Designing an RF/microwave circuit requires some knowledge of printed-circuit-board (PCB) qualities, especially when selecting a PCB material for a particular application. Modern computer-aided-engineering (CAE) simulation tools can help predict the electrical performance of circuits on different PCB materials, using material parameters such as relative dielectric constant in the calculations. But one PCB material parameter that is often overlooked in the design process is the surface roughness of the conductors. In the past, conductor surfaces were assumed to be perfectly smooth. What happens when they are not?
The Effects of PCB Conductor Surface Roughness
The effects of conductor surface roughness on PCB performance have been known for some time. In fact, work reported in 1949 by S. P. Morgan detailed the impact of square and triangular shaped grooves on the surface of a PCB’s conductors. The grooves caused additional losses through the conductors, as great as a factor of two under worst-case conditions. The losses were explained by electromagnetic (EM) waves mostly traveling along the surface of a conductor, such as a copper signal trace, and the grooves effectively causing longer signal paths as the EM waves moved along the surface and into and out of the grooved shapes. In a similar way, the surface roughness of a conductor creates a longer mean path, resulting in additional losses. Essentially, higher degrees of conductor surface roughness result in higher resistance from skin-depth effects. In a conductor with propagating EM wave, the skin effect is the tendency of the current distribution of the EM wave to concentrate more towards the surface of the conductor than deeper within the conductive metal.
The “Morgan Correlation”
Commercial CAE tools, such as EM simulators, have traditionally relied on the “Morgan correlation,” as it is known, to account for the effects of conductor surface roughness when calculating the loss of high-frequency microstrip lines. Calculations usually involve a surface-roughness correction factor, Kr, which is a numerical factor based on a ratio of the smooth surface to the rough surface. In many cases, these calculations are quite good and will closely match measured results for conductor losses. But there are also many cases where the computer predictions and the measurements don’t match so closely. Such deviations can be costly at the design stage, possibly resulting in additional design iterations to achieve desired performance specifications. The deviations, and the delays, might be avoided by carefully considering the choice of a microwave PCB laminate in terms of its conductor surface roughness.
RA and RT Foils
Most PCB substrates are clad with some form of copper conductor, including rolled-annealed (RA) copper, electrodeposited (ED) copper, or reverse-treated (RT) copper. As the name suggests, RA copper foils are formed by rolling an ingot of copper through a rolling mill. Successive passes through the mill can achieve a thin copper foil with good thickness consistency. ED copper is formed by depositing copper from a copper sulfate solution (bath) onto a slowing rotating, polished stainless-steel drum. The surface roughness of the copper on side of the stainless-steel drum is similar to that of the RA copper, although the copper surface is much rougher on the solution side of the deposition. RT foils are formed by producing low-profile foils on the bath side of the process, and plating the foil on the drum side.
Because the copper must adhere to different dielectric materials, such as FR-4 and polytetrafluoroethylene (PTFE) substrates, it is typically treated to increase adhesion. Of course, a perfectly smooth copper surface may not be the most ideal case for adhesion to a dielectric. Untreated copper film, formed by RA or ED process, has a surface that is covered by what might be thought of as small “teeth.” These jagged edges are ideal for forming a strong bond between the copper and the dielectric material. This same type of surface is less than ideal for use as a transmission line. But the foil-to-dielectric adhesion would be inadequate if using a perfectly smooth copper foil, one with a mirror-like finish. The solution lies in achieving a compromise in surface composition, to support the fabrication of low-loss conductors while maintaining good adhesion between the copper and the dielectric material.
Commercial PCB materials suppliers like Rogers produce laminates with copper foils having numerous profiles as a result of the different levels of copper treatment. For example, PCB materials are available with standard copper conductor profiles which provide excellent adhesion of the copper to the dielectric material. Laminates are also offered with low-profile (LP) copper where the copper conductor surface is smoother to improve etch definition. This will also reduce conductor losses.
RO4000® LoPro™ laminates from Rogers Corp. are examples of materials with low-profile, reverse-treated copper foils. These materials, including RO4003C™ and RO4350B™ laminates, are ideal for high-performance digital and analog circuits. They are available with a variety of standard dielectric thicknesses and panel sizes and with 0.5 or 1-oz. low-profile, reverse-treated ED copper cladding. RO4003C laminates have a dielectric constant of 3.38 and dissipation factor of 0.0027 in the z direction at 10 GHz, while RO4350B laminates have a dielectric constant of 3.48 and dissipation factor of 0,0037 in the z direction at 10 GHz. Both materials support high-density circuits capable of low insertion loss, low passive intermodulation (PIM) distortion, and excellent signal integrity.
These materials can help overcome the effects of conductor surface roughness, but choosing a PCB material for minimal surface-roughness effects is not a simple task. In general, when selecting a PCB material for minimal surface-roughness effects, PCB materials with lower-profile copper foils will exhibit lower conductor losses at higher frequencies than materials with higher-profile foils.
The next installment of this Blog series will delve deeper into the effects of PCB conductor surface roughness, including propagation and phase-shift effects, and will detail various methods for measuring the surface roughness of a conductor and how the electrical effects of such conductors can be effectively modeled in a computer. In the meantime, for those who seek more information on the effects of PCB conductor surface roughness, download a free copy of the article, “Effect of conductor profile on the insertion loss, phase constant, and dispersion in thin high frequency transmission lines”.