Copper is an excellent electrical conductor for RF/microwave printed-circuit boards (PCBs). It is the foundation for low-loss transmission lines, such as microstrip and stripline. However, the surface roughness of copper can vary from one circuit material to the next, even across a single sheet of circuit material, affecting high-frequency performance. Ideally, a circuit laminate’s copper would be uniformly smooth, providing consistent signal transmission characteristics across a circuit board and from board to board. But any practical copper-laminated circuit board has some amount of copper surface roughness which contributes to the final performance possible with that circuit board.

Fortunately, the latest electromagnetic (EM) simulation software allows users to include key circuit material properties, such as dielectric constant (Dk) and copper surface roughness, in the circuit design and performance simulation process, achieving simulated results that can be close to the results from measurements on an actual prototype circuit, even for circuits fabricated on circuit materials with copper surface roughness that may vary across the board.

Understanding That Dk Value

When simulating circuits in a commercial EM simulator, with the goal of including the effects of the circuit material’s copper surface roughness in the simulation, it is important to understand how the copper surface roughness can affect the performance of a high-frequency circuit, and to have a good idea about the relationship between the Dk and the copper surface roughness for a particular material. In fact, because the Dk value or values for a circuit material may have been determined by including such effects as copper surface roughness, the Dk values developed for modeling purposes in EM simulators are often referred to as “Design Dk” values.

Depending upon the severity of the copper surface roughness, for example, it can result in unexpected variations in the phase response of a circuit fabricated on that material. Those variations can become more significant at higher frequencies (with smaller wavelengths), such as millimeter-wave frequencies being used at present in advanced driver assistance systems (ADAS) electronic safety systems in automobiles and being planned for high-speed, short-haul data links in Fifth Generation (5G) wireless communications networks.

The Design Dk value for any circuit material is dependent upon frequency, often referenced to a test frequency of 10 GHz. The value may be different at other frequencies. Design Dk is obtained from testing microstrip transmission line circuits and extracting the Dk value from circuit performance, based on the z-axis (thickness) of the material.

Some EM simulators may work with only z-axis Design Dk values while others may require values for both the z-axis and x-y plane Dk of a circuit material. The Dk value for the material in the x-y plane is typically used in software when anisotropy data can be entered.  

Which Dk Measurement?

The Design Dk values of a circuit material are extremely important to the accuracy of an EM circuit simulation, and it is helpful to know the manner in which a circuit material manufacturer determined the published Design Dk values for a particular material. The Design Dk of a circuit material is found by using the microstrip differential phase length test method.

While it is possible to determine the Dk value of bulk circuit materials through measurement under extremely controlled environments, many Dk test methods are based on the use of known circuits, such as the microstrip ring resonator method and the microstrip differential phase length method. Measurements of the performance of these fabricated circuits reveal information about the circuit material which helps determine its Dk value, again under those precise test conditions (frequency). Unfortunately, any variations in the circuitry, such as in conductor etching and copper plating thickness, can cause errors in the determination of a material’s Dk value. When a multilayer reference circuit, such as a stripline-based circuit, is used to find a material’s Dk, additional variables can corrupt the measurements for determining a circuit material’s Dk value. For example, the thicknesses of the multilayer’s inner layers may vary, or the Dk of the bonding materials used to attach the multiple layers may differ from the Dk of the core circuit material. Such variables must be accounted for when determining the Dk or, ultimately, the Design Dk of a circuit material that can most accurately be used in an EM simulator.

Circuit materials from Rogers Corp. are characterized in terms of Design Dk values, determined by means of extracting Dk values of a material based on measurements of well-known microstrip transmission-line circuits fabricated on the material. These Design Dk values are included on circuit material data sheets and do not include the effects of copper surface roughness. However, within the MWI-2018 software, available for free download from the Rogers Tech Support Hub www.rogerscorp.com/techub, much more information is also available that is extremely useful for circuit modeling in a commercial EM simulator.

Rogers’ MWI-2018 software can show Design Dk values for each circuit material with a variety of options. One option is Bulk Dk, for the material alone, without copper surface roughness effects. This is the Design Dk value that should be used with an EM simulator that has its own built-in capability to calculate the effects of circuit material copper surface roughness on a circuit’s phase response, and does not need a Design Dk value that is “preloaded” with factors that will enable the prediction of copper surface roughness effects when the EM simulator does not have the built-in calculator.  

Numerous commercial EM simulators are now available for modeling circuits which can include the effects of circuit material copper surface roughness on phase response, such as the HFSS EM simulator from ANSYS, CST Studio Suite from Computer Simulation Technology, and the Sonnet Suites of EM simulation software from Sonnet Software. The ANSYS HFSS software is quite capable of predicting circuit phase effects due to circuit laminate copper surface roughness; unfortunately, a blog posted earlier this year stated otherwise, which was in error and apologies are due to ANSYS. These EM simulators already calculate the effects of copper surface roughness on a circuit’s phase performance and do not need additional data or Design Dk values that have been determined in a way that they are meant for use with EM simulators without the capability to include copper surface roughness effects.

For EM simulators without the capabilities to predict the effects of a circuit material’s copper surface roughness, Design Dk values other than these “Bulk Dk” values should be used, and these values are also available within the free MWI-2018 software. This choice of Design Dk values for a given EM simulator will impact the accuracy of the simulated results. For the EM simulators with the capability to predict the effects of a circuit material’s copper surface roughness on a circuit’s phase response, the Bulk Dk values are the best choice, since the EM simulator is already accounting for those phase effects and there is a kind of “doubling” effect due to the phase effects being also accounted for in the Design Dk values that were determined by extraction of measurements performed on a reference circuit fabricated on the circuit material.

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.