10/2006 Transmission Line System Computer (not required for PNA) Network Analyzer PNA, PNA-L, ENA, ENA-L Legacy 8712/14, 8752, 8753, 8719, 8720, 8722, or 8510 LOG MAG PHASE DELAY SMITH CHART POLAR LIN MAG SWR MORE START N MHZ CH1 S11 1 U FS Cor Hid HP-IB A typical transmission line system consists of a vector network analyzer, a coaxial airline or waveguide section, an external computer with HP-IB card and software. For the PNA family computer is not required. 85071E Transmission Line Fixture Materials Measurement Software (coaxial, waveguide, or free-space set up)

Transmission Line Algorithms in 85071E
1/10/2006 Transmission Line Algorithms in 85071E Optimum Length Algorithm Measured Output Nicolson-Ross S11,S21,S12,S lg/ er and mr (PN ) (or S11,S21) Precision (NIST) S11,S21,S12,S nlg/ er Fast S21,S12 nlg/ er (S21) Short-circuited S lg/ er back These are the algorithms used in 85070E. They will convert the measured S-parameters to permittivity or permeability. The first three require a two-port fixture. The last two require a one-port fixture which may be better for liquids or powders where a shorted waveguide section can be turned on end and filled. One-port fixtures may also be better for measurements at high temperatures where one end of the waveguide can be heated while cooling mechanisms keep the network analyzer cool. Arbitrary dielectric S lg/ er back

Nicolson-Ross Measurement Model
1/10/2006 Nicolson-Ross Measurement Model Region 1: V1, I1, Z0 Region 2: V2, I2, Zs Region 1: V3, I3, Z0 Air MUT Air Here is some idea of how the Nicolson-Ross algorithm is derived. Considered is part of transmission line with three regions – region 2 is the material under test with length d and 1 and 3 is air. The boundary conditions on the two interfaces l = 0 and l = d are applied and a system of four equations is formed. ______________________ A.M. Nicolson, G.F. Ross, "Measurement of the intrinsic properties of materials by time-domain techniques," IEEE Trans. on Instrum. Meas., vol. IM-19, Nov 1970, pp Boundary conditions A.M. Nicolson, G.F. Ross, "Measurement of the intrinsic properties of materials by time-domain techniques," IEEE Trans. on Instrum. Meas., vol. IM-19, Nov 1970, pp

Nicolson-Ross Measurement Model Continued
1/10/2006 Nicolson-Ross Measurement Model Continued Boundary conditions (system of 4 equations) Related quantities Here the four equations are shown in more detail and also all of the related quantities. Next G, T, S11 and S21 are introduced in the equations and the four voltages are eliminated.

1/10/2006 Nicolson-Ross Measurement Model Continued Solution of the system Here are the results of solving the system of four equations. These are the equations showing the relation between the measured s-parameters and the dielectric properties. This is the Nickolson-Ross formulation. Flow graph can be used also to solve this problem and get the same equations. Flow graph can be used also to solve the system

1/10/2006 Nicolson-Ross Measurement Model Continued From only one measurement the solution is not unique. We need to know either approximate value of the dielectric constant or perform another measurement (measurement of reversed S-parameters or another sample with different length. Here is shown how from the measured S-parameters the dielectric and magnetic properties are calculated. In this case we are lucky that we ca solve the “inverse problem”, i.e. to get analytical solution for the dielectric constant. For the probe for example such solution does not exist and iterative methods to find the dielectric properties are used. Still the equation is not unique, which holds for most of the algorithms. This means that many values of the dielectric properties will satisfy the equation which can be explained with the repeatability of the phase. To get the exact value of the dielectric constant we need to know its approximate value a priory or make an additional measurement which may be sample with different length or the S-parameters in reverse direction.

Phase Rotation a b Calibration planes L sample holder - phase shift
1/10/2006 Phase Rotation Calibration planes a b L sample holder Here is shown how the phase can be rotated to the faces of the sample from the calibration planes. For some of the methods the exact position of the sample is not required, because there are more measured parameters from which the position can be determined. If the method requires the operator to measure the exact position the best approach is to put the face of the sample at the calibration plane and put 0 for a. - phase shift f0 – measurement frequency fc – cutoff frequency (fc = 0 for coaxial measurement) c – velocity of light

Nicolson-Ross Assumptions and Features
1/10/2006 Nicolson-Ross Assumptions and Features Single mode propagation assumed valid when homogenous sample fills cross section of transmission line and sample interfaces are perpendicular to longitudinal axes practical measurements of solids usually limited to low values of dielectric constant (<~15 for 7mm coaxial measurements) Can determine both permittivity and permeability Important to understand sources of error. Measurement of both forward and reverse s-parameters yields redundant information to enable sample position invariance. For low loss materials, sample thicknesses near nlg/2 cause discontinuities in the measurement results

Nicolson-Ross - Measurements
1/10/2006 Nicolson-Ross - Measurements These two plots show measurements made on a sample of Teflon. In the first case the measured value of S11 never approaches zero. In the second case, because of the longer length of the sample, the measured value of S11 approaches zero at several frequencies. Since the equations used to solve for u and e are ill-conditioned the computed results are in error.

Nicolson-Ross Model Measurement Requirements
1/10/2006 Nicolson-Ross Model Measurement Requirements S-parameter test set Measurement of S11, S21, S22, and S12 Full 2-port calibration Approximate sample position TR test set Measurement of S11 and S21 One path 2-port calibration Exact sample position and One sample lg/4 wavelength sample thickness is optimum The Nicolson-Ross model measures all four, or a pair of, S-parameters of the material under test. Both m and e for the material are computed. The materials parameters are obtained by a direct solution calculation (i.e. m and e can be obtained directly from the S-parameter data). For low loss materials, sample thicknesses near nlg/2 cause discontinuities in the measurement results. At the first frequency of measurement, the calculation routine must determine the number of 360-degree phase shifts through the sample to correctly solve for materials parameters. This is determined by the sample thickness and an initial estimate for m and e of the sample. m and e of air are used to determine the number of phase rotations at the first frequency unless other materials parameters are entered using the _Verify estimate_ command.

Precision NIST Algorithm
1/10/2006 Precision NIST Algorithm Model requirements: S-parameter test set only Measurement of S11, S21, S22, and S12 Full 2-port calibration Approximate sample position One sample nlg/2 wavelength sample thickness is optimum Sometimes has a problem converging to an answer when the measurement errors in S11 and S22 is large. This model measures all four S-parameters of the material under test, but calculates only e. The dielectric properties of the material parameters are obtained by an iterative calculation. This technique is an implementation of work published by the National Institute of Standards and Technology (NIST). The e value at the first frequency is obtained by a direct calculation and is used to “seed” the iterative calculation. Since all four S-parameters are used in the calculation, this technique has a desirable feature of being independent of the entered position of the sample in the sample holder. The distance to the sample is used only to obtain the estimate of e at the first frequency and thus “seed” the calculation routine. This technique has no calculation anomalies at frequencies where the sample thickness is an integer multiple of one half-wavelength ( nlg/2). This technique is very useful for long samples and for characterizing very low loss materials. If the _Verify estimate_ command is turned on, then the software presents its estimate of e at the first frequency. You can enter a new estimate of e or acknowledge the estimate presented by the software. ______________________________ J. Baker-Jarvis, M.D. Janezic, R.F. Riddle, R.T. Johnk, P. Kabos, C. Holloway, R.G. Geyer, C.A. Grosvenor, “Measuring the Permittivity and Permeability of Lossy Materials: Solids, Liquids, Metals, Building Materials, and Negative-Index Materials,” NIST Technical Note J. Baker-Jarvis, M.D. Janezic, R.F. Riddle, R.T. Johnk, P. Kabos, C. Holloway, R.G. Geyer, C.A. Grosvenor, “Measuring the Permittivity and Permeability of Lossy Materials: Solids, Liquids, Metals, Building Materials, and Negative-Index Materials,” NIST Technical Note J. Baker-Jarvis, E. Vanzura, W. Kissick. “Improved Technique for Determining Complex Permittivity with the Transmission/Reflection Method.” IEEE Transactions on Microwave Theory and Techniques, vol 38, no. 8, pp , August 1990.

Fast Algorithm S-parameter test set
1/10/2006 Fast Algorithm S-parameter test set Measurement of S11, S21, S22, and S12 Full 2-port calibration Approximate sample position TR test set Measurement of S11 and S21 One path 2-port calibration Exact sample position and One sample lg/4 wavelength sample thickness is optimum This model measures all four or a pair of S-parameters of the material under test. Only e for the material is computed. The dielectric properties of the material parameters are obtained by an iterative calculation. The e value at the first frequency is obtained by a direct calculation and is used to “seed” the iterative calculation. This technique computes the uncertainty of the transmission and reflection measurement at each frequency. (Uncertainty is based on the systematic error terms of the network measurement system: directivity, source match, load match, and isolation.) The model then uses the measurement less affected by systematic uncertainties to determine e. This calculation is faster than the “refl/tran e prec'n” technique. This technique has no calculation anomalies at frequencies where the sample thickness is an integer multiple of one half-wavelength (lg/2). This technique is very useful for long samples and for quick characterization of dielectric materials. If the _Verify estimate_ command is turned on, then the software presents its estimate of e at the first frequency. You can enter a new estimate of e or acknowledge the estimate presented by the software. This technique minimizes the difference between the measured and calculated values of S21.. The sample is assumed to be non-magnetic. Often converges to a solution when the NIST model fails. This is because it doesn’t depend on S11. The error in measuring S11 is often a order of magnitude worst than when measuring S21.

Weakness of both the NIST and Fast Models
1/10/2006 Weakness of both the NIST and Fast Models Both models computes the wrong solution when the phase shift of S21 is greater than -360 degrees at the first measurement frequency. This can often be overcome by computing the group delay and computing an estimate of the permittivity. An alternative is to provide the model with an approximate value of the permittivity. Both models can become “confused” when the length of the sample is long compared to the wavelength of the measurement frequency. There are several values of permittivity that satisfies the measurements. This problem can be overcome by either making a shorter sample, lowering the first measurement frequency or providing additional information such as group delay or an initial guess of permittivity.

Short-Circuited Back Model requirements: Any test set
1/10/2006 Short-Circuited Back Model requirements: Any test set Measurement of S11 S port calibration Defined sample position One sample lg/2 wavelength sample thickness is optimum This model measures the reflection coefficient, S11, of a sample in a transmission line backed by a short circuit. The sample can either be “butted” against a short circuit at the end of the transmission line, or bonded to a ground plane which serves as a short at the end of the transmission line. Only e for the material is computed. The dielectric properties of the material parameters are obtained by a iterative calculation. This technique is an extension of several published approaches. You must enter a e value for the first frequency because the software is unable to directly calculate that initial value. The value you enter should be as accurate as possible to avoid measurement anomalies. If the subsequent results are unexpected, recalculate the measurement parameters by entering another value. This technique is convenient for materials that must be bonded to a ground plane. It has also proven to be a convenient technique for measuring liquids with vertical cells (the metal “floor” at the bottom of the cell acts as a dam).

Arbitrary Dielectric Back
1/10/2006 Arbitrary Dielectric Back Model requirements: Any test set Measurement of S11 S port calibration Defined sample position One sample lg/2 wavelength sample thickness is optimum Two measurements are required: one with backing alone and the other with the sample and backing together It is simple and best for thin film measurements. MUT Arbitrary back E-field at the short is 0 This model requires a sample that is backed by an arbitrary but repeatable termination. Two measurements are required: one with backing alone and the other with the sample and backing together. It is simple and best for thin film measurements. It is not applicable to magnetic materials. Use the verify estimate feature to ensure that the correct seed value is selected.

m and e Single or Double Model requirements: Any test set
1/10/2006 m and e Single or Double Model requirements: Any test set Measurement of S11 S port calibration Defined sample position Measurement requires Two samples backed by short or One shorted sample in two positions Optimum sample thickness: Selected for transmission loss of 5 dB or less (shorter sample, lossy materials) About lg/4 and lg/2 wavelength (lower loss materials) Two samples backed by short One shorted sample in two positions This is the only reflection-only model that measures permeability of magnetic materials. The model requires two measurements: two measurements of one sample in different positions backed by a short circuit or two samples backed by a short circuit each measured once. It is best for liquid or powder measurements. Use the verify estimate feature to ensure a correct seed value is selected. Where possible, a transmission/reflection measurement gives much better results: T/R measurements are possible with thicker samples T/R measurements are not compromised by errors of relative length of the samples

Transmission-Reflection versus Short-Circuited Back
1/10/2006 Transmission-Reflection versus Short-Circuited Back Where possible, a transmission/reflection measurement gives much better results: T/R measurements are possible with thicker samples T/R measurements are not compromised by errors of relative length of the samples

Measurements of 1.5 mm thick Duroid
1/10/2006 Duroid Measurements Measurements of 1.5 mm thick Duroid This comparison measurement demonstrates that for thin, low loss and low dielectric sample the short backed measurement will not provide accurate results.

Measurements of 1.5 mm thick Duroid
1/10/2006 Duroid Measurements Measurements of 1.5 mm thick Duroid

Transmission Line Measurement Error Sources
1/10/2006 Transmission Line Measurement Error Sources Sample geometry air gaps sample length Network analyzer systematic errors usually less important that sample geometry minimized when measuring longer samples

Transmission Line Measurement Error Sources
1/10/2006 Transmission Line Measurement Error Sources Air gaps between sample and fixture Network analyzer errors Sample length uncertainty Careful calibration Use good standards Use TRL or time domain gating Measure length precisely Use larger fixture Focus on fit of center conductor (coaxial) or on fit of broad waveguide wall Measure gap precisely and correct in software Fill gap with conductive grease Metalize sample sides Even after calibrating the network analyzer there is additional measurement uncertainty introduced by sample length uncertainty and air gap between the sample and fixture walls. These effects can be minimized but never completely removed.

S21 phase shift >> S21 uncertainty
1/10/2006 Sample Length Minimum length Maximum length S21 phase shift >> S21 uncertainty (approx. 20o ) Avoid drop-outs in Nicolson-Ross algorithm Sample loss Long samples may create multiple roots Choosing the optimum sample length will improve the accuracy of a measurement. The minimum length of the sample is limited by the phase uncertainty of the network analyzer. The maximum sample length is limited by the l/2 wavelength dropouts with the Nicolson-Ross technique, the sample loss and by the fact that long samples may lead to multiple roots. The optimum sample length depends on the chosen algorithm. Optimum length for low loss materials For Nicolson-Ross: For Precision or Fast:

Transmission Line Air Gaps
1/10/2006 Transmission Line Air Gaps (Altschuler, 1963) E field in waveguide d b d1 d2 d3 d4 a neglect gaps along a Air gap between the fixture walls and the sample can be one of the largest sources of error in a transmission line measurement. For coaxial fixtures, the air gap along the center conductor wall has a much bigger effect than the air gap along the outer conductor wall. Likewise, for waveguide fixtures, the air gap along the long wall has a much bigger effect than the air gap along the short wall. Air gap correction algorithms can improve the accuracy of a measurement if the air gap is uniform and can be precisely measured. where where

Typical Errors Caused By Air Gaps
1/10/2006 Typical Errors Caused By Air Gaps Permittivity of material High er materials in coaxial lines = 20% to 50% Size of transmission line For er = 10 and air gap = 0.25 mm (coaxial line) Coaxial line dimensions Error 3.0 mm 35% 7.0 mm 14% Materials with higher permittivities and smaller diameter transmission lines will be more susceptible to error from air gap. 14.0 mm 8% 25.0 mm 4% 1.625 in 3.2% 3.125 in 1.7%

Minimize Sample Holder Ambiguities
1/10/2006 Minimize Sample Holder Ambiguities Coax Measure S-parameters of sample holder using Unknown Thru Calibration and use explicit deembedding. define sample holder length=0 in the softare for computation Use sample holder as THRU cal standard (coaxial) modify cal kit definition of THRU offset delay using value of sample holder length Waveguide Include sample holder as part of port 2 (implicit deembedding) define sample holder length=0 for computation Port 2 Port 1 The accuracy of a measurement can be improved by accounting for the loss of the sample holder which is assumed negligible. For coaxial fixtures, the sample holder can be defined as part of the Thru standard by modifying the offset delay in the calibration kit definition. For waveguide fixtures, the sample holder can be included as part of port 2 during the calibration, such that the calibration standards are inserted between port 1 and the sample holder. In this case the sample holder length must be defined to have zero length. Note: Implicit or explicit deembedding is best approach to compensate for sample holder loss. Thru

Plexiglas Measurement Results
1/10/2006 Plexiglas Measurement Results 25 mm 31 mm calibrated out sample holder 9 10 11 12 2.54 2.56 2.58 f, GHz This figure shows measurement results of permittivity (this slide) and loss tangent (next slide) of two Plexiglas samples with length of 25 mm and 31 mm in an X-band waveguide. The sample holder is the precise waveguide section of 140 mm length that is provided with the X11644A calibration kit. The network analyzer is a PNA, the calibration type is TRL, and the precision NIST algorithm is used for calculation. There are two pairs of traces for two different measurements of the same samples. The top two measurements of each slide are performed for the case when the sample holder is not calibrated out. In this case based on the sample length and sample holder length, the software will rotate the calibration plane correctly to the sample face, but will not compensate for the losses of the waveguide. The bottom two measurements of the same samples are performed for the case when the sample holder is part of the calibration and the waveguide losses and electrical length are calibrated out. As expected, the loss tangent curves (next slide) show lower values when the sample holder is calibrated out, and they are more constant with respect to frequency. This is due to the fact that the waveguide losses are not added to the sample’s losses. With the PNA type of network analyzer besides calibrating out the sample holder, it is possible to perform fixture deembedding, which will lead to the same results. This approach requires measuring of the empty sample holder after the calibration.

