Achieving consistent and predictable phase from any printed circuit board (PCB) at higher frequencies is not a trivial or routine pursuit. The signal phase of a high frequency, high speed PCB depends very much on the construction of its transmission lines and the dielectric constant (Dk) of its circuit material. Electromagnetic (EM) wave propagation is fastest within anything with the lowest Dk, such as air with a Dk of 1.0. As Dk increases, wave propagation slows, with a corresponding impact on the phase responses of propagating signals. Waveform phase distortion occurs when the Dk of a propagating medium changes, since the waveform may speed up or slow down, respectively, within a propagation medium with a change to a lower or higher Dk, respectively.

The Dk of a circuit material is typically anisotropic, with different Dk values in the three dimensions (3D) of length, width, and thickness (x, y, and z). For some types of circuit design, not only must the Dk differences be accounted for, circuit fabrication methods must be considered to include the effects of Dk on phase. Phase stability and predictability will be increasingly important as PCBs reach higher in frequency, especially at microwave and millimeter-wave frequencies as used in Fifth Generation (5G) cellular wireless communications network infrastructure equipment and advanced driver assistance systems (ADAS) in electronically assisted motor vehicles.

What causes changes in a circuit material’s Dk? In some cases, differences in Dk across a PCB are due to material effects such as variations in copper surface roughness. In some cases, Dk variations are caused by PCB fabrication methods. And some PCB Dk variations are because of tough environments, such as high operating temperatures. By understanding how the Dk of a PCB can change from some nominal value, because of material properties, fabrication approaches, the environment, or even Dk test methods, Dk variations that translate to PCB phase variations can be better understood, anticipated and, hopefully, minimized.

Anisotropy is an important circuit material property, with Dk behaving very much like a 3D mathematical tensor. The different Dk values in the three axes result in differences in electric flux and electric field intensity in the three dimensions. Depending on the type of transmission lines used for the circuits, the phase of circuits with coupled architectures can be altered by material anisotropy, with the performance of a circuit depending upon its orientation on the circuit material. In general, circuit material anisotropy varies with thickness and frequency and materials with lower Dk values are less anisotropic. Material reinforcement can also make a difference: circuit materials with woven glass reinforcement are typically more anisotropic than circuit materials without it. When phase is critical and PCB Dk is part of modeling a circuit design, comparisons of Dk values between two materials should always be for the same axes. (For more details on many of the factors, including measurement methods, that can alter the Dk of a circuit material, refer to the Rogers Corp. webinar “Understand How Circuit Materials and Fabrication Can Affect PCB Dk Variation and Phase Consistency.”)

Digging into Design Dk
The effective Dk of a circuit is a value based on how an EM wave propagates through certain types of transmission line circuits. Depending upon the transmission line, some of the EM wave will travel through the combination of the conductive metal forming the transmission line, some through the PCB’s dielectric material, and some through the air around the PCB. Air has a lower Dk value (1.00) than any circuit material, so the effective Dk is a combined Dk value for an EM wave propagating in a transmission line conductor and being in the dielectric material and partially in air around the substrate. Design Dk attempts to provide an even more practical version of effective Dk, incorporating the effects of different transmission line technologies, fabrication methods, conductors, and even the test methods used to measure Dk. Design Dk is the extracted Dk of the material when tested in circuit form and is the appropriate Dk value to use in circuit design and simulation. Design Dk is not the effective Dk of the circuit, but Design Dk uses effective Dk measurements to determine the Dk of the material as indicated by circuit performance.

Variations in the different parts of a circuit on a given circuit material cause variations in the Design Dk. For example, variations in the thickness of the copper that forms the circuit’s conductors mean differences in Design Dk for each different thickness and changes in the phase response of a circuit formed with those conductors. The amount of roughness for the surface of the copper conductor also affects Design Dk and the phase response, with smoother copper, such as rolled copper, having less effect on Design Dk or the phase response than rougher copper.

The thickness of a PCB’s dielectric material will determine how much impact conductor copper surface roughness will have on Design Dk and circuit phase response. Thicker substrate materials tend to minimize the effects of copper conductor surface roughness, yielding Design Dk values closer to the intrinsic Dk of the substrate material even for copper conductors with rougher surfaces. As an example, 6.6-mil-thick RO4350B™ circuit materials from Rogers Corp. have an average Design Dk value of 3.96 from 8 to 40 GHz. For the same material with 30-mil thickness, the Design Dk drops to an average of 3.68 across the same frequency range. At double that thickness (60 mils), the Design Dk is 3.66, which is the intrinsic Dk of the glass reinforced laminate.

From this example, thicker circuit substrates can provide lower Design Dk values with their associated benefits. But achieving consistent amplitude and phase at higher frequencies tends to be more difficult on circuits fabricated on thicker substrate materials, especially at millimeter-wave frequencies where signal wavelengths are smaller. Higher frequency circuits are better suited for thinner circuit materials, where the dielectric portion of the material has less impact on the Design Dk and performance of the circuit. Thinner PCB substrates are more dominated by conductor effects for signal loss and phase performance. At millimeter-wave frequencies, they are also more sensitive than thicker substrates to conductor characteristics such as copper surface roughness in terms of the Design Dk of the circuit material.

Choosing a Circuit
At RF/microwave and millimeter-wave frequencies circuit designers depend on several different transmission line technologies, such as microstrip, stripline, and Grounded Coplanar Waveguide (GCPW) circuits and each call for different fabrication approaches and challenges along with associated benefits. For example, differences in the coupling behaviors of GCPW circuits will affect the Design Dk for a circuit. Tightly coupled GCPW circuits, with closely spaced transmission lines, minimize losses by using the air between the coplanar coupled areas more effectively for EM propagation. By using thicker copper conductors, the sidewalls of the coupled conductors are taller and more of the air in the coupled areas is used for EM propagation. This helps minimize circuit loss but emphasizes the importance of minimal variations in copper conductor thickness.

Many factors can affect the Design Dk for a given circuit and circuit material. Operating temperature will change the Design Dk and performance according to the temperature coefficient of Dk (TCDk) for a circuit material, with lower values indicating less temperature dependence. And high relative humidity (RH) which can raise a circuit material’s Design Dk, especially for materials with high moisture absorption. Circuit material characteristics and factors within the circuit fabrication process and operating environment all play roles in determining a circuit material’s Design Dk. By being aware of the effects, their impacts can be minimized.

Do you have a design or fabrication question? Rogers Corporation’s experts are available to help. Log in to the Rogers Technology Support Hub and “Ask an Engineer” today.