# Searching for a Standard Millimeter-Wave Dk Test Method

Millimeter-wave (mmWave) frequencies were once part of the frequency spectrum reserved for R & D. But their time has come for more widespread use. With automotive Advanced Driver Assistance Systems (ADAS), and their mmWave radar safety systems, and Fifth Generation (5G) cellular communications technology extending into higher frequencies, mmWave frequencies will be used by billions around the world. That means a growing need for PCB materials capable of supporting circuits at 28 GHz and higher frequencies. Characterizing a circuit material for such higher-frequency circuits, typically to about 80 GHz, requires measuring the material’s dielectric constant (Dk) or relative permittivity at mmWave frequencies, within a frequency range where industry-standard Dk measurements have not yet been established.

Dk is a starting point for many circuit material specifiers since it impacts a circuit’s dimensions for an operating frequency. Because wavelengths shrink with increasing frequency, circuit dimensions can become quite small at mmWave frequencies, and it is important to accurately know the Dk of the dielectric material on which the circuits are built. Essentially, the Dk or relative permittivity of a dielectric material can be defined as the ratio of the amount of charge that can be stored between two metal plates with the dielectric material between them compared to those same two metal plate with a vacuum or air between them. The Dk of a vacuum is unity while the Dk or air is slightly higher than unity.

**Dk Basics**

As noted in an early ROG Blog, “Understanding the True Meaning of Dielectric Constant,” dozens of measurement methods are available for determining a circuit material’s Dk (from the August 30, 2010 ROG Blog, see http://www.microwavejournal.com/blogs/1-rog-blog/post/16663-understanding-the-true-meaning-of-dielectric-constant). Most circuit material suppliers use a measurement approach that is accepted as an industry standard, and is performed at a specific test frequency, such as 10 GHz or below. Measurements to determine a circuit material’s Dk at mmWave frequencies also exist, but they may not be as well known as the test methods used at lower frequencies.

What are the concerns for determining accurate Dk values at mmWave frequencies? Measurements to determine Dk are performed on either a raw material under test (MUT) or on material used to create some form of reference circuit on which measurements can be made. Whether at RF, microwave, or millimeter-wave frequencies, circuit materials tend to be anisotropic in terms of Dk characteristics, so a Dk value determined from a test method depends on the axis of the material being testing, typically the z-axis (thickness) or x-y plane (across the length and width of the material). The values are often different for the different material axes and typically a function of frequency, so for a mmWave circuit designer, Dk values at 10 GHz in the z-axis cannot be assumed to be equivalent to Dk values at 60 GHz in the x-y plane for the same material. Accurate circuit material Dk measurements at mmWave frequencies are extremely important in support of circuit designers for the many upcoming mmWave applications.

**Checking Out Candidates**

Many measurement methods have been used for determining material Dk at mmWave frequencies, but none have been accepted by a technical standards organization such as the IEEE or IPC as an industry standard test technique for that purpose. However, several Dk test methods offer very good measurement accuracy and repeatability to make them candidates worth considering for use as industry standards for mmWave Dk measurements.

One of these potential standard mmWave Dk measurement techniques is the microstrip differential phase-length method. It is a circuit-based test method in which 50-Ω microstrip transmission-line circuits of different lengths are fabricated on a MUT so that differences in the phase-angle measurements on the two circuits provide insights into the Dk characteristics of the MUT. Because the Dk of a MUT can vary across a section of material, the two microstrip circuits should be fabricated as close together as possible on the MUT to minimize the effects of typical material Dk variations when determining the Dk for that material. Many high-quality commercial vector network analyzers (VNAs) are available with frequency coverage as high as 110 GHz for S-parameter amplitude and phase measurements of the two different-length microstrip circuits on the MUT.

Another well-proven approach for determining circuit material Dk at mmWave frequencies is the ring resonator method, in which ring resonators serve as the test circuits fabricated on a MUT. The dimensions and design equations for these resonant circuits will detail an exact resonant frequency. When precisely fabricated on a MUT, the measured resonant frequency will provide tremendous insights into the Dk of the material. By measuring the responses of gap-coupled ring resonators at mmWave frequencies using a VNA and comparing those responses with the math-based results provided by commercial electromagnetic (EM) field-solver software, it is possible to extract the Dk of the MUT for the circuit dimensions and conditions entered into the software.

Of course, in real-world use, especially for the dimensions of mmWave circuits, circuit dimensions and tolerances can result in variations of the measured resonant frequency and thus the Dk determined for that MUT. Variations in conductor width and in the circuit substrate—the MUT—can also impact the frequency of a ring resonator. In addition, the thickness of the copper plating on the ring resonator~~s~~ circuits can vary across the processing panel. Variations in the circuit copper thickness will make a difference in the coupling and the resonant frequency of a gap-coupled ring resonator, so it is critical to minimize circuit copper thickness variations when applying the ring resonator test method for determining the Dk of a circuit material at mmWave frequencies.

This is a sampling of several of the well-established test techniques for determining circuit material DK which could serve as industry-standard approaches for measuring and determining circuit material Dk at mmWave frequencies. These are just two of the circuit-based test approaches, with raw material methods also available. For much greater details on these and other potential industry-standard mmWave Dk measurement methods, don’t miss the author’s article, “Characterizing Circuit Materials at mmWave Frequencies,” in the **May, 2019** issue of Microwave Journal, which analyzes various test methods for extraction of circuit material Dk at mmWave frequencies and how they differ.

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