Published: 02 April 2014

by Mike Miller
PCB performance strongly depends on the laminate material’s dielectric constant (Dk) and dissipation factor (Df) related to complex dielectric constant, ε = ε’ – jε” through Dk=ε’/ε0 and Df=ε”/ ε’. Complex permittivity can be measured using a number of techniques, including waveguide, cavity resonator, open resonant cavities, split-post dielectric resonator and free-space techniques.

Each has advantages and disadvantages. Complete characterization of a material typically requires use of multiple techniques based on a number of factors, including frequency range of interest, temperature, humidity and sample size available. Here, we focus on the free-space technique for measuring complex permittivity of planar PCB laminate material samples.

The free-space technique is illustrated in **Figure 1**. Here, the dielectric test sample is placed between the transmitting and receiving antenna, and the attenuation and phase shift due to the sample are measured. To isolate the effect of the sample, the measurement is typically calibrated with the test apparatus empty. The resulting insertion loss and phase are used to extract the complex dielectric constant. For accuracy, a vector network analyzer (VNA) is used. Ports 1 and 2 in Figure 1 are connected to the VNA inputs using low-loss microwave transmission line.

**Figure 1.** Free space measurement apparatus for determining dielectric constant.

Advantages of the free-space method include the ability to yield accurate results over a broad frequency range, ease of adaptation for measurement vs. temperature, and ease of sample preparation. The sample size should be a few wavelengths or larger at the lowest frequency measured, however, making the technique more suitable for high-frequency measurements in the GHz range through mm-wave. Sample flatness and uniform thickness are required for accuracy, as extraction techniques (to be described) carry the assumption of an infinite perfectly flat sheet. Additionally, the test apparatus must be mechanically stable for phase accuracy.

**Permittivity extraction.** The boundary value problem of **Figure 2** is the basis for the extraction of permittivity from measured insertion and reflection (magnitude and phase). Here, a plane wave is incident upon a dielectric slab of thickness (d). On either side of the slab is air. This 1D boundary-value problem can be solved to yield expressions for transmission and reflection coefficients using the Fresnel equation formulation. The details of this are illustrated in Stratton.^{1} The transmission and reflection coefficients are cast into forms that can be solved for complex permittivity, using measured transmission and reflection coefficients. One approach to solving the transmission equation for ε using a least squares technique is presented by Friedsam and Biebl.^{2} It is straightforward to apply the Levenberg-Marquardt Algorithm to the nonlinear transmission equation presented.

**Figure 2.** Electromagnetic plane wave normally incident on infinite dielectric slab of thickness (d) and constitutive properties (ε1, µ1).

Extraction of complex permittivity using the above technique requires physical assumptions be made regarding the emitted electromagnetic wave from the antenna and its interaction with the test sample. First, it is assumed that the wave incident on the sample is a uniform plane wave. This is an approximation, as the wave emitted from the antenna is spherical and only truly planar at the limit of infinite distance. From antenna theory, it is common practice to assume plane-wave nature at distances greater than 2D2/λ where D is the dimension of the antenna radiator.^{3}**Figure 3** illustrates three radiation field regions for antennas having dimensions greater than the wavelength of the emitted radiation. Antennas used for the free-space technique have high directivity and satisfy this requirement. Practical test apparatus using high-directivity antennas such as corrugated or ridged horns can be constructed meeting the far-field 2D2/λ requirement. Second, it is assumed the sample is infinite in extent. Measurement samples are finite in size, so this assumption is approximately satisfied using sample sizes and antenna directivity, whereby the incident electric field is greatly reduced at the sample edges vs. the center. A lens is often used to collimate the beam.

**Figure 3.** Three regions of antenna radiation: Near Field, Fresnel Region and Radiating Far Field region.

**Implications for PCB laminate materials.** PCB laminate dielectric materials consist of woven fibers in a resin matrix and are inherently inhomogeneous and anisotropic. The fiber dielectric constant differs from that of the resin, and the fiber weave presents azimuthal anisotropy even at normal incidence. The free-space measurement of Figure 1 yields εz for normal incidence on the sample for a specific orientation of electric field with respect to fiber warp and fill directions.

Additional measurement techniques used for PCB materials include the Bereskin Test Method4 and traveling wave technique.^{5} The Bereskin Test Method is a recognized industry standard with details found in IPC-TM-650, Method 2.5.5.5.1. The traveling wave technique is a TEM transmission line technique, which yields permittivity in the plane of the sample (εx and εy). For the traveling wave technique, measurement is performed with the copper clad intact, while the free-space technique requires its removal. This difference accounts for observed differences in extracted Dk and Df due to additional capacitance associated with the copper dielectric interface. This effect has been investigated in a recent publication by Koledintseva, Drewniak and Hinaga.^{6}

The free-space technique is a nondestructive method that offers advantages in terms of simplicity and ease of obtaining broadband data. By combining the results with those of other techniques, PCB materials can be effectively characterized. **References**

1. J.A. Stratton, *Electromagnetic Theory*, McGraw-Hill, New York, 1941.

2. G. L. Friedsam and E.M. Biebl, “A Broadband Free-Space Dielectric Properties Measurement System at Millimeter Wavelengths,” *IEEE Trans. Instrumentation and Measurement*, vol. 46, no. 1997, pp. 515-518.

3. C. A. Balanis, *Antenna Theory: Analysis and Design*, Wiley, New York, 1982.

4. I. Araktingi and R. Hoard, “New Developments in high frequency measurements of PWB materials Part II: Application of the Bereskin Method to PWB materials,” IPC Printed Circuits Expo, 1999.

5. A. Koul, P. K. R. Anmula, M.Y. Koledintseva and J.L. Dreniak, “Improved Technique for Extracting Parameters of Low-Loss Dielectrics on Printed Circuit Boards,” Proc. IEEE Symp. Electromag. Compat., 2009, pp. 191-196.

6. M.Y. Koledintseva, J.L. Dreniak and S. Hinaga, “Effect of Anisotropy on External Dielectric Properties of PCB Laminate Dielectrics,” IEEE International Symposium on Electromagnetic Compatibility, 2001, pp. 514-517.**Mike Miller** is an OEM marketing manager at Isola Group (Isola-Group.com); This email address is being protected from spambots. You need JavaScript enabled to view it..

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