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Characterization of circuit board materials at millimeter wave frequency

The dielectric constant (Dk) or relative dielectric constant of the PCB circuit board material is not a constant constant-although it looks like a constant from its name. For example, the Dk of a material changes with frequency. Similarly, if different Dk test methods are used on the same material, different Dk values may also be measured, even if these test methods are accurate. As circuit board materials are increasingly used in millimeter wave frequencies, such as 5G and advanced driving assistance systems, it is very important to understand the variation of Dk with frequency and which Dk test method is "appropriate".

Although organizations such as IEEE and IPC have dedicated committees to discuss this issue, there is no best industry standard test method to measure the Dk of circuit board materials at millimeter wave frequencies. This is not because of the lack of measurement methods. In fact, a reference paper published by Chen et al. 1 described more than 80 methods of measuring Dk. However, no one method is ideal. Each method has its advantages and disadvantages, especially in the frequency range of 30 to 300 GHz.
Circuit test and raw material test

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There are generally two types of test methods used to determine the Dk or Df (loss tangent or tanδ) of circuit board materials: that is, measuring raw materials or measuring circuits made of materials. Raw material-based testing relies on high-quality and reliable test fixtures and equipment, and Dk and Df values can be obtained by directly testing raw materials. Circuit-based testing usually uses common circuits and extracts material parameters from circuit performance, such as measuring the center frequency or frequency response of a resonator. Raw material test methods usually introduce uncertainties related to test fixtures or test devices, while circuit test methods include uncertainties from the circuit design and processing technology under test. Because these two methods are different, the measurement results and accuracy levels are usually inconsistent.

For example, the X-band clamped stripline test method defined by IPC is a raw material test method, and the result cannot be consistent with the Dk result of the circuit test of the same material. The clamping type stripline raw material testing method is to clamp two pieces of material under test (MUT) in a special test fixture to construct a stripline resonator. There will be air between the material under test and the thin resonator circuit in the test fixture, and the presence of air will reduce the measured Dk. If the circuit test is performed on the same circuit board material, the measured Dk is different because there is no entrained air. For high-frequency circuit board materials with a Dk tolerance of ±0.050 determined by the raw material test, the circuit test will get a tolerance of about ±0.075.
The circuit board material is anisotropic and usually has different Dk values on the three material axes. The Dk value usually has a small difference between the x-axis and the y-axis, so for most high-frequency materials, Dk anisotropy usually refers to the Dk comparison between the z-axis and the x-y plane. Due to the anisotropy of the material, for the same material to be tested, the measured Dk on the z-axis is different from the Dk on the x-y plane, although the test method and the Dk value obtained by the test are both "correct".
The type of circuit used for circuit testing also affects the measured Dk value. Generally, two types of test circuits are used: resonant structure and transmission/reflection structure. Resonant structures usually provide narrowband results, while transmission/reflection tests usually provide broadband results. The method of using a resonant structure is generally more accurate.

Examples of test methods
A typical example of raw material testing is the X-band clamped stripline method. It has been used by high-frequency circuit board manufacturers for many years and is a reliable method to determine the Dk and Df (tanδ) in the z-axis of the circuit board material. It uses a clamping fixture to form a loosely coupled stripline resonator for the material sample to be tested. The measured quality factor (Q) of the resonator is no-load Q, so the cable, connector, and fixture calibration have little effect on the final measurement result. The copper clad circuit board needs to be etched off all the copper foil before testing, and only the dielectric raw material substrate is tested. The circuit raw materials are cut into a certain size under certain environmental conditions and placed in the clamps on both sides of the resonator circuit (see Figure 1).

The resonator is designed as a half-wavelength resonator with a frequency of 2.5 GHz, so the fourth resonance frequency is 10 GHz, which is a resonance point commonly used for Dk and Df measurements. You can use a lower resonance point and resonance frequency—even a higher fifth resonance frequency can be used, but because of the influence of harmonics and spurious waves, a higher resonance point is usually avoided. Measure and extract Dk or relative permittivity
Where n is the number of resonance frequency points, c is the speed of light in free space, fr is the center frequency of resonance, and ΔL compensates for the electrical length extension caused by the electric field in the coupling gap. It is also very simple to extract tanδ (Df) from the measurement, which is the 3dB bandwidth-related loss of the resonance peak minus the conductor loss (1/Qc) related to the resonator circuit.
Although approximate, these formulas are useful for determining the initial Dk value. Using electromagnetic (EM) field solver and accurate resonator circuit size can get more accurate Dk.
Using loosely coupled resonators when measuring Dk and Df can minimize the resonator loading effect. If the insertion loss at the resonance peak is less than 20 dB, it can be considered as loose coupling. In some cases, the resonance peak may not be measured due to extremely weak coupling. This usually occurs in thinner resonant circuits. Thinner circuit materials are commonly used in millimeter wave applications because the higher the frequency, the shorter the wavelength, and the smaller the circuit size.