# Which Dk Value is “Right” for my Computer Simulation?

High-frequency circuit designs usually start with a choice of printed-circuit-board (PCB) material and including that material into a model within a computer-aided-engineering (CAE) program. Circuit laminates are characterized by a number of parameters, with one of the more important for CAE modeling purposes being the dielectric constant or Dk. Because of the importance of this material parameter for computer circuit modeling, Rogers Corp. has developed suggested Dk values for its circuit laminates for use with commercial circuit modeling programs, known as “Design Dk” values.

These Design Dk values may or may not be the same as other forms of Dk values, such as specification Dk or process Dk, for the same circuit material, however. Many different test methods are used to determine a circuit laminate’s Dk value, often resulting in several values for one material. This leads to the question: Which Dk value is the one to use with a CAE circuit modeling program? Is the Design Dk the “right” Dk value when performing a circuit simulation, or might there be a case when one of the other Dk values for the same material might work better with a particular computer model?

Many different test methods are used to determine circuit laminate Dk, with 13 different approaches defined by IPC standards and many more by the American Society for Testing and Materials (ASTM). Some Dk test methods are based on particular high-frequency transmission-line structures, such as microstrip and stripline resonators; the most accurate Dk test methods are also very engineering intensive. Design Dk values are those that are meant to provide accurate calculations of circuit performance in CAE modeling/simulation software programs. While a circuit material supplier such as Rogers Corp. is attempting to characterize its own materials as precisely as possible, and provide circuit laminate Dk values that reflect such precision, a CAE software supplier is also attempting to include corrections in its software tools to compensate for any variables in the Dk measurement methods.

Many CAE simulation software tools try to account for differences in circuit material Dk value resulting from material effects or differences in Dk test methods. No one Dk test method is the best and, as noted, high accuracy usually comes at great cost and effort. For example, depending upon how anisotropic a circuit material is, it may have different Dk values in its planar (x and y) and thickness (z) dimensions. The thickness can contribute to the results of a Dk measurement. Having measurements and Dk values for each thickness of a circuit material would be ideal but costly and time-consuming.

The “Design Dk” values provided by Rogers Corp. for many of its circuit materials for modeling purposes are based on measurements performed with the microstrip-based differential phase-length method. It is a test approach that looks for signal phase variations in microstrip transmission lines on a circuit material of interest since those phase variations will result from inconsistent impedance in the transmission lines, possibly caused by variations in a laminate’s reinforcement materials, such as glass, fiberglass, and ceramic materials.

The copper portion of a circuit laminate can also contribute to the accuracy of a Dk measurement: copper surface roughness effects can significantly affect Dk measurements. For example, a circuit material with rougher copper surface will exhibit a higher apparent Dk than the same circuit material with smoother copper surface. The copper surface roughness of particular interest is not at the air side of a circuit material but at the substrate/copper interface.

Because a rougher copper surface at that interface can slow the phase velocity of EM waves propagating across transmission lines fabricated on that circuit material, any Dk measurements that are based on phase measurements can be affected by circuit materials with rough copper surfaces. The slower phase velocity translates into a higher apparent Dk value for that material. In addition to slowing the phase velocity, a circuit laminate’s rough copper surface has impact on its conductor loss, which is one component of a circuit’s total loss, which also includes dielectric loss, leakage loss, and radiation loss.

The Design Dk values that are provided by Rogers Corp. with its many different circuit materials are the Dk values that are perceived by actual RF/microwave circuits, in particular, microstrip transmission lines. These Design Dk values are the values determined by measurements when each material is tested with microstrip transmission lines and the effects of copper surface roughness for that material are included in the measurements.

These Design Dk values are well suited for most of the CAE simulation software programs used in the RF/microwave industry, since most of those software programs do not make corrections for the predicted RF/microwave circuit performance as a function of the effects of the copper surface roughness on the transmission-line phase velocity. Some modeling software programs include the effects of copper surface roughness on a circuit material’s conductor loss or insertion loss but not on the phase velocity (which can alter the effective Dk of the circuit material). As a result, the Design Dk values presented by Rogers Corp. with its circuit materials are the most accurate Dk values available for most software modeling tools.

Any modeling software that does account for a circuit laminate’s copper surface roughness effects on phase velocity should not use the frequency-dependent Design Dk values provided by Rogers Corp. since there would be a doubling effect on the phase calculations for that material’s circuits. Several commercial modeling software programs do account for the effects of a circuit laminate’s copper surface roughness on phase velocity, such as the CST Studio Suite® EM simulator from CST (www.cst.com) and the planar EM simulator from Sonnet® Software (www.sonnetsoftware.com). But even a modeling tool as popular as the High Frequency Structure Simulator (HFSS) EM simulator from Ansys (www.ansys.com) accounts for the effects of a circuit material’s copper surface roughness on attenuation/loss but not on phase response (according to what is currently known by this author).

Rogers Corp. provides “bulk Dk” values along with the copper surface roughness for modeling purposes and these values are meant for use with any RF/microwave simulation software that does not account for a circuit material’s copper surface roughness effects on phase response. These “bulk Dk” values are published in Rogers Corp.’s circuit material data sheets as the “Design Dk” for each material. To ensure the “right” results with any modeling tool, a circuit designer can always contact a CAE software supplier to confirm whether a particular modeling program accounts for circuit material surface roughness effects on the phase response of a circuit fabricated on that material.

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