Figure 1 Free-space measurement test setup. Source: Compass Technology Group.
Knowing a material’s RF properties, such as its complex permittivity and permeability, can be very important. The radome protecting an outdoor radar from the elements must have a known permittivity and thickness to pass radar frequencies with minimal attenuation. How will a thin coating of water on the radome effect performance? The protective cover over the radar embedded in an automobile bumper must be designed to pass the mmWave frequencies emitted and received. How will paint affect the RF transmission through the cover? Antennas are encased in our cellular phones. How do the plastic materials affect the antenna performance? Material measurements with a vector network analyzer (VNA) can measure material properties and answer these important questions.
HOW IS A VNA USED TO MEASURE MATERIAL PROPERTIES?
Microwave or mmWave signals are applied to a flat material sample with known thickness. Signals incident on the sample should be plane waves applied normal to the sample’s surface. This way, RF signals that transit the material pass through the known thickness and not some longer path at an angle. It is sufficient to measure the thickness and the transmission and reflection characteristics of a material to determine its complex permittivity. Permeability may also be determined, but the calculation is greatly simplified if it can be assumed to be unitary.
Figure 2 SwissTo12 MCK measurement system.
Figure 3 SPEAG DAK measurement system.
Figure 4 SPEAG DAK-TL2 measurement system.
The VNA is either attached to a pair of antennas for a free-space measurement or to a waveguide with a sample holder. In the free-space method, a pair of horns may be used to send and receive the signal and dielectric lenses are positioned to focus the beams onto the specimen. In Figure 1, the sample is held by a fixture in the center between the antennas of a system offered by Compass Technology Group and at a position where the focused beams are most planar. Calibration is performed using a shorting plate as the reflect and an empty sample holder as the through. Time domain gating is used around the sample position in bandpass mode to eliminate stray reflections and multipath. The sample is then inserted and S-parameter measurements are made.
A material might also be measured by inserting it in a waveguide path. The MCK measurement system from SwissTo12, shown in Figure 2, is configured in this manner. Two corrugated horn antennas operating over a given waveguide bandwidth are placed end to end and a material under test (MUT) is placed between them. These systems measure the S-parameters, reflection and transmission through the MUT and a mathematical inversion converts these measurements to a complex permittivity.
SPEAG’s Dielectric Assessment Kit (DAK) product line, based on the open coaxial probe method, provides high-precision dielectric parameter measurements, including permittivity, conductivity and loss tangent, over a wide frequency range from 4 MHz to 67 GHz. The advanced hardware technology and user-friendly software of DAK instruments are designed for accurate, precise and non-destructive measurements, making them ideal for use in telecommunications, material science, bioelectromagnetics, biomedical research and industries like automotive, electronics and food.
The DAK System (DAKS) is the first system capable of measuring thin-layer materials and small liquid volumes, as well as DAK single probes. DAKS is a low-cost, portable and easy-to-use dielectric assessment system kit that combines the DAK technology, shown in Figure 3, with the miniature portable R60 and R140B vector reflectometers from Copper Mountain Technologies. The direct and rigid connection of the probe to the reflectometer allows the probe to be moved to the MUT after calibration, greatly simplifying measurements in the lab. The DAK product line includes the DAK-TL2, shown in Figure 4.
HOW IS THE PERMITTIVITY INVERSION COMPUTATION DONE?
The computation is an inversion because the material’s complex permittivity determines the transmission and reflection of the RF waves. The inversion must solve for the unique permittivity that causes the measured reflections. Uniqueness is an important consideration. In any inversion problem, multiple parameter values could create the same outcome, so seeding the problem with a best-guess solution is usually necessary.
How is complex permittivity calculated from the S-parameters? First, the transmission and reflection properties at the interfaces and within the material are modeled when illuminated by a plane wave. As detailed by Dr. Schultz1 and shown in Figure 5, the MUT can be divided into three zones: Zone A is an infinitely thin left-hand surface to model signal reflection, Zone B is a central section to model signal transmission and Zone C is another infinitely thin surface to model a second reflection with a 180-degree phase shift compared to the first reflection. Reflections occur whenever a wave passes from a medium with one dielectric constant to another, ε0 to εm and εm back to ε0, in this case.
Figure 5 Modeled material zones.
In this analysis, ε0, the permittivity of air, is 8.854 pF/m or may be normalized to 1.0. The material permittivity, εm, will also be normalized by this value. For non-magnetic materials, the permeability, μm, can be set to 1.0.
S-parameter matrices can be built for the three zones, but transfer parameters are more useful since they can be multiplied to obtain the composite result for the entire slab of material.
Transfer parameters relate the a and b used in Figure 4 by Equation 1:
