source: Microwave & RF article

Dielectric constant and dissipation factor are among the essential material parameters used by circuit designers and they must be measured precisely for accurate models.

Circuit materials like those based on polymers and resins serve as foundations for high-frequency circuits. They are characterized by various parameters that describe electrical and mechanical properties, such as the complex permittivity (the real part of which is the dielectric constant) and complex permeability (which also has imaginary and real parts that can be used to find a materials loss tangent or dissipation factor).

Proven measurement methods are vital for ensuring accurate results of material measurements and for making valid comparisons of material parameters from different material suppliers. Knowing which test methods were applied and at which frequencies can also ensure that proper material parameter input data is supplied to a computer-aided-engineering (CAE) software simulator used as part of the circuit-design process.

Many of the various measurement methods developed for permittivity and permeability use calculations based on scattering (S) parameter measurements of a material sample with a microwave vector network analyzer (VNA). Different test methods have been adopted by different material manufacturers and technical organizations. In fact, the IPC offers 13 different test methods for determining dielectric constant and/or dissipation factor. These disparate test methods may yield different results, but there are usually reasons for those differences if the details of the various test methods are understood.

Printed-circuit-board (PCB) materials for RF/microwave circuits are anisotropic in nature, meaning that some characteristics, such as dielectric constant, vary in the different axes of the material. The z-axis or thickness of a circuit material is usually of most interest, since this will serve as the dielectric layer, for example, between transmission lines and a ground plane in a microstrip circuit.

PCB materials are supplied as laminates, with copper or other conductive metals attached to the dielectric, or as prepregs, without metal backing (Fig. 1). Measurements of PCB dielectric properties are performed on prepregs or laminates from which the conductive metals have been completely removed. That’s because the presence of metal in the material will change the material’s dielectric nature and any subsequent S-parameter measurements.

**Make a Reference**

Some material characterization methods involve fabricating a reference circuit, such as a microstrip resonator, on a material under test (MUT). By relating the resonator’s physical dimensions/wavelength to theoretical values for relative permittivity (dielectric constant) and dissipation factor, it is possible to determine the relative dielectric constant and dissipation factor based on measured resonant frequency, resonator bandwidth, and electrical lengths. In such a measurement, the effects of the copper conductor are included in the dielectric-material analysis. While the approach can yield accurate results, it provides values at only one frequency rather than broadband analysis.

Another commonly referenced measurement method for PCB dielectric constant and dissipation factor, which also uses a resonant circuit, is the clamped stripline resonator test. The approach involves forming a stripline resonator in a ground-signal-ground layer configuration that is mounted in a clamping test fixture to determine the dielectric constant and dissipation factor as a function of the MUT’s thickness (Fig. 2).

Other methods based on measuring resonant frequencies of known structures are used to evaluate the dielectric constant and dissipation factor of a MUT in the x and y axes (length and width). These include the split-post dielectric resonator (SPDR) method, the rectangular cavity approach, and the open-cavity resonance method. In all three techniques, the electric field is perpendicular to the MUT, revealing the characteristics of the dielectric material in the x-y plane rather than in the z-direction (thickness). For many PCB materials, the value of the dielectric constant can be quite different in the x-y plane than in the z-axis due to use of materials, such as ceramic or woven glass, that serve to reinforce the polymer or resin circuit material.

**Leveraging the VNA**

The availability of high-performance commercial microwave VNAs has put basic material parameter measurements within reach of many engineers seeking validation of their PCB datasheets. Many leading VNA instrument makers offer application notes related to material measurements, based on test methods that convert S-parameters to material parameters.

Some of these methods are as straightforward as connecting a section of waveguide or coaxial transmission line to the VNA and inserting a small sample of the MUT within the end of the transmission line in order to perform transmission and reflection measurements. Others, such as the full-sheet-resonance (FSR) method, measure a known length of circuit board, evaluating the resonant peaks or standing waves at different frequencies to calculate the dielectric constant.

The appropriate equations can relate the S-parameter measurements of reflection and transmission to the permittivity and permeability of the MUT. Although not considered “nondestructive” measurements, which require precisely machined samples of the MUT for insertion within the waveguide or coaxial line, they can provide information about the broadband characteristics of dielectric material. Unfortunately, because such small samples are involved in the measurements, they are not applicable to determining material characteristics across a large sheet of material, such as the tolerance of the dielectric constant.

Additional material measurement techniques using a VNA include the short-circuit-line (SCL) and open-ended coaxial probe methods, both of which provide broadband values for complex permittivity and permeability. These VNA measurement methods test for S-parameters and then solve for the material unknowns, including complex permittivity and permeability. Errors in the calculations can arise at half-wavelength multiples of the test frequency and the size of the material sample. Therefore, normal practice is to test a material sample that is less than one-half wavelength long at the highest frequency of interest.

The various transmission-line methods based on insertion of a sample also rely on precise machining of the same to avoid the presence air pockets between the probe or transmission-line conductor and the surface of the material sample. Any air in the sample will effectively lower the result of any calculations of dielectric constant from the measured S-parameters.

**From Complex to Simple**

Some material measurements are considerably more elaborate, such as dielectric constant as a function of temperature and coefficient of thermal expansion (CTE). This measures how the different material components of PCB expand with temperature and how a PCB might react when attached to another material (e.g., a metal heat sink). The measurement is also critical for portions of the PCB on which metal meets dielectric surfaces—for instance, plated through holes (PTHs)—since significant differences in CTEs may result in stress and reliability problems.

Some material measurement methods are quite intuitive and can be performed with fairly simple test circuits. The differential phase-length method, for example, is based on using a VNA to measure the unwrapped phase of different lengths of microstrip transmission lines formed on the MUT. The method was clearly explained during a technical presentation by John Coonrod of Rogers Corp. during the 2013 International Microwave Symposium (IMS) in Seattle, Wash. In fact, it is available as part of a YouTube video on the company’s website. The firm also offers free downloadable personal-computer (PC) software to determine a material’s dielectric constant from the phase measurements.