How to measure the dielectric constant of PCB material 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 currently no standard industry 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 for testing 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 vs raw material test
There are usually two main types of test methods used to determine the Dk or Df (loss tangent or tanδ) of circuit board materials: raw material measurement, or measurement in a circuit 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 testing methods usually introduce uncertainties related to test fixtures or test devices, while circuit testing methods include uncertainties from test circuit design and processing technology. 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 (MUT) 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 from that of 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 under test (MUT), the measured Dk on the z-axis is different from the Dk on the xy plane, although the test method and the measured Dk value are both "correct" .
The type of circuit used for circuit testing also affects the value of Dk under test. 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.
Test method example
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 make the material under test (MUT) sample form a loosely coupled stripline resonator. 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).


Figure 1 X-band clamped stripline test fixture side (a), schematic diagram of resonator (b), and actual fixture diagram (c)
The 　　 resonator design is 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. Lower resonance points and resonance frequencies can be used-even a higher fifth resonance frequency can be used, but higher resonance points are usually avoided due to the influence of harmonics and spurious waves. Measuring and extracting Dk or relative permittivity (εr) is very simple:

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 loss associated with the 3dB bandwidth of the resonance peak minus the conductor loss associated with the resonator circuit (1/Qc).

Figure 2 Broadband clamped stripline measuring 60mils material under test (MUT), Dk = 3.48.
Figure 2 shows the broadband test results of 60 mils and Dk = 3.48 using the clamped stripline method to measure the material under test (MUT).
The ring resonator is usually used as a test circuit. It has a simple structure and resonates at an integer multiple of the average perimeter of the microstrip loop (see Figure 3a). Signal coupling is usually loosely coupled because the loose coupling between the feeder and the loop can make the coupling gap between them capacitive. The capacitance will vary with frequency, causing the resonant frequency to shift, causing errors when extracting the material Dk. The conductor width of the resonant ring should be much smaller than the radius of the ring-according to experience, less than a quarter of the radius of the ring.


Figure 3 Microstrip ring resonator (a) and broadband measurement (b)
Figure 3b is the S21 response of a microstrip ring resonator based on a 10mil-thick circuit board material, where Dk = 3.48. The approximate calculation of Dk is given by


Although they are approximate, these formulas are useful for determining the initial Dk value. Using the electromagnetic (EM) field solver and the resonator circuit size can get a higher Dk.
The use of loosely coupled resonators when measuring Dk and Df can minimize the load effect of the resonator. Making the insertion loss at the resonance peak less than 20 dB 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 resonant circuits with a thinner thickness. 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.
millimeter wave test method
Although there are many Dk test methods, only some are applicable to millimeter wave frequencies, and none of them are recognized as industry standards. The following two methods are more accurate and have high repeatability in millimeter wave testing.
differential phase length method
The microstrip line differential phase length method has been used for many years. This is a transmission line test method that measures the phase of two circuits that differ only in physical length (see Figure 4). In order to avoid any changes in the material properties of the circuit board, the test circuit is designed to be as close together as possible on the material under test (MUT). These circuits are 50Ω microstrip transmission lines with different lengths, and the signal feed is in the form of grounded coplanar waveguide (GCPW). At millimeter wave frequencies, the GCPW signal feeding method is very important, because the design of the feeding place may have a significant impact on the return loss. A non-welded terminal connector should also be used. On the one hand, a good contact can be formed between the coaxial connector and the test circuit without soldering. On the other hand, the same connector can be used to test two circuits of different lengths. This minimizes the influence of the connector on the measurement results. To maintain consistency, the same connector should always correspond to the same port of the vector network analyzer (VNA). For example, if connector A is connected to port 1 of the VNA and connector B is connected to port 2 to test a shorter circuit, the same should be done when testing a longer circuit.


Figure 4 The long and short microstrip circuit used in the differential phase length method
The phase subtraction of the long and short circuit also reduces the influence of the connector and the signal feeding area. If the return loss of the two circuits is good and the connector has the same direction, most of the influence of the connector can be reduced. When using the differential phase length method at millimeter wave frequencies, the return loss is better than 15 dB below 60 GHz, and better than 12 dB from 60 GHz to 110 GHz are acceptable.
The Dk extraction equation of the microstrip differential phase length method is based on the phase response formula of the microstrip line of circuits with different physical lengths:


