Similar questions, coming from different applications, have created a continual demand to accurately measure dielectric and magnetic properties of materials.
In this scenario, the Vector Network Analyser (VNA), represents a tool that allows fast, accurate, often non-destructive and sometimes even contactless, measurements of the Material Under Test (MUT). Over the years, several methods have been developed to characterise the dielectric properties of materials.
These techniques include open-ended coaxial probe methods, free-space techniques, resonators, and transmission-line methods.
Each technique has its own field of applicability depending on several factors, such as frequency of interest, required measurement accuracy, isotropic and homogeneity properties, form (i.e., powder, liquid, solid), size, requirements in terms of non-destructive or contactless testing, and temperature range. This article presents an overview of the different VNA-based techniques, along with some actual examples of novel applications.
Dielectric Properties of Materials
Materials can be grouped into insulators (i.e. dielectrics), conductors, and semiconductors. When a dielectric material is exposed to an external electric field, it will be polarised. The amount of electromagnetic energy that a material stores and dissipates is measured by its dielectric and magnetic properties, namely electrical permittivity and magnetic permeability. Both are complex quantities.
The real part of the permittivity is often referred to as dielectric constant. Materials can be divided into dispersive and non-dispersive, depending whether their permittivity changes as a function of frequency or not, respectively. For dispersive materials, it is necessary to quantify their frequency behaviour. Accordingly, the permittivity is typically measured as a function of frequency. The complex relative permittivity, εr, is defined as
Where σ = ωε'' is the electrical conductivity (S/m), j=√-1 is the imaginary unit, and ω=2πf is the angular frequency (rad/s). The complex permittivity εr consists of a real part and an imaginary part.
The real part ε' measures the amount of energy stored in the material, the imaginary part ε'', also known as loss factor, measures the amount of energy loss from the material. The ratio of the imaginary part to the real part of the complex permittivity is defined as loss tangent (dissipation factor or loss factor)
It measures the inherent dissipation of electromagnetic energy by the Material Under Test (MUT).
VNA-based materials measurements techniques
Several VNA-based methods exist that allow measuring materials’ electrical properties, namely electric permittivity ε and magnetic permeability µ, from few kHz up to THz. From complex S-parameters measurements, the real and imaginary part of ε and µ can be obtained, simultaneously.
Four approaches can be identified: open-ended coaxial probe methods, transmission-line methods, free-space techniques, and resonators. The dielectric properties of the MUT depend on frequency, anisotropy, homogeneity, temperature, and other parameters. Accordingly, there is no such thing as the best technique to accurately measure all materials’ dielectric properties at all frequencies and temperatures.
The best method to choose will depend on: frequency, temperature, loss regime, MUT form (powder, solid, liquid, etc.), size (thin film, large panel, etc.), non-destructiveness test needs, and possibility to contact with the MUT or not. What follows is an overview of the four most commonly used methods to probe materials properties at RF and microwave frequencies.
Open-ended coaxial probe
An open-ended coaxial probe is used to measure lossy materials at high frequencies over a broad frequency range of 0.5 GHz to 110 GHz. Dielectric properties are extracted from 1-port reflection measurements through a metallic probe pressed against the MUT.
A calibration step is used to reference the measured reflected signal at the probe’s aperture plane. Flat solids and liquids are well suited samples for this technique. For materials with low permittivity, the method introduces some uncertainties and deflections.
Figure 1. Open-end coaxial probe method. (a) Sketch of the probe with E-field lines at the probe/MUT interface. (b) Application of the method at mm-Wave frequencies using Anritsu 3743A mm-Wave modules and with a coaxial cable and zoom of 1.85 mm (70 GHz) and 1 mm (125 GHz) connectors.
In the transmission-line method, the MUT is placed inside a transmission line (i.e. waveguide or coaxial). Permittivity and permeability are extracted from transmission and reflection S-parameters measurements.
The method is applicable to both solids and fluids, and has higher accuracy and sensitivity than the open-ended coaxial probe technique. Error rates are <5% for the permittivity and permeability, and, at sufficiently high-loss levels, < 10% for the loss tangent. The resolution of the loss tangent is ±0.01; accordingly, materials having tanδ < 0.01 are not characterisable.
Figure 2. Transmission line setup for materials measurements. The setup is composed of an Anritsu VectorStar ME7838E VNA with 70 kHz to 110 GHz (1 mm coaxial output) full sweep capability, and a set of waveguide components, covering the wideband range. At the bottom, a zoom of a WR-19 waveguide transmission line is shown, with the MUT located at the central junction.
In free-space setups, the S-parameters are calculated between two antennas with the sample placed in the line of sight. From the analysis of the reflected and transmitted portions of an EM wave that propagates from free-space into the sample, the dielectric properties of the MUT can be extracted. The transmitting horn radiates a collimated Gaussian beam via dielectric lenses, thus limiting diffraction contributions from the MUT edges.
Common sources of error are probe/sample misalignments, as well as diffraction effects. Precise lenses manufacturing and alignment is required to limit wave-front aberrations and multiple reflections. Accordingly, free-space setups, especially for broadband applications, are quite expensive. Net accuracies and loss resolutions are similar to those reported for the transmission-line method.
Figure 3. Free-Space setup for E-Band material measurements from a project involving Fraunhofer FHR, RWTH Aachen IHF, and Anritsu. The setup is composed of an Anritsu Shockline MS46522B-082 VNA with small tethered source/receiver modules and a base chassis. The remote modules have native WR-12 waveguide interface and are coupled to horn antennas and a custom designed lens system. The three steps of a TRM calibration are shown, together with the actual measurement of the MUT. The video below offers a demonstration of this:
Resonant methods enable the extraction of dielectric properties at a single frequency or at a set of discrete frequencies. This allows reaching higher accuracy – e.g. 4 digits in the permittivity and loss tangent – and sensitivity with respect to the previously described methods.
The MUT is placed inside a resonant cavity having known resonance frequency and quality factor. The change in the latter quantities introduced by the MUT is thus measured, and the permittivity and permeability are determined. Errors are <1% for the permittivity and 0.3% for the loss tangent. Such high accuracy fails for high-loss materials, because the resonant peak broadens as the loss increases.
Figure 4. Cavity resonator setup for materials measurements. (a) Sketch of the sample holder stage, showing the dielectric supports and resonators, the sample plane (red), and the coupling loops. (b) and (c) show actual cavity resonators.
Comparison of different methods
Each methodology has its own field of applicability and the best choice depends on: frequency range of interest, required measurement accuracy, isotropic and homogeneity properties, form (i.e., powder, liquid, solid), size, requirements in terms of non-destructive or contactless testing, and temperature range. The table below summarises the advantages, fields of applicability, and limitations of each technique.
The use of VNA as a flexible and versatile tool to accurately and quantitatively characterise materials properties, such as electrical permittivity and magnetic permeability, from few kHz up to THz range, has been discussed. Different methods have been presented to extract permittivity and permeability of the MUT from either 2-ports or 1-port S-parameters measurements.
The type of MUT that can be characterised using a VNA ranges from biological matter and liquids to solids and powders, highlighting the broad applicability of the VNA as a tool to characterise materials properties at high frequencies.