Plexiglas Measurement Results
1/10/2006 Plexiglas Measurement Results 9 10 11 12 0.003 0.004 0.005 25 mm 31 mm tand f, GHz calibrated out sample holder Results of the loss tangent measurements of the same two Plexiglas samples, see the notes on the previous slide.

Measured Parameter Uncertainty Effects on Material Properties
1/10/2006 Measured Parameter Uncertainty Effects on Material Properties Length and Air gaps recalculate results adding and subtracting dimensional ambiguity S-parameters accuracy Monte Carlo method such as uncertainty “noise”

Transmission Line Typical Accuracy
1/10/2006 Transmission Line Typical Accuracy Coaxial line 2% % % Waveguide % % % For low loss, nonmagnetic, isotropic, rigid material Requires precise sample machining (e.g mm). It will depend on the frequency. Reported 2-4 times better accuracy with no air gaps The typical accuracy of a transmission line measurement ranges from 1% to 10% or higher depending on the MUT and how well it is machined. The numbers shown above are typical, for comparison purpose. The uncertainty analysis should be performed for particular sample, measurement set up, frequency range etc. Full error analysis will be involved and tedious and, again, it will be fully valid only for the particular measurement situation. Many authors treat the uncertainty of transmission type of measurements, but a good overview is: J. Baker-Jarvis, M.D. Janezic, R.F. Riddle, R.T. Johnk, P. Kabos, C. Holloway, R.G. Geyer, C.A. Grosvenor, “Measuring the Permittivity and Permeability of Lossy Materials: Solids, Liquids, Metals, Building Materials, and Negative-Index Materials,” NIST Technical Note

Transmission Line Calibration
1/10/2006 Transmission Line Calibration Frequency response calibration (not recommended for materials measurements) Open, short or thru only One-port reflection calibration (3 term error correction) Open (offset short)/Short/Load (fixed, sliding, offset) ECAL Full two-port calibration (12 term error correction) The network analyzer must be calibrated before making a measurement to remove the systematic errors from the system. The simplest calibration is a frequency response calibration because it requires only one calibration standard. One-port fixtures require a one-port calibration to compensate for all three error terms in a reflection measurement. Two-port fixtures require a more time-consuming two-port calibration for the greatest accuracy in removing all twelve error terms in a transmission and reflection measurement. Short/ Open (offset short)/Load (fixed, sliding, offset)/Thru Thru/Reflect/Line Unknown Thru ECAL

TRL Calibration Thru Zero or non-zero length Reflect
1/10/2006 TRL Calibration Thru Zero or non-zero length Port 1 Port 2 Reflect Unknown high reflect Same response to Port 1 and 2 Port 1 Port 2 A TRL or Thru-Reflect-Line calibration is the most accurate type of two-port calibration. The Thru can be a zero length or non-zero length Thru that connects port 1 to port 2. The Reflect can be any unknown high reflection device as long as it presents the same high reflection to port 1 and port 2. The Line must be different in length from the Thru and is assumed to be reflectionless. Line Different in length than “Thru” Reflectionless Port 1 Port 2

TRL Calibration Residual Errors
1/10/2006 TRL Calibration Residual Errors Fewer known standards required Simple standards (especially for non-coaxial media) Highest precision Residual Offset Fixed Sliding Errors Load Load Load TRL A TRL calibration requires fewer standards which do not have to be well known. It offers the highest precision of any network analyzer calibration. Not all network analyzer families have a TRL calibration. Directivity -40 dB -52 dB -60 dB -60 dB Match -35 dB -41 dB -42 dB -60 dB Tracking 0.1 dB 0.047 dB 0.035 dB 0 dB

Unknown Thru Calibration
1/10/2006 Unknown Thru Calibration Short Open Load Do a one-port calibration on port 1 Port 1 Short Open Load Do a one-port calibration on port 2 Port 2 The unknown thru calibration is available in the PNA family of network analyzers. This calibration method will allow calibration when the sample holder is used as unknown thru, characterize the sample holder (measure and store the s2p file with all of the s-parameters) and then deembed the sample holder from the measurement when sample is present. PNA family of analyzers have deembedding function. Measure unknown thru calibration standard: Must be reciprocal (Sij = Sji) Phase known to within a quarter wavelength Confirm estimated electrical delay of unknown thru Port 1 Unknown Thru Port 2

Coaxial Transmission Line Fixtures
1/10/2006 Coaxial Transmission Line Fixtures Agilent Technologies coaxial transmission lines (part of the verification kits) N type from 85055A verification kit, airline 7 mm from 85051B verification kit, airline 3.5 mm from 85053B verification kit, airline 2.4 mm from 85057B verification kit, airline For coaxial fixtures we recommend to use the airlines from the verification kits. The connector type will determine the frequency range. We have the following precision airlines: N type from 85055A verification kit, airline 7 mm from 85051B verification kit, airline 3.5 mm from 85053B verification kit, airline 2.4 mm from 85057B verification kit, airline Obviously a calibration kit in the same type of connector is also needed.

Waveguide Transmission Line Fixtures
1/10/2006 Waveguide Transmission Line Fixtures Agilent Technologies waveguide components: - X/P/K/R/Q/U/V/W 11644A calibration kits (contain l /4 line as well as a straight waveguide section that can be used as sample holder) Agilent Technologies offers waveguide calibration kits for all the frequency bands above X-band. For waveguide calibration kits below X-band, we recommend Maury Microwave Corporation.

Transmission Line Summary
1/10/2006 Transmission Line Summary Frequency limited to >100 MHz (banded in waveguide) Provides both er and mr Precise sample shape required (usually destructive) Simple fixtures Broad frequency range ( GHz) Limited low loss resolution The transmission line method is best for solid materials that can be precisely machined to fit inside a coaxial or waveguide airline. Although it is more accurate that the coaxial probe technique, it is still somewhat limited in resolution for low loss materials. Adaptable to "free space" Liquids and gases must be contained

Free Space Technique Material assumptions:
1/10/2006 Free Space Technique Material assumptions: large, flat, parallel-faced samples ( > 10l) homogeneous Method features: Non-contacting, non-destructive High frequency - low end limited by practical sample size Useful for high temperature Antenna polarization may be varied for anisotropic materials Measures magnetic materials Free space is best for high temperature measurements since the sample is not enclosed in any kind of fixture. The MUT is assumed to be large, flat and uniform throughout. The free space antennas are connected to a vector network analyzer that measures the reflection and transmission from the MUT which are then converted to permittivity and permeability.

Free Space Methods Reflection RCS (Radar Cross Section) NRL arch
1/10/2006 Free Space Methods Reflection RCS (Radar Cross Section) RCS NRL arch NRL Arch Transmission Tunnel Tunnel S-parameter (reflection/transmission) There are many free space measurement methods available to choose from. Free space techniques use antennas to focus microwave energy at a through a slab of material without the need of a test fixture. The same algorithms that are used for the transmission line technique can be applied to free space. Cavity Open (Fabry-Perot) resonator

Free Space System Network Analyzer 85071E Computer
1/10/2006 Free Space System Computer (not required for PNA) Network Analyzer PNA, PNA-L, ENA, ENA-L Legacy 8712/14, 8752, 8753, 8719, 8720, 8722, or 8510 LOG MAG PHASE DELAY SMITH CHART POLAR LIN MAG SWR MORE START N MHZ CH1 S11 1 U FS Cor Hid HP-IB Antennae A typical free space system consists of a vector network analyzer, antenna hardware, an external computer with HP-IB card and software. For the PNA family computer is not required. Agilent Technologies does not provide antennae. 85071E Materials Measurement Software Fixture to hold the sample

NRL (Naval Research Lab) Arch
1/10/2006 NRL (Naval Research Lab) Arch To Port 1 of network analyzer To Port 2 of network analyzer a Measure s21 with the network analyzer Another free-space measurement of interest is reflectivity. It is often desired to know the reflectivity at a given angle. The material of interest may be an absorber as illustrated of a material intended to be applied to a metal surface. Reflectivity measurements are often performed on a NRL (Naval Research Laboratory) Arch. The arch allows the user to adjust the angle of the antennas being used while maintaining a constant distance to the sample. The material being measured is placed on the table. Prior to making a measurement the system is calibrated. The most commonly used calibration is an isolation-response cal. Time-domain gates are often employed to eliminate unwanted transmission paths. NRL arch is used usually to measure absorbing materials. For absorbers is desired to know the frequency response of reflectivity at a given angle.

Measurement with NRL Arch and option 200 of 85071E
1/10/2006 Measurement with NRL Arch and option 200 of 85071E A typical reflectivity measurement with PNA network analyzer, 85071E software with option 200 and NRL arch. For this measurement (option 200) a PNA or 8510 network analyzer with time domain option is required. The measurement shows distinct minimum of reflectivity for lower frequencies.

1/10/2006 Free Space Set-Up Material Sample To Port 1 of network analyzer To Port 2 of network analyzer Fixture to hold the sample and short An S-parameter configuration offers several advantages in the area of calibration to provide a more accurate measurement. By measuring all four S-parameters, a TRL (Thru-Reflect-Line) or TRM (Thru-Reflect-Match) calibration can be used.. Some systems incorporate focusing lenses into the antenna that convert spherical waves to plane waves. This allows the antenna spacing to be closer and the sample size to be smaller. Plane wave incident on homogeneous sample of infinite transverse dimensions Focusing lenses convert spherical waves to plane waves

Free Space High Temperature
1/10/2006 Free Space High Temperature Heating panels Furnace Thermal insulation High temperature measurements are not a problem in free space since the sample is never touched or contacted. The sample can be heated by placing it within a furnace that has “windows” of insulation material that are transparent to microwaves. Sample Thermocouple No tolerance requirements on sample Sample is easily thermally isolated Fibrous insulation virtually transparent to microwaves

Free Space Calibration
1/10/2006 Free Space Calibration Response calibration (reflection) Response and isolation calibration (transmission) TRL/TRM 2-port calibration Thru: focal points are coincident Reflect: metal plate at focal point Line or Match: focal points separated by l/4 or use absorber as a match Time domain gating eliminates multiple reflections Gated Reflect Line (GRL) Calibration Free space calibration standards present special problems since they are “connectorless”. A calibration can be as simple as a response calibration to a full two-port calibration depending on the convenience and accuracy desired. A TRL (Thru-Reflect-Line) or TRM (Thru-Reflect-Match) calibration may actually be easier than other calibration techniques in free space. Time domain gating is often used to take the place of or supplement an existing calibration. The best calibration in for free-space measurements is the Gated Reflect Line or GRL calibration, which will be covered in detail later on.

Two-Port Error Correction
1/10/2006 Two-Port Error Correction Port 1 Port 2 S 11 12 22 E S' D' RT' TT' L' a 1 b A X' 21 2 Reverse model Port 1 Port 2 E S 11 21 12 22 D RT TT L a 1 b A X 2 Forward model = fwd directivity = fwd source match = fwd reflection tracking = fwd load match = fwd transmission tracking = fwd isolation E S D RT TT L X = rev reflection tracking = rev transmission tracking = rev directivity = rev source match = rev load match = rev isolation S' D' RT' TT' L' X' Each actual S-parameter is a function of all four measured S-parameters Analyzer must make forward and reverse sweep to update any one S-parameter Two-port error correction is the most accurate form of error correction since it accounts for all of the majorsources of systematic error. The error model for a two-port device is shown above. Shown below are the equations to derive the actual device S-parameters from the measured S-parameters, once the systematic error terms have been characterized. Notice that each actual S- parameter is a function of all four measured S-parameters. The network analyzer must make a forward and reverse sweep to update any one S- parameter. It looks complicated, but with modern network analzyers, it is as easy as connecting calibration standards and pressing a button.

TRM Calibration Thru Reflect Match
1/10/2006 TRM Calibration Thru Reflect One widely use technique has been TRM. This technique uses a thru, reflect standard and matched load standards to calculate the error coefficients. Problem is finding a broad band absorbing material for the match standard. Imperfections in the match standard cause residual errors after calibration. Match Hard to get broadband absorbers for match

TRL Calibration Thru Reflect Line
1/10/2006 TRL Calibration Thru Move the antenna away to compensate for the thickness of the short. Move it back for the next step. Reflect A second widely used technique is TRL. TRL uses a thru, reflect and line standard to determine the error coefficients. However, to measure the reflect, the port two antenna must be moved back by the thickness of the metal plate. The line standard is then realized by precisely moving the port two antenna on quarter wavelength. After the calibration the antenna needs to be precisely moved back to its original position. In order to do this accurately enough to get a good calibration, expensive positioning fixturing is required like optical table. For both TRM and TRL calibration the main problem is the third standard (Match or Line). The GRL calibration avoids using the third standard as it will be explained next. Move the antenna away on a quarter-wavelength and then back in the original position. Line Precise positioning fixtures are expensive

ECal, SOLT or TRL Cal done here
1/10/2006 Gated Reflect Line (GRL) Calibration Step one of two Two port calibration at waveguide or coax input into antennas removes errors associated with network analyzer and cables. 1. ECal, SOLT or TRL Cal done here Recently, Agilent introduced a new free space calibration technique that overcomes the weaknesses of the two previously discussed techniques. It is a simple two step process. The standards are easily obtained and it is completely automated. Two step Calibration process 1. Remove the antennae. Perform two port calibration at the coax or waveguide input into the antennae using ECal, TRL or SOLT calibration processes. The antennas are removed for this calibration.

GRL Calibration Continued
1/10/2006 GRL Calibration Continued Step two of two 2. Two additional free space calibration standards remove errors from antennas and fixture. Line (empty fixture) Reflect (metal plate of known thickness) Step 2. Attach the antennae. Measure two simple standards: a thru and a metal plate. Complete the calibration by removing the errors associated with the antennas and fixturing.

GRL Calibration – How It Works?
1/10/2006 GRL Calibration – How It Works? GRL Cal Error Model (forward only) 2-port Cal Terms MUT 2-port Cal Terms 1 S21 Tt GRL Error Adapter GRL Error Adapter D Ms S11 S22 Ml Tr S12 Coax or Waveguide 2-port Cal corrects errors from end of cable back into the instrument. Errors from Antennas and Fixture can be thought of as being lumped into a GRL error adapter. The GRL error adapter is quantified by measurements of reflect and line standards. The original 2-port Cal is modified to correct for the error adapter. Gated Reflect Line Calibration Here is how it works. The GRL technique requires that a calibration be performed at the ends of the cables that connect to the antennas. The GRL technique modifies this calibration such that the reference plane is transformed from the end of the cables to the surface of the metal plate used for calibration. When the calibration is complete the empty fixture measures as a slice of air the thickness of the metal plate. Before the modification the fixture can be thought of as two error adapters between the end of the cables and the space that the metal plate occupies.

MUT and GRL Error Adapters
1/10/2006 MUT and GRL Error Adapters After 2-Port Calibration MUT O21 S21 T12 O11 O22 S11 S22 T22 T11 O12 S12 T21 Six Unknowns Here is a signal flow graph showing just the GRL adapters and a MUT. The Oxx parameters refer to port 1 and the Txx refers to port 2. The goal is to determine all the Oxxs and Txxs and embeding them into the orginal calibration. Each of the error adapters can be modeled by their four s-parameters. Because of the passive nature of these error adapters O21=O12 and T21 = T12. This leaves six unknowns. O21 = O12 O11 O22 T21 = T12 T11 T22

GRL Calibration – How It Works?
1/10/2006 GRL Calibration – How It Works? Time Domain of Empty Free Space Fixture gate Above is a time domain S11 graph of the measured fixture when the fixture is empty Note that you can identify the various responses as the reflection associated to the transmitting antenna, followed by the low reflection of air and then the reflection associated with the receiving antenna and its associated supporting structure. The GRL places time domain gates around the responses associated with the transmitting antenna. The frequency domain of this gated measurement is O11 of the port one error adapter. The same approach can be used to determine T11 of the port 2 error adapter.. These terms can be then embedded into the original 2-port calibration. Using this new calibration set the other terms of the error adapters can be calculated from the s-parameter measurements of the Thru (empty fixture or air) and the Reflect (metal plate) standards. Transmitting Antenna Receiving Antenna Air

MUT and GRL Error Adapters
1/10/2006 MUT and GRL Error Adapters After O11 and T11 are embedded into the original 2-Port calibration. MUT T22 T12 T21 O22 O21 O12 S11 S22 S21 S12 Four Unknowns Once O11 and T11 are embedded into the original 2-port calibration, the signal flow graph looks like this, with four remaining terms in the error adapter. They will be removed by measuring two additional standards, the Thru and Reflect. O21 = O12 O22 T21 = T12 T22

GRL Metal Plate Standard
1/10/2006 GRL Metal Plate Standard MUT T22 T12 T21 O22 O21 O12 S11 S22 S21 S12 The plate standard is the metal plate of know thickness. In a perfect freespace system, the metal plate will reflect all energy back, so P11 and P22 are set to minus one. Since all energy is reflected, no energy passes through, so P12 and P21 are set to zero. Using Mason’s rule, the S-parameters of the port one and two plate standards are established.