where c is the speed of light in free space, f is the frequency of the phase angle of S21, ΔL is the difference between the physical lengths of the two circuits, and ΔΦ is the phase difference between the long and short circuits.
The test method includes a few simple steps:
Measure the S21 phase angle of a long and short circuit circuit at a given frequency.
Use the formula to determine the effective Dk.
Test the circuit size of the circuit, determine the initial Dk value of the material and input it into the EM field solver.
Use software to generate simulated effective Dk value. Change the Dk in the solver until the measured effective Dk of the material at the same frequency matches the simulated effective Dk value.
By increasing the frequency to the millimeter wave and repeating this process, the definite Dk value at the millimeter wave frequency can be obtained.
Figure 5 shows the Dk of 5mil RO3003G2TM circuit board material tested with frequency using the microstrip line differential phase length method. This curve is obtained by using the Dk calculation tool developed by Rogers Corporation. This data reflects the decreasing trend of Dk as the frequency increases. At lower frequencies, Dk varies greatly with frequency; however, Dk from 10 to 110 GHz varies little with frequency. This curve reflects materials with low loss and smooth rolled copper. Materials with high loss and/or higher copper surface roughness exhibit approximately a large negative slope in the relationship of Dk with frequency. Using this test method, the insertion loss of the material under test (MUT) circuit can also be obtained by the S21 loss value of the long and short lines at each frequency (see Figure 6).


Figure 5 The relationship between Dk and frequency measured by the microstrip line differential phase length method


Figure 6 Microstrip line differential length method to measure the relationship between insertion loss and frequency
ring resonator method
The "ring resonator method" is another method for millimeter wave characterization. Although the ring resonator is usually used below 10 GHz, it can also be used effectively at millimeter wave frequencies with appropriate processing accuracy. Processing accuracy is very important, because the influence of circuit size and dimensional tolerance is more prominent in millimeter waves, and any change will reduce the accuracy. Most millimeter wave ring resonators are very thin (usually 5 mils), and the gap between the feeder line and the resonator ring is also very small. The thickness of the ring resonator, the copper plating thickness of the line, and the change of the gap size will all affect it, thereby affecting the resonant frequency.
When comparing two circuits using the same circuit board material but different copper plating thickness, the circuit with thicker copper exhibits a lower Dk. Similarly, the resonant frequency of the two circuits will be different, even though they use the same circuit board materials and test methods. Figure 7 is an example of this. The thickness variation of the final plating surface of the circuit results in a difference in the calculated Dk of the same material. This effect is similar whether the surface treatment is electroless gold plating (ENIG) or other plating surfaces.


Fig. 7 millimeter wave ring resonator measurement, the plating is 63mil (a) and 175mil (b) thickness of nickel plating.
In addition to these processing problems, changes in conductor width, etch coupling gap changes, trapezoidal effect and substrate thickness changes also have similar effects. If all these changes are taken into account when testing Dk with a ring resonator, a single ring resonator measurement can get the correct Dk value. However, many tests often use the nominal circuit size to test the calculated Dk, so it is not necessarily correct. Moreover, the lower frequency is tested, and these effects will not significantly affect the Dk accuracy like the millimeter wave frequency.
Another important variable in the use of ring resonators in the millimeter wave band is that the coupling gap varies with frequency. Under normal circumstances, ring resonators are evaluated with multiple different resonance points, and the coupling gap usually has a significant frequency difference with different resonance points. Therefore, the variation of the coupling gap may be an important source of error. In order to overcome this problem, the method of differential circle can be used. The two ring resonators used in this method are basically the same except for the difference in circumference, and are integer multiples of each other (see Figure 8). For two ring resonators, the high-order resonance point has a common resonance frequency in the Dk test. Since the feeder and the gap are the same, the influence of the coupling gap is reduced-theoretically eliminated-which makes the measured Dk more accurate. The calculation formula of Dk is as follows:


Figure 8 Microstrip differential circular ring resonator


The ring resonator in Fig. 8 is a microstrip structure, and the feeder is tightly coupled GCPW to avoid feeder resonance at the open end and to avoid interference with the resonance peak of the ring resonator. Usually if the feeders are open, they will have their own resonance. The way to avoid this is to make the feeder shorter or use a tightly coupled GCPW feeder. Since the differential circular ring resonator method directly obtains the effective Dk of the circuit, it is still necessary to measure the circuit size and use a field solver to obtain the material Dk.
  in conclusion
The millimeter wave test methods discussed here are all circuit-based. There are many other test methods, such as raw material-based test methods. But most methods test the material Dk of the x-y plane instead of the z-axis (thickness) Dk. Circuit designers use the z-axis Dk more often, but for those who need to use the material's xy-plane Dk value in some applications, the free space test method, the separated cylindrical resonator test method and the waveguide perturbation test method are all xy plane test method.
It was also proposed to use a clamped broadside coupled stripline resonator test method to determine the Dk of the circuit board material at the millimeter wave frequency. However, this method is only effective for a small range of materials under test (MUT), and is not suitable for mass testing. Therefore, the research on the test methods of raw materials that can be used for millimeter wave frequencies is still continuing.