How to measure the dielectric constant of PCB circuit board material at millimeter wave frequency?
The dielectric constant (Dk) or relative dielectric constant of a PCB board material is not a constant constant-although it looks like a constant by its name. For example, the Dk of a material changes with frequency. Similarly, if different Dk test methods are used on the same piece of material, different Dk values may 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 driver assistance systems, it is important to understand the changes in Dk with frequency and which Dk test method is "suitable."
Although organizations such as IEEE and IPC have special 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 due to the lack of measurement methods. In fact, a reference paper published by Chen et al.1 et al. Describes more than 80 methods for testing Dk. However, no method is ideal, and 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 two general types of test methods used to determine the Dk or Df (loss tangent or tan δ) of circuit board materials: raw material measurements, or measurements on circuits made of materials. Raw material-based testing relies on high-quality and reliable test fixtures and equipment. Direct testing of raw materials can obtain Dk and Df values. Circuit-based testing typically uses common circuits and extracts material parameters from circuit performance, such as measuring the center frequency or frequency response of a resonator. Test methods for raw materials often introduce uncertainty associated with test fixtures or test devices, while circuit test methods involve uncertainty from test circuit design and processing technology. Because these two methods are different, measurement results and accuracy levels are often not consistent.
For example, the X-band clamped stripline test method defined by IPC is a test method for raw materials, and the result cannot be consistent with the Dk result of the circuit test of the same material. The clamped stripline raw material test method is to sandwich two pieces of material under test (MUT) in a special test fixture to build 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 without air entrainment. For high-frequency circuit board materials with a Dk tolerance of ± 0.050 determined by raw material testing, a circuit test will yield a tolerance of about ± 0.075.
The circuit board material is anisotropic and usually has different Dk values on the three material axes. Dk values usually differ little between the x-axis and 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 Dk values obtained by the test are "correct" .
The type of circuit used for circuit testing will also affect the value of Dk under test. Generally, two types of test circuits are used: a resonant structure and a transmission / reflection structure. Resonant structures usually provide narrow-band results, while transmission / reflection tests are usually broadband results. Methods using resonant structures are often 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 way to determine Dk and Df (tanδ) in the z-axis of circuit board materials. It uses a clamping fixture to form a loosely coupled stripline resonator of the material under test (MUT) sample. The measured quality factor (Q) of the resonator is the no-load Q, so the calibration of cables, connectors and fixtures has little effect on the final measurement results. Before testing the copper-clad circuit board, all copper foils need to be etched away, and only the dielectric raw material substrate is tested. The circuit raw materials are cut into a certain size and placed in fixtures on both sides of the resonator circuit under certain environmental conditions (see Figure 1).
Figure 1 Side (a) of the X-band clamped stripline test fixture, schematic diagram of the resonator (b), and physical view of the fixture (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 the resonance point commonly used for Dk and Df measurements. Lower resonance points and frequencies can be used-even higher fifth resonance frequencies can be used, but higher resonance points are generally avoided due to the effects of harmonics and spurious waves. Measuring and extracting Dk or relative dielectric constant (εr) is simple:
Where n is the number of resonance frequencies, c is the speed of light in free space, fr is the center frequency of resonance, and ΔL compensates for the extension of the electrical length 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 resonance peak minus the conductor loss (1 / Qc) of the resonator circuit.
Figure 2 Broadband clamped stripline measuring 60mils of material under test (MUT), Dk = 3.48
Figure 2 shows the results of a broadband test using the clamped stripline method to measure a material under test (MUT) at 60 mils and Dk = 3.48.
Ring resonators are often used as test circuits. It has a simple structure and resonates at integer multiples 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 minimizes the coupling gap capacitance between them. This capacitance will change with the frequency, which will cause the resonance frequency to shift and cause 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 ring radius.
Figure 3 Microstrip ring resonator (a) and broadband measurement (b)
Figure 3b is the S21 response of a microstrip ring resonator based on a 10 mil thick board material, where Dk = 3.48. The approximate calculation of Dk is given by
Although approximate, these formulas are useful for determining the initial Dk value. More accurate Dk can be obtained using electromagnetic (EM) field solvers and accurate resonator circuit size.
Using loosely coupled resonators when measuring Dk and Df can minimize resonator loading effects. Making the insertion loss at the resonance peak less than 20 dB can be considered loose coupling. In some cases, resonance peaks may not be measurable due to weak coupling. This usually occurs on thinner resonant circuits, and 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 suitable for millimeter wave frequencies, and none have been recognized as industry standards. The following two methods are more accurate and highly repeatable in the millimeter wave test.
Differential phase length method
The microstrip 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 change 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 a grounded coplanar waveguide (GCPW). At millimeter-wave frequencies, the GCPW signal feeding method is very important, because the design of the feeding point may have a significant impact on the return loss. Terminated non-welded connectors should also be used, on the one hand, to make good contact between the coaxial connector and the test circuit without soldering, on the other hand, the same connector can be used for two different circuit tests. This minimizes the effect of the connector on the measurement results. To maintain consistency, the same connector should always correspond to the same port on 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, this should also be the case when testing a longer circuit.
Figure 4 Long and short microstrip lines used in the differential phase length method
Subtracting the phase of the long and short-circuit circuits also reduces the effects of connectors and signal feed areas. If the return loss of both circuits is good and the connectors have the same orientation, most of the effects of the connectors can be minimized. When using the differential phase length method at millimeter wave frequency, the return loss is better than 15 dB below 60 GHz, and 60 GHz to 110 GHz is better than 12 dB.
The Dk extraction equation of the microstrip differential phase length method is based on the microstrip line phase response formula for 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 short and long circuit.
The test method includes several simple steps:
Measure the S21 phase angle of a long-short circuit at a given frequency.
Use formulas to determine effective Dk.
Test the exact circuit size of the circuit, determine the initial Dk value of the material and enter it into the EM field solver.
The simulated effective Dk values were generated using software. Change the Dk in the solver until the measured effective Dk of the material at the same frequency matches the effective Dk value of the simulation.
By increasing the frequency to the millimeter wave and repeating this process, the determined Dk value at the millimeter wave frequency can be obtained.
Figure 5 shows the Dk vs. frequency of a 5mil RO3003G2TM circuit board material tested using the microstrip differential phase length method. This curve was obtained using a Dk calculation tool developed by Rogers. This data reflects the tendency of Dk to decrease with increasing frequency. At lower frequencies, Dk varies greatly with frequency; however, Dk varies from 10 to 110 GHz with frequency. This curve reflects materials with low loss and smooth rolled copper, and materials with high loss and / or high copper surface roughness have approximately a large negative slope of Dk as a function of frequency. Using this test method, the insertion loss of the circuit under test (MUT) can also be obtained by the S21 loss value of the long and short lines at each frequency (see Figure 6).
Fig. 5 Relationship between Dk and frequency measured by microstrip line differential phase length method
Fig. 6.Relationship between insertion loss and frequency measured by microstrip differential length method.
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 has proper processing accuracy and it can also be effectively used at millimeter wave frequencies. Machining accuracy is important because the effects of circuit size and dimensional tolerance are more prominent at millimeter waves, and any change will reduce accuracy. Most millimeter-wave ring resonators are thin (usually 5 mils) and the gap between the feeder and the resonator ring is small. Changes in the thickness of the ring resonator, the thickness of the copper plating of the circuit, and the size of the gap will affect it, which will affect the resonance frequency.
When comparing two circuits using the same circuit board material but different copper plating thicknesses, circuits with thicker copper exhibit lower Dk. Similarly, the resonant frequencies of the two circuits will be different, even though they use the same board materials and test methods. Figure 7 is an example of this. The variation in the thickness of the final plated 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 ENIG or other plated surfaces.
Figure 7 Measurement of a millimeter-wave ring resonator. The coatings are nickel-plated with a thickness of 63 mil (a) and 175 mil (b).
In addition to these processing issues, changes in conductor widths, changes in etch coupling gaps, trapezoidal effects, and changes in substrate thickness can 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, lower frequencies are tested, and these effects do not significantly affect Dk accuracy like millimeter wave frequencies.
Another important variable for using ring resonators in the millimeter wave band is the change in coupling gap with frequency. Under normal circumstances, ring resonators are evaluated with multiple different resonance points, and the coupling gap usually has obvious frequency differences with different resonance points. Therefore, changes in the coupling gap can be an important source of error. To overcome this problem, the method of differential circles can be used. The two ring resonators used in this method are basically the same except for their perimeters, 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. Because the feeder and the gap are the same, the effect of the coupling gap is reduced-theoretically eliminated-which makes the measured Dk more accurate. Dk is calculated as follows:
Figure 8 Microstrip differential circumferential ring resonator
The ring resonator in FIG. 8 is a microstrip structure, and the feeder is tightly coupled to the GCPW to avoid the feeder resonance at the open end and to avoid disturbing the resonance peak of the ring resonator. Usually if the feeders are open, they will have their own resonance. The only way to avoid this is to make the feeder shorter or use a tightly coupled GCPW feeder. Since the differential circumferential ring resonator method directly obtains the effective Dk of the circuit, it is still necessary to make accurate circuit size measurements and use the field solver to obtain the material Dk.
The millimeter-wave test methods discussed here are all circuit-based. There are many other test methods, such as those based on raw materials. But most methods test the material Dk on the x-y plane instead of the z-axis (thickness) Dk. Circuit designers often use the z-axis Dk, but for those who need to use the 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 Test method for xy plane.
It has also been proposed to use a clamped wide-side coupled stripline resonator test method to determine the board material Dk at the millimeter wave frequency. However, this method is only effective for materials under test (MUT) in a small range, and is not suitable for large-scale testing. Therefore, research continues on testing methods for raw materials that can be used at millimeter wave frequencies.