Modeling the effect of surface roughness for screen-printed silver ink on flexible substrates

Abstract

The role of surface roughness of printed RF components becomes more crucial as the frequency increases. Thus, modeling surface roughness for printed RF components is fundamental for accurate results. At multi-GHz range, the skin depth becomes comparable to the root-means-square height of the rough conductor surface. Failure to model the increased attenuation caused by conductor surface roughness can result in losses past the design margin and cause severe signal integrity problems. In this paper, we build a model to simulate the surface roughness of microstrip-lines; the model is based on real surface roughness measurements. We focus on theoretically modeling of screen-printed silver