Nico Garcia
Physical measurements are expensive and time consuming. Ideally, you would only do a single measurement run for a new type of composite structure/material. A typical flow is as follows: characterize a material/structure in electromagnetic simulation, fabricate some samples, measure the samples in NRW, then tune the simulation model to better reflect measurements and iterate as needed. This has been sufficient for our applications. I should emphasize that NRW does have weaknesses, such as difficulty measuring low loss tangents. Free-space measurements are difficult because you need spot-focusing antennas that are manufactured to metrology grade and you must use relatively large samples that occupy the full cross-section of the antenna beam.
John Schultz
Free-space measurements are good, in general, for wideband characterizations, as you can measure a wide range of frequencies with one measurement. Free-space methods, however, are not typically good for measuring loss tangents of low loss materials, such as high density polyethylene, Rexolite or other conventional low loss polymers, like Teflon. The reason is that by passing through the material once, in a free-space focus-beam method, for example, you cannot accurately capture the loss tangent. Also, with free-space focus-beam methods, the number one uncertainty for measurements of the real part of permittivity is the tolerance of the thickness of the sample. Any variation in thickness, flatness, camber or nonuniformity (inhomogeneity) within the sample results in uncertainty.
If you want to measure loss tangent accurately, you need to move to a resonant device. By definition, a resonant device is a narrowband and not a wideband measurement, which is a disadvantage of the Fabry-Perot method. Resonant methods have good sensitivity for low loss materials, as the stimulus energy basically sloshes back and forth multiple times through the material and effectively amplifies the significance of the loss in the material. That said, another drawback of the Fabry-Perot method is that the sample thickness must be less than half a wavelength. This has an impact on the types of metamaterials or patterned artificial dielectrics that you can measure, as a representative sample is needed and if that cannot be achieved in a limited thickness then the measurement results won’t accurately capture the response of a larger metastructure. Another drawback of the Fabry-Perot is that the performance of this method starts to decline at E-Band frequencies and beyond. The reason is that the mirrors used in the system are not as conductive at higher frequencies where the skin depth starts to become electrically thick. This then reduces the Q of the measurement device and hence accuracy. The Epsilometer was designed to make measurements of microwave substrates. Therefore, it is good at measuring relatively thin sheets, 3 to 4 mm, of dielectric materials, but only at lower frequencies, say up to 6 GHz.
What tolerances for effective Dk and Df are acceptable for your applications and do you have any guidance or rules of thumb that you would suggest to others testing these dielectrics?
Marzena Olszewska-Placha
For the design activities that we run for microwave devices and systems, we focus on tolerances that are achievable with our test fixtures for materials characterization. For SPDR and FPOR, this is typically less than 0.5 percent for Dk and less than 2 percent for Df. For measurement methods like split-post dielectric resonators, Fabry-Perot open resonators or split-cylinder resonators, thickness variation or in other words, the uncertainty of thickness measurement translates almost one-to-one to Dk measurement uncertainty. For the Df, a crucial factor is the uncertainty of measuring quality factors with a vector network analyzer or other, like dedicated microwave Q-meters and this is of highest importance for low loss and high loss materials. If I were to choose one thing I would say, the quality of your material sample under test (SUT) is extremely crucial for the final uncertainty of your measurement in most of the commonly known and used material measurement methods. Therefore, much attention shall be put into preparing the SUT. Flatness and sample thickness variation across its surface are those factors, which are most pronounced in measurement uncertainty.
Jonathan Chisum
Variation in the effective permittivity of a unit cell degrades phase collimation and hence, antenna efficiency. For large-area GRIN lenses, for example, 10 to 20 across, it may be necessary to collimate as much as 15 to 20 radians of phase. A phase error of as little as 0.5 radians results in a gain reduction of several dB. Supposing a homogeneous effective medium, a 0.5 radian error upon 15 radians of collimated phase would result from a permittivity error of seven percent. Therefore, in order to achieve the expected phase collimation and hence maintain maximum gain, it is important to know the effective permittivity of a GRIN medium to within a small percentage error. Furthermore, to predict and anticipate losses through the thickness of the lens one must have an accurate measurement of the loss tangent.
Nico Garcia
I do not recommend using the rectangular waveguide NRW method with materials that have a dielectric constant above 10 because the samples either have to be extremely thin or the measurement data will exhibit resonances. I also do not recommend this method for use beyond 40 GHz because the samples will require very small cross-sections and measurements will be more sensitive to fabrication tolerance. You want the sample to fit snugly inside the waveguide and errors due to mechanical slop will scale with frequency. I recommend using WR-28 waveguides or larger, that is WR-62, WR-42 and WR-90. With bigger waveguides, it is easier to fabricate/handle the sample and the measurement is less sensitive to fabrication tolerance. However, the samples need to be thicker for lower-frequency characterization.
My advice is to do your due diligence. Make sure you have a good basis for your effective media approximation and be sure to validate your simulation model with real measurements. It is worth taking the time to identify the real measurements’ deviations from theory in order to generate a robust simulation model for future designs. Once you fabricate your structures, physically measure your samples’ mechanical tolerances (looking under a microscope, counting image pixels, etc.) and determine if errors are systematic or individual. Identify and quantify any idiosyncrasies in your process. For high contrast GRIN lens antennas, which use a wide range of dielectric constants, it is essential that these process quirks are replicated in the full antenna simulation. Lastly, most GRIN materials are non-magnetic but it is possible that a GRIN structure/component may create a magnetic response. Specifically, if you use metal inclusions in metamaterial cells, you need to be mindful of rings and other inductor-like structures. In these cases, you will want to use a measurement paradigm that can also detect changes in effective permeability. If your measurement implicitly makes the simplifying assumption that your structure has no magnetic response when it actually does, then your measurement results will be inaccurate.
