How to measure the dielectric constant of PCB circuit board material at millimeter wave frequency?

The permittivity (Dk) or relative permittivity of a PCB board material is not a constant constant - although it looks like a constant from its name. For example, the Dk of a material will vary with frequency. Similarly, if different Dk tests are used on the same piece of material, different Dk values may be measured, even if they are all accurate. As PCB materials are increasingly used in areas such as millimeter wave frequencies such as 5G and advanced assisted driving systems, it is important to understand how Dk varies with frequency and which Dk test methods are "appropriate".

There is no standard industry test method for measuring the Dk of circuit board materials at millimeter-wave frequencies, although organizations such as IEEE and IPC have committees to explore this issue. This is not for lack of measurement, in fact, more than 80 methods of testing Dk are described in a reference paper published by Chen et al.1. However, no one method is ideal, and each has its advantages and disadvantages, especially in the frequency range of 30 to 300 GHz.

Circuit testing vs. raw material testing

There are generally two broad classes of test methods used to determine the Dk or Df (loss Angle tangent or tanδ) of circuit board materials: that is, raw material measurements, or measurements made in circuits made from materials. Raw material based testing relies on high quality and reliable test fixtures and equipment, and Dk and Df values can be obtained by testing raw materials directly. 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. While raw material test methods often introduce uncertainties related to test fixtures or test devices, circuit test methods include uncertainties from test circuit design and fabrication techniques. Because the two methods are different, measurement results and accuracy levels are often inconsistent.

For example, the X-band clamped strip line test method defined by IPC is a test method for a raw material, and its results will not be consistent with the Dk results of circuit tests for the same material. The clamp type strip line raw material test method is to construct a strip line resonator by clamping two pieces of material under test (MUT) in a special test fixture. There will be air between the material under test (MUT) and the thin resonator circuit in the test fixture, and the presence of air will reduce the Dk of measurement. If the circuit is tested on the same circuit board material, the Dk measured will be different from that without air entrain. For a high-frequency circuit board material with a Dk tolerance of ±0.050 as determined by raw material testing, the circuit test will result in a tolerance of approximately ±0.075.

Circuit board materials are anisotropic and typically have different Dk values on the three material axes. Dk values usually differ very little between the x and y axes, so for most high-frequency materials Dk anisotropy usually refers to Dk comparisons between the z axis and the x-y plane. Due to the anisotropy of the material, the measured Dk in the z-axis is different from the Dk in the x-y plane for the same material under test (MUT), although both the test method and the values of the tested Dk are "correct".

The type of circuit used for circuit testing also affects the Dk value under test. Typically, two types of test circuits are used: resonant structures and transmission/reflection structures. Resonant structures usually provide narrow band results, while transmission/reflection tests are usually broadband results. Methods using resonant structures are usually more accurate.

Test method example

A typical example of raw material testing is the X-band clamped ribbon method. It has been used by high-frequency circuit board manufacturers for many years and is a reliable means of determining Dk and Df (tanδ) in the z-axis of circuit board materials. It uses a clamping device to form loosely coupled strip-line resonators for the material under test (MUT) sample. The measured quality factor (Q) of the resonator is no-load Q, so the calibration of the cable, connector and fixture has little influence on the final measurement result. Copper-covered circuit boards need to be etched off all the copper foil before testing, only testing the medium raw material substrate. The raw material of the circuit is cut into a certain size under certain environmental conditions and placed in the jigs on both sides of the resonator circuit (see Figure 1).

The resonator design is a half wavelength resonator with a frequency of 2.5 GHz, so the fourth resonant frequency is 10 GHz, which is often used for Dk and Df measurement of the resonant point. A lower resonant point and resonant frequency can be used -- even a higher fifth resonant frequency can be used, but a higher resonant point is usually avoided because of the effects of harmonics and stray waves. Measuring and extracting Dk or the relative dielectric constant (εr) is simple:

Where n is the number of resonant frequency points, c is the speed of light in free space, fr is the central frequency of resonance, ΔL compensates the electric length extension caused by the electric field in the coupling gap. It is also simple to extract tanδ (Df) from the measurement, which is the loss associated with the 3dB bandwidth of the resonant peak minus the conductor loss associated with the resonator circuit (1 / Qc).