GRL Thru Standard (Air)
1/10/2006 GRL Thru Standard (Air) MUT T22 T12 T21 O22 O21 O12 S11 S22 S21 S12  = frequency 0 = permeability of air 0 = permittivity of air d = thickness of the metal plate The Thru standard is the empty fixture or air and designated here by A. Since in a perfect free space system, S11 or air, or A11 here, would see no reflection back, A11 and A22 are set to zero. A21 and A12 are equal to the expression above. Once again, using Mason’s loop rule, we can establish expressions for the S-parameters of the port one and two air standards. With these four equations, the two here and the on the previous slide, the four remaining coefficients of the error adapters can be solved for. These are then embedded into the original calibration. The result is a full two-port calibration with the reference planes at the surface of the metal plate. The two equations on the previous slide and these equations are used to solve for the remaining coefficients of the error adapters. These terms are then embedded into the original calibration. The result is a full two-port calibration with the reference planes at the surface of the metal plate.

GRL Calibration – System Considerations
1/10/2006 GRL Calibration – System Considerations Fixture with Metal Plate Metal Plate Determine Sample Position Determine Sample Size Choose Metal Plate There are several considerations when setting up a system to performing a GRL cal. Distance to Sample The distance from the antenna to the sample can be determined by looking at the time domain response of the metal plate measurement. There should be a low reflection span of time between the last response of the antenna and the metal plate. Sample Size The size of the sample and the distance the sample needs to be from the antenna can be determined by analyzing your fixture using time domain. The antennas used determine the minimum sample size. First locate the position of the metal plate in time. When the plate is removed, the difference in the response should be large. You should not be able to see the fixture's supporting structure. At least 50 dB. The greater the better. The sample height and width should be large enough that the beam fits inside. This can be easily checked by sliding the metal plate in from the side and seeing when it starts to show in time domain. Metal Plate Another consideration is the selection of the metal plate. Ideally the metal plate should approximately the same thickness as the sample to be measured. This puts the measurement reference planes at the surface of the sample. While this is ideal, any thickness differences are accounted mathematically by the sample holder description entries of the 85071E.

1/10/2006 GRL Calibration – System Considerations Choose Time Domain Parameters Empty Fixture Fixture with Metal Plate Time domain parameters. After the initial 2-port calibration is performed, the location of the metal plate in time must be determined. Above is a plot of the empty fixture and a plot of the fixture with the metal plate. By comparing the two plots, the time position of the plate fall between 2 and 6 nsec. The exact position is not important as long as you specify times where no other reflection has a larger amplitude than the reflection off the plate. This can occur when the reflection off the antenna is larger than the plate. The final parameters to set are the gate shape and the gate span. These parameters are used during the gated response isolation portion of the calibration. This calibration is separate from the GRL cal and is used to reduce any residual errors. The GRL corrected measurements of the empty fixture and the fixture with the metal plate are gated and used as a separate response /isolation calibration. These terms are applied in the software. The gate span should be set wide enough to include the entire response of the reflection off the plate or the transmission of the empty fixture but narrow enough to minimize the unwanted responses. Air at 3.5nS Metal Plate at 3.5nS

1/10/2006 GRL Calibration – System Considerations Choose Number of points to Avoid Aliasing Minumum Number of Points = 1 + Range * (Stop Frequency – Start Frequency) Where Range is the needed alias free range in Seconds Empty Fixture Receiving Antenna Transmitting Antenna Number of measurement points. Time domain is used to isolate the reflections off each of the two antennas. Because of this, aliasing must be considered. The alias-free range can be calculated as shown. Range= (number of points-1)/ (stop frequency - start frequency) It is important that the alias-free range be greater than the length of the free-space fixture. This includes all paths until the signal is attenuated to an insignificant level. Above is a plot of S11 of the empty fixture with a calibration coaxial/waveguide calibration turned on. In the plot above, the first series of reflections, after t=0, is the reflections associated with the antenna. Next we see the reflections off the receiving antenna and the supporting structure. The response then reduces to approximately zero at about 20 nsec. Since the measurement was made over x-band ( GHz) the minimum number of points can be calculated as: Number of points= 1 + Range*(stop frequency - start frequency)=1 + 20e-9*(12.4 e e9) = 85 Based on the required range the minimum number of points requires is 85. In general the more points the better to insure that as little aliasing occurs as possible. The same analysis should be performed on S21. 20nS

75–110 GHz Standard Gain Form System
1/10/2006 75–110 GHz Standard Gain Form System Here’s a look at a W-band setup using standard gain horns. These are from Custom Microwave in Colorado for around $300 each. The sample holder was made in house. Fairly good results can be obtained with this system.

75–110 GHz Quasi-Optical (QO) System
1/10/2006 75–110 GHz Quasi-Optical (QO) System Here’s a look at another W-band setup, this time using corrugated horns that produce a controlled Gaussian beam. The mirrors redirect and reshape the beam so that the wave front is flat and the beam spot is ~30mm in dia. More accurate results for e’ can be achieved with this fixture. It is available from Thomas Keating Ltd. In the UK for around 20K$ US.

1/10/2006 QO System Schematic Additional information available at :

Measurement Results 1/10/2006
Here is a comparison of the results with both setups – standard gain horn set up and Quasy Optical table.

Free Space Sources of Error
1/10/2006 Free Space Sources of Error Sample Finite size Contact with conducting backplane Non-plane-wave illumination Mechanical stabilty/alignment of sample and antennae Quality of anechoic environment Free space measurements are susceptible to errors due to finite sample size and non-plane wave illumination. Care should be taken to minimize these effects.

Free Space Summary Special calibration Noncontacting, often
1/10/2006 Free Space Summary Special calibration considerations Requires connectorless standards (TRL, LRM) Tightly controlled distance from antenna to sample (TRL) Noncontacting, often nondestructive Sample not contained Useful for high temperatures Remote sensing . GRL calibration Time domain gating eliminates errors Requires large, flat, thin, parallel faced sample

Three Resonance Techniques
1/10/2006 Three Resonance Techniques Sample Iris-coupled end plates MUT E Post Dielectric resonator Copper ASTM 2520 (Waveguide TE10n Cavity) SPDR (Split Post Dielectric Resonator) Split Cylinder Resonator MUT E

Kramers-Kronig Equations
1/10/2006 Resonant versus Broadband Techniques Resonant techniques high impedance environment reasonable measurements possible with small samples measurements at only a few frequencies well suited for low loss materials Broadband techniques low impedance environment requires larger samples to obtain reasonable measurements measurement at “any” frequency When using resonator technique we have measurement(s) at discrete frequency points. This should be enough, because lossless materials are nearly non- dispersive. This means that their dielectric constant and loss tangent will stay constant over the frequency range. This can be deduced from the Kramers-Kronig equations above. If the imaginary part is zero (or close to), the real part will stay constant. Kramers-Kronig Equations

Resonant versus Broadband Techniques
1/10/2006 Resonant versus Broadband Techniques

Resonant Cavity f Q z Q0 QS f 1/10/2006
Dielectric Resonator Sample z Metal Enclosure hG h l Coupling Loop Q0 f C QS S Sample Iris-coupled end plates Resonant cavities are high Q structures that resonate at certain frequencies. A sample of the material affects the center frequency (fc) and quality factor (Q) of the cavity. From these parameters, the complex permittivity (er) or permeability (mr) of the material can be calculated at a single frequency. For dielectric measurements the sample should be placed in maximum of the electric field and for magnetic in maximum of the magnetic field. If the sample is inserted through a hole in the middle of the waveguide length, then odd number of half wave lengths will bring electric field where the sample is and even number will be for magnetic measurements. f Q

Resonant Cavity System
1/10/2006 Resonant Cavity System Network Analyzer PNA, PNA-L, ENA, ENA-L Legacy 8712/14, 8752, 8753, 8719, 8720, 8722, or 8510 LOG MAG PHASE DELAY SMITH CHART POLAR LIN MAG SWR MORE START N MHz CH1 S11 1 U FS Cor Hid Sample Iris-coupled end plates A typical resonant cavity system consists of a network analyzer, cavity fixture and an external computer and software. Cavity fixtures and software are not available from Agilent. Cavity Fixture

Cavity Methods (Exact and Perturbation)
1/10/2006 Cavity Methods (Exact and Perturbation) Resonator (absolute) TE cavity 01n Sample fills a significant portion of cavity volume. Exact theories applied to cavities for low loss materials. Transmission line (waveguide) cavity Cavity perturbation There are two cavity methods that can be employed. The most accurate is the resonator or absolute method which requires a sample that fills a large portion of the cavity and a very precise knowledge of the fields in the cavity. The simpler method is the perturbation method which requires a very small sample such that the fields in the cavity are only slightly disturbed to shift the measured resonant frequency and cavity Q. Sample disturbs (without changing) fields in cavity. f < 0.1% (recommended frequency shift of the sample) Measure shift in resonant frequency and Q.