John Schultz
With free-space methods, the short answer is that it depends. You can make this method pretty precise, but there is a relation of uncertainty with loss. For low loss dielectric materials, this method can start to get more accurate toward E-Band frequencies. We have found ways of doing corrections with the focusing error and beam shift that have enabled high frequency loss tangent sensitivity down below ±0.002 to 40 GHz and ±0.0002 at E-Band frequencies. With the square, loaded transmission line method, it is possible to measure the cubic sample in three different orientations and get the three main directions of anisotropy. All of these measurement methods are just tools in a toolbox. Every good measurement laboratory will have a variety of techniques, as no technique is going to be a winner for all situations, they all have their tradeoffs. It is just like a screwdriver; it will not work for every fastener. That is why I always tell people to have multiple tools.
Is dielectric isotropicity, homogeneity or linearity a concern for your applications? For anisotropic materials, which axis is important to you?
Marzena Olszewska-Placha
In our research and development activities, we typically deal with isotropic materials. However, from our experience and discussions with project partners and customers, we know that the importance of being able to confirm isotropy or quantify anisotropy is continuously growing. With our solutions, we test in-plane complex permittivity and in fact, Fabry-Perot open resonator enables us to separate in-plane components evaluating a material’s anisotropy.
Jonathan Chisum
In general, waves propagate from a feed to a lens with varying incident angles relative to the unit cell coordinate system. As such, the effective medium should be isotropic over a particular range of angles. Lens antennas are characterized by F/D where D is the lens diameter and F is the focal distance from the lens to the feed with typical ranges being 0.5 to 0.8. Waves propagate from the feed to the lens at angles ranging from broadside to tan-1(0.5/(F/D)) or from about 0 to 45 degrees (F/D=0.5); hence, permittivity should be relatively constant over this range of incident angles. We typically design unit cells for an isotropic response out to 45 degrees. In general, all-dielectric unit cells are more isotropic than metallo-dielectric unit cells and circular features on a hexagonal lattice are better than, for example, square features on a square lattice.2
In our typical application, we are exploiting inhomogeneity to realize a GRIN medium and hence we simply require that the host material be consistent and that our mixture of air to dielectric be predictable. The same print requirements that would maintain a homogeneous medium in another application also ensure our GRIN media is printed as designed.
Some of our lenses are intended to be operated in an interference-dominated environment where we rely upon the linear lens radiation pattern to provide angular filtering of interferers. Other of our lenses are intended for use in high-power, kW-level, applications. In both cases, we require highly linear dielectrics. We have performed high-power testing and determined that representative all-dielectric GRIN media is highly linear and this is a major advantage of lens antennas over, for example, a phased array with active components.
Nico Garcia
The rectangular waveguide NRW method exclusively examines the TE10 mode, so you only ever see one diagonal term of the permittivity tensor at a time. To measure other diagonal terms, you would need to make different samples with the structure rotated. Most structures tend to be fairly isotropic but if the simulations indicate high anisotropic character, then it’s probably worth characterizing the other tensor values.
John Schultz
If you have a composite material that is a mixture of two different things, even old-school-type stuff without purposeful patterning, like a fiberglass composite, you will have inhomogeneity and anisotropy. This is definitely another very large source of uncertainty with these material measurement techniques. The accuracy often is not limited by the device, because the material is not necessarily mixed well enough, or the fibers are not aligned properly, or there are voids. The limit to accuracy is often limited by the homogeneity of the material. That is the reality of these metamaterials and of complex, artificial dielectrics in general. Often the quality of these complex materials depends on how much money it will take to get them more homogenous. Another option is just to characterize the material over a larger area or take multiple samples and get a statistical average of performance. That may be what is needed for dealing with a given material, depending on the application requirements.
Anisotropy is very common, and it is critical as some may not realize that their materials are anisotropic. Say you are making a composite with fiberglass; the orientation of the fibers will induce some anisotropy. Often when manufacturing something with fibers, they will try to alternate layers with different fiber orientations to enhance the isotropy and create an approximately homogeneous material, though a composite will always be inhomogeneous to some extent. Even some homogeneous materials can be anisotropic. For example, stretched acrylic enables the polymer chains to align preferentially, which changes the in-plane versus out-of-plane properties of an RF window.
CONCLUSION
The latest AM techniques have enabled the fabrication of new types of complex dielectric structures, including lattice dielectrics and dielectric metastructures. These new fabrication technologies have opened doors to creating innovative new solutions, at the cost of more complex testing and dielectric measurement requirements. Having a solid foundation in dielectric physics and dielectric measurement can enable a designer to more effectively harness these new AM technologies and realize new solutions leveraging AM.
References
- J. Krupka, “Frequency Domain Complex Permittivity Measurements at Microwave Frequencies,” Measurement Science and Technology, Vol. 17, No. 6, 2006, Web: https://iopscience.iop.org/article/10.1088/0957-0233/17/6/R01/meta.
- J. Krupka, “Microwave Measurements of Electromagnetic Properties of Materials,” Materials, Vol. 14, No. 17, Sept. 2021, Web: https://www.mdpi.com/1996-1944/14/17/5097.
