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64 DESIGN007 MAGAZINE I DECEMBER 2020 wave speed (or increased propagation delay) will report a higher Dk value. There are other circuit and material prop- erties which can slow the propagating wave, besides the Dk of the material. The copper sur- face roughness can slow the wave and cause the Dk extraction from the circuit evaluation to report a higher Dk than what the material possesses. We conducted a simple experiment years ago that conclusively showed the influ- ence of copper surface roughness on the Dk extraction process. Figure 1 provides a simple overview. Figure 1 shows the results of testing lami- nates in circuit form, using the microstrip dif- ferential phase length method, which uses microstrip transmission line circuits of differ- ent lengths. Before the laminates were made, the copper surface roughness was evaluated using a non-contact laser profilometer, and the average roughness values are reported in the legend of the chart. After determining the surface roughness of these four different types of copper, the same dielectric material was used to make four laminates. The laminates were fabricated into microstrip circuits and evaluated for effective dielectric constant based on phase angle mea- surements. The effective dielectric constant (the Y-axis of Figure 1) is the dielectric constant that the wave experiences. For a microstrip cir- cuit, it is a combination of the dielectric con- stant of the substrate and air. Figure 1 shows four distinct trends of an increased Dk curve for an increased copper surface roughness. Basically, circuits using a smooth copper (red curve) will not slow the wave much, and the reported effective Dk will be closer to the ideal value. A circuit using copper with a much rougher surface (blue curve) will slow the wave significantly, and the reported effective Dk value will be much higher than the ideal effective Dk value of the substrate-air combination. Keep in mind that the same dielectric mate- rial was used for collecting data reported in this chart, and there is a difference of 0.3 for effec- tive Dk, which is due to differences in copper surface roughness only. This is very important because if the dielectric material is evaluated in a fixture without copper roughness effects, the Dk values will be significantly differ- ent than shown in this chart. Additionally, if a thicker substrate is used, which implies the copper planes are farther apart, the influence of copper surface roughness is reduced, and the reported effective Dk value will decrease. The copper roughness effects can be very important Figure 1: A 4-mil LCP laminate effective dielectric constant vs. frequency for various copper foil types on a 50-ohm microstrip transmission line.