Waveguide Transmission Line Cavity (ASTM 2520)
1/10/2006 Waveguide Transmission Line Cavity (ASTM 2520) Next we will focus on resonance measurements of dielectric properties using TE10n waveguide resonance cavity. The method is cavity perturbation method and is base on procedure described in ASTM 2520 document.

Transmission Line Cavity (ASTM 2520)
1/10/2006 Transmission Line Cavity (ASTM 2520) Based on ASTM 2520 E-field Rectangular waveguide cavity propagates TE10n mode Sample placed parallel to cavity E-field Fibers may be inserted through a fused silica rod The simplest example of a cavity is made from a section of rectangular waveguide with iris coupled end plates. The sample is placed parallel to the electric field. The technique is based on ASTM standard D2520. ________________ “Test methods for complex permittivity (Dielectric Constant) of solid electrical insulating materials at microwave frequencies and temperatures to 1650°,” ASTM Standard D2520, American Society for Testing and Materials “Test methods for complex permittivity (Dielectric Constant) of solid electrical insulating materials at microwave frequencies and temperatures to 1650°,” ASTM Standard D2520, American Society for Testing and Materials

Transmission Line Cavity
1/10/2006 Transmission Line Cavity

Odd and Even Number of Half Wavelengths in the Resonator
1/10/2006 Odd and Even Number of Half Wavelengths in the Resonator L E field H field Sample One and the same resonator can be used for dielectric or magnetic measurements depending on the frequency (number of half wavelengths in the resonator. Odd numbers of half wavelengths will bring the electric field in the center of the resonator and allow for permittivity measurements. Even numbers of half wavelengths will bring the magnetic field in the center of the resonator and allow for permeability measurements. Even number of half wavelengths. The sample is in the max of the magnetic field, for magnetic measurements. Odd number of half wavelengths. The sample is in the max of the electric field, for electric measurements.

Calculation of the Resonance Frequency
1/10/2006 Calculation of the Resonance Frequency L b a f, GHz a, mm L, mm p, number of half wavelengths on L The resonance frequencies can be calculated from the resonator dimensions. Conversely, for given resonance frequency, the dimensions of the resonator can be calculated.

Cavity Perturbation Algorithm
1/10/2006 Cavity Perturbation Algorithm ASTM 2520 Method A vertical rod or bar sample is inserted in a TE10n rectangular waveguide resonant cavity. There is no need to calibrate the analyzer since only frequency is measured. Scalar analyzer can be used. empty cavity sample inserted Q c Q The algorithm to determine permittivity is dependent on the center frequency and Q measured with and without the sample inserted. The exact volume of the empty cavity and sample are also required. s f f f s c

TE10n Waveguide Cavity Transmission |s21| Frequency, GHz Sample 1
1/10/2006 TE10n Waveguide Cavity 9.8 9.82 9.84 9.86 9.88 9.9 9.92 9.94 9.96 9.98 10 5 4 0.001 0.002 0.0025 0.003 0.0035 0.004 9.9375 9.895 Sample 1 Empty cavity Sample 2 Transmission |s21| Sample 3 Transmission measurement of the empty cavity and several samples. The presence of sample in the resonator will shift the frequency to lower frequencies and broaden the resonance curve (lower the Q-factor). Frequency, GHz

TE10n Waveguide Cavity Calculations
1/10/2006 TE10n Waveguide Cavity Calculations Sample 2 is 2.9 mm x 1.57 mm plastic rod Calculation for a specific sample

Alternative Calculation of Losses (er”)
1/10/2006 Alternative Calculation of Losses (er”) DL is the difference of the attenuation of the empty and loaded with the sample resonator. This measurement will offer better sensitivity for low-loss materials, but there is a need of good calibration. Empty cavity Transmission 9.8 9.82 9.84 9.86 9.88 9.9 9.92 9.94 9.96 9.98 10 Frequency, GHz

TE10n Waveguide Cavity Calculations
1/10/2006 TE10n Waveguide Cavity Calculations Comparative measurements of the tand using Q-factor measurement (tand1) and attenuation measurement (tand2)

Sources of Error for ASTM Cavity
1/10/2006 Sources of Error for ASTM Cavity Network analyzer frequency resolution Sample dimension uncertainty and parallel sides Approximations in analysis Although a resonant cavity technique is extremely accurate, it is still subject to errors. The network analyzer must have excellent frequency resolution (1 Hz) to measure the very small changes. The sample dimensions must be known precisely. There is also additional error due to approximations in the analysis.

Cavity Fixtures Agilent waveguide components
1/10/2006 Cavity Fixtures Agilent waveguide components X/P/K/R/Q/U/V/W 11644A calibration kits (standard section) ASTM standard D-2520 Customer would need to modify this standard section of waveguide to make it a resonant cavity.

SPDR (Split Post Dielectric Resonator)
1/10/2006 SPDR (Split Post Dielectric Resonator) Next we will focus on the Split Post Dielectric Resonator (SPDR). It provides an accurate technique for measuring the complex permittivity of dielectric and ferrite substrates and thin films at a single frequency point in the frequency range 1–20 GHz. The resonator needs to be purchased. It is not easy to be manufactured like ASTM resonator.

SPDR (Split Post Dielectric Resonator)
1/10/2006 SPDR (Split Post Dielectric Resonator) SPDR Resonators for different frequencies

1/10/2006 SPDR for 10 GHz The split-post dielectric resonator (SPDR) provides an accurate technique for measuring the complex permittivity of dielectric and ferrite substrates and thin films at a single frequency point in the frequency range 1–20 GHz. Besides the SPDR fixture, a vector network analyzer of the PNA family and the software 83071E, option 300, are required for the measurement. The measurement is automatic and easy to perform.

Cross-Section of SPDR fixture
1/10/2006 Cross-Section of SPDR fixture Dielectric Resonator Sample z Metal Enclosure hG h l Coupling Loop The geometry of a split dielectric resonator is shown above. This is a simplified schematic to illustrate the main parts of the SPDR. A pair of thin dielectric resonators and a metal enclosure of relatively small height are used in the construction of the SPDR fixture. This allows creating a strong evanescent electromagnetic field, not only in the air gap between the dielectric resonators, but also in the cavity region for radii greater than the radius of dielectric resonators. This simplifies numerical analysis and reduces possible radiation.

PNA Network Analyzer with installed 85071E software, opt. 300
1/10/2006 Measurement Set-Up SPDR fixture PNA Network Analyzer with installed 85071E software, opt. 300 Sample The measurement set-up shown above consists of the following components: PNA network analyzer, operating in appropriate frequency range for the fixture Software 85071E with option 300, installed in the PNA SPDR fixture

Choosing the Sample Dimensions for Known SPDR Frequency
1/10/2006 Choosing the Sample Dimensions for Known SPDR Frequency h Minimum measurable area L l E field in plane The method is nondestructive, since no special sample preparation is needed as long as the substrate can fit in the SPDR. The electric field in the resonator is parallel to the surface of the sample as shown on above. The main sample requirements are to have two strictly parallel faces, the thickness of the sample h to be less than the fixture air gap hG and to have enough area to cover the inside of the fixture. The air gap between the sample and the dielectric resonator (see above) does not affect the accuracy of the measurement. The sample may have a rectangular or round shape as shown in the above. For easy handling of the sample it is recommended that the sample area dimension L is bigger than the dimension of the minimum measurable area l (or active area of the fixture).

1/10/2006 Frequency versus Permittivity and Sample Thickness for 10 GHz Resonator 7.2 7.6 8.0 8.4 8.8 9.2 9.6 10.0 1 10 100 1000 h=0.97 mm h=0.7 mm h=0.5 mm h=0.35 mm h=0.2 mm h=0.1 mm h=0.05 mm h=0.025 mm empty resonator f, GHz Max recommended frequency shift The required thickness of the sample also depends on the dielectric constant of the material. Materials with high dielectric constants must have less thickness. Above figure shows the typical resonant frequency f versus permittivity in the case of a 10 GHz SPDR. For this fixture, if the permittivity of the sample is more than 10, the maximum sample thickness must be smaller than the fixture gap thickness hG. At the same time, the sample must also be thick enough to create enough frequency shift to be easily measured. If the sample permittivity is greater than 10, the sample thickness may have to be reduced to keep the frequency shift within the recommended range. The thickness should be chosen from the above figure, knowing that the frequency should not be much smaller than 8.5 GHz.

Sample Related Dimensions of SPDR Fixtures for Different Frequencies
1/10/2006 Sample Related Dimensions of SPDR Fixtures for Different Frequencies The fixture air gap hG and the active area dimension l of the fixture depend on the operating frequency f of the resonator. Table 1 shows approximate values of these dimensions for resonators operating at different frequencies. The sample dimension L should be less than Lf, which is the maximal dimension that the fixture can accommodate. * The fixture can be ordered with Lf dimension up to this value, but is recommended to be less, if there is no special need.

Measurement of Thin Films
1/10/2006 Measurement of Thin Films The SPDR technique can also be used for measuring thin films. The above figure shows the typical resonance frequencies f versus the permittivity for a 10 GHz resonator.

Thin Film on Substrate (1) Measure only substrate
1/10/2006 Thin Film on Substrate If the film is deposited on a substrate, the resonant frequency shift due to presence of the thin film is very similar to the previous slide (differences are about 1%-2%). To separate the frequency shift of the film from the overall frequency shift of the substrate and the film, the substrate alone should be measured initially (without film). Permittivity and loss tangent of thin films deposited on substrates having a diameter >20 mm can be evaluated directly with systematic 1%-2% error using the same program as for uniform dielectrics. In this case one has to measure the empty resonator (f01,Q01), empty resonator with a substrate only (fs,Qs) and, after film deposition, repeat the measurement of the empty resonator (f02, Q02) and resonator with film and substrate (f2,Q2). The film should face down during this measurement. (1) Measure only substrate (2) Measure the substrate with the film

Measuring Thin Film not Deposited on Substrate
1/10/2006 Measuring Thin Film not Deposited on Substrate When measuring films alone (not on a substrate), it is possible to stack them. The structure of the field is such that possible air gaps between the films will not affect the measurement. Results from measurements of stacked polymer films are independent of the number of films, which proves that the split dielectric resonator method is not sensitive to the presence of air gaps between the stacked films.

Permittivity Calculation
1/10/2006 Permittivity Calculation h sample thickness f0, fs - the resonant frequency of the SPDR – empty and with sample Ks - function computed and tabulated for specific SPDR This the equation used to calculate the real part of the dielectric constant. All of the parameters in the above equation are measured besides the function Ks. The function Ks is calculated and tabulated for specific resonator.

Loss Tangent Calculation
1/10/2006 Loss Tangent Calculation measured unloaded Q-factor of the SPDR with the dielectric sample QDR, QDR0- Q-factors depending on losses in the dielectric resonators with and without sample This the equation used to calculate the loss tangent. All of the parameters in the above equation are measured besides the function K1 and K2 .The K functions are calculated and tabulated for specific resonator. Qc,Qc0 - Q-factors depending on metal losses of the resonant fixture with and without the sample Electric energy filling factor of the sample

Uncertainty of the Real Dielectric Constant
1/10/2006 Uncertainty of the Real Dielectric Constant The main source of uncertainty of the real permittivity is due to the uncertainty of the thickness of the sample under the test. For most of the samples T is equal to one. Only for thick, large permittivity samples the value of T increases, but always is < 2. The most significant contribution to the overall Ks error arises from coefficients related to the thickness and permittivity of the dielectric resonators. Calculation errors The main source of uncertainty of the real permittivity is related to uncertainty of the thickness of the sample under the test. Relative error of real permittivity due to thickness uncertainty can be expressed as (1), where: 1<T<2. Usually T value is very close to unity except for thick, large permittivity samples. For such samples the value of T increases, but always remains smaller than two. Additional factors affect the overall uncertainty, e.g. differences between real dimensions of the resonant fixture and permittivity of dielectric resonators, and the values assumed in computations. The most significant contribution to the overall Ks error arises from coefficients related to the thickness and permittivity of the dielectric resonators. Assuming a given value for the thickness of the split post resonators and all other dimensions of the resonant structure, it is possible to choose a permittivity for the dielectric resonators such that we will get identical computed and measured resonant frequency values for an empty fixture. Exact numerical analysis has shown that in such a case Ks errors due to uncertainty of dielectric resonator thickness and permittivity practically cancel out. If such an approach is used it is possible to compute Ks coefficients for specific resonant structures with uncertainties better then 0.15% so one can estimate the total uncertainty for real permittivity as (2). In principle, it is possible to further decrease systematic errors by 0.15% by making measurements of standard reference materials and introducing corrections of Ks coefficients, but this would require perfectly machined specimens whose permittivity is defined with precision better than 0.15%. Total error Exact numerical analysis has shown that the Ks errors due to uncertainty of dielectric resonator thickness and permittivity can practically cancel out under some conditions. In such case it is possible to compute Ks coefficients for specific resonant structures with uncertainties better then 0.15% .

Uncertainty of the Loss Tangent
1/10/2006 Uncertainty of the Loss Tangent Depends mainly on the Q-factor measurement uncertainty Typical uncertainty of 1% with resolution of 2 x 10-5 Dielectric loss tangent uncertainty depends on many factors, but mainly the Q-factor measurement uncertainty and the value of the electric energy filling factor. For a properly chosen sample thickness it is possible to resolve dielectric loss tangents to approximately 2x10-5 for Q-factor measurements with an accuracy of about 1%. NOTE: For very low loss materials, like sapphire or quartz, the measured Q-factor of the SPDR with a sample is often greater than the Q-factor for the empty SPDR. In spite of this, evaluated dielectric loss tangent values are greater than zero due to proper Qc and QDR corrections.

Split Cylinder Resonator
1/10/2006 Split Cylinder Resonator Next we will focus on the Split Cylinder Resonator. It provides an accurate technique for measuring the complex permittivity of dielectric substrates and thin films at several frequency points. The resonator is not easy to be manufactured like ASTM resonator.

Split Cylinder Resonator Overview
1/10/2006 Split Cylinder Resonator Overview relative permittivity uncertainty: ’r ~ 1% loss tangent uncertainty: tan < 1x10-4 measurements in GHz range planar samples no sample machining (nondestructive) simple measurement procedure Originally proposed by Gordon Kent as nondestructive technique. Single-frequency technique: only TE011 resonant mode. Sample in maximum electric field: high measurement sensitivity Later the method was improved by NIST G. Kent, “Nondestructive permittivity measurements of substrate,” IEEE Trans. Instrum. Meas., vol. 45, pp , Feb Janezic M. and Baker-Jarvis J., “Full-wave Analysis of a Split-Cylinder Resonator for Nondestructive Permittivity Measurements,” IEEE Transactions on Microwave Theory and Techniques, vol. 47, no. 10, Oct 1999, pg

Split Cylinder Resonator Overview
1/10/2006 Split Cylinder Resonator Overview Upper Cylindrical Cavity Region MUT E Coupling loop to Network Analyzer Lower Cylindrical Cavity Region Place substrate between two halves of the split-cylinder resonator. Measure resonant frequency f and quality factor Q and calculate the permittivity and loss tangent of the substrate.

1/10/2006 NIST Improvements Developed new theoretical model for split-cylinder resonator to improve accuracy of relative permittivity and loss tangent measurements: Properly model fringing fields in substrate region. Include higher-order TE0np modes to broaden frequency coverage. Account for conductive losses of cavity walls and endplates. Janezic M. and Baker-Jarvis J., “Full-wave Analysis of a Split-Cylinder Resonator for Nondestructive Permittivity Measurements,” IEEE Transactions on Microwave Theory and Techniques, vol. 47, no. 10, Oct 1999, pg

NIST Theoretical Model - Mode-Matching Method
1/10/2006 NIST Theoretical Model - Mode-Matching Method Divide geometry into regions. Represent fields in each region by finite sum of normal modes with unknown mode coefficients. Enforce boundary conditions at junction of regions to derive system of linear equations. Simplify system of linear equations and resonance condition with orthogonality relations.

NIST Resonator Design Precise alignment of two resonator sections.
1/10/2006 NIST Resonator Design Precise alignment of two resonator sections. Easily adjustable coupling level. Designed for use in environmental chamber. Accommodates samples up to 5 mm thick. In-situ measurement of sample thickness.

NIST Measurement Comparison
1/10/2006 NIST Measurement Comparison Relative Permittivity Loss Tangent The Split-Cylinder resonator measurements are compared against the measurements of the same materials with the highest precision circular cylindrical cavity. More information about the circular cylindrical cavity is available in the following NIST Technical Note: E. Vanzura, R. Geyer, M. Janezic, “The NIST 60-Millimeter Diameter Cylindrical Cavity Resonator: Performance Evaluation for Permittivity Measurements,” NIST Technical Note 1354, 236 pages, August 1993.

Split Cylinder Resonator
1/10/2006 Split Cylinder Resonator Advantages Accurate nondestructive measurement of dielectric substrates. No sample machining necessary. Broadband frequency coverage. Characterization of thin materials possible. Disadvantages Electric field parallel to the dielectric substrate. Difficult to measure loss tangents below 5x10-5. Identification of TE0np resonant modes sometimes difficult.

Cavity Summary Does not provide broadband frequency data Very accurate
1/10/2006 Cavity Summary Does not provide broadband frequency data Very accurate Precise sample shape required (usually destructive). Very sensitive to low loss (to 10-6 for some cavities) The cavity technique is the most accurate one, especially for low loss materials. But measurement are made at single frequencies only and the analysis can be complex SPDR and SCR methods are nondestructive Analysis may be complex

Summary of Techniques Loss Coaxial Probe Transmission Line Free Space
1/10/2006 Summary of Techniques Loss Coaxial Probe High Transmission Line Free Space Medium The different measurement techniques are mapped out according to frequency range of operation and the MUT losses. Parallel Open Resonator Low Resonant Cavity Plate Fabry-Perot 50 MHz 5 GHz 20 GHz 40 GHz 60 GHz Frequency Low frequency RF Microwave Millimeter-wave

Measurement Technique Summary
1/10/2006 Measurement Technique Summary Free Space Cavity Transmission Line Coaxial Probe One way to select a measurement technique is by frequency range. The techniques discussed previously range in frequency from dc to over 100 GHz. Parallel plate 1 2 3 4 5 6 7 8 9 10 11 12 DC 10 10 10 10 10 10 10 10 10 10 10 10 Frequency (Hz)

Summary of Techniques Coaxial Probe Transmission Line Free Space
1/10/2006 Summary of Techniques Coaxial Probe Transmission Line Best for lossy MUTs; liquids or semi-solids Broadband, convenient, non-destructive Best for lossy to low loss MUTs; machineable solids Broadband Resonant Cavity Best for low loss MUTs; small samples, Substrates, Thin Films Accurate Free Space Best for high temperatures; large, flat samples Non-contacting Parallel Plate Best for low frequencies; thin, flat sheets Other factors such as accuracy, convenience and the material shape and form are also factors in selecting a measurement technique.

Agilent Technologies Instruments and Fixtures
1/10/2006 Agilent Technologies Instruments and Fixtures 10Hz 100Hz 1kHz 10kHz 100kHz 1MHz 10MHz 100MHz 1GHz 10GHz 100GHz Legacy – 8712, 8753, 8720, 8510 ENA, ENA-L 85070E 85071E 4263B, 4284A, 4285A, 4294A 16451B Dielectric test fixture Dielectric probe Transmission line software LCR meters/impedance analyzers Network analyzers DC 16452A Liquid test fixture E4991A Impedance/Material Analyzer 16453A Dielectric material test fixture PNA, PNA-L 16454A Magnetic test fixture

Which Technique is Best?
1/10/2006 Which Technique is Best? It depends on: Frequency range Expected value of er and mr Required measurement accuracy Material properties (i.e., homogeneous, isotropic) Form of material (i.e., liquid, powder, solid, sheet) Sample size restrictions Destructive or nondestructive Contacting or noncontacting Temperature Cost And more . . . Choosing the best technique for a given application is not always easy since it is dependent upon many factors.

Appendix: Other Methods
1/10/2006 Appendix: Other Methods

Open-Ended Waveguide a b 1/10/2006
Ganchev, S.I. Bakhtiari, S. Zoughi, R, “A novel numerical technique for dielectric measurement of generally lossy dielectrics,” IEEE Transactions on Instrumentation and Measurement, Volume: 41, Issue: 3, June 1992, pp .

Centrally Located Substrate in a Waveguide
1/10/2006 Centrally Located Substrate in a Waveguide analysis is straightforward no errors from air gaps non-destructive for non-metalized sheets simple and inexpensive E-fields in x-y plane of the sample (not z) frequency limited in the waveguide band

Line Resonators (Stripline)
1/10/2006 Line Resonators (Stripline) Rectangular resonator industry-standard method (ASTM D3380, IPC TM , MIL-P-13949E) accurate and reproducible to < 1% provides estimate of the dielectric losses destructive, large sample, sample preparation errors due to air gaps and fringing based on stripline (not microstrip) limited in range of measurable materials DL L DL DL compensates for the extra capacitance at the end of the line

Line Resonators (Strip and Microstrip)
1/10/2006 Line Resonators (Strip and Microstrip) Ring resonator d1 inner diameter of the ring d2 outer diameter of the ring The ring resonator is not subject of to errors from end effects. The ring resonator technique requires a microstrip line that is etched such that the circumference is a multiple integer number of full wavelengths. Like the line resonator technique, the resonant frequency measured by a network analyzer is used to compute the dielectric constant. The ring resonator is not subject of to errors from end effects. The ring is loosely coupled to transmission lines that are separated about the circumference by 180 degrees to minimize coupling around the ring.

Full-Sheet Resonance L m W n entire sheet resonates both sides clad
1/10/2006 Full-Sheet Resonance E L W m n entire sheet resonates both sides clad m and n are number of half wavelength along sides W and L 7 mm nondestructive suitable to many substrates not sensitive to thickness simple and inexpensive fringing and radiation errors multiple modes confusing difficult to get the losses The full sheet resonance technique requires a metallized rectangular substrate to create a “parallel plate dielectric loaded waveguide resonator”. It is inexpensive and non destructive, but subject to fringe and radiation errors and complex multiple modes. The resonant frequency measured by a network analyzer is used to compute dielectric constant at the m-th order of transverse resonance and n-th order of longitudinal resonance.

1/10/2006 References “Basics of Measuring the Dielectric Properties of Materials” Agilent Application Note, PN EN. R N Clarke (Ed.), “A Guide to the Characterisation of Dielectric Materials at RF and Microwave Frequencies,” Published by The Institute of Measurement & Control (UK) & NPL, 2003 J. Baker-Jarvis, M.D. Janezic, R.F. Riddle, R.T. Johnk, P. Kabos, C. Holloway, R.G. Geyer, C.A. Grosvenor, “Measuring the Permittivity and Permeability of Lossy Materials: Solids, Liquids, Metals, Building Materials, and Negative-Index Materials,” NIST Technical Note “Test methods for complex permittivity (Dielectric Constant) of solid electrical insulating materials at microwave frequencies and temperatures to 1650°,” ASTM Standard D2520, American Society for Testing and Materials Janezic M. and Baker-Jarvis J., “Full-wave Analysis of a Split-Cylinder Resonator for Nondestructive Permittivity Measurements,” IEEE Transactions on Microwave Theory and Techniques vol. 47, no. 10, Oct 1999, pg Krupka J., Gregory A.P., Rochard O.C., Clarke R.N., Riddle B., Baker-Jarvis J. “Uncertainty of Complex Permittivity Measurement by Split-Post Dielectric Resonator Techniques,” Journal of the European Ceramic Society, Number 10, 2001, pg Krupka, J., Geyer, R.G., Baker-Jarvis, J., Ceremuga, J., ”Measurements of the complex permittivity of microwave circuit board substrates using split dielectric resonator and reentrant cavity techniques,” Seventh International Conference on Dielectric Materials, Measurements and Applications, (Conf. Publ. No. 430), Sep 1996, pp 21-24, Bath, UK K. J. Coakley, J. D. Splett, M. D. Janezic, R. K. Kaiser, “Estimation of Q-factors and Resonant Frequencies,” IEEE Transactions on Microwave Theory and Techniques, Vol. 51, No. 3, pp , 2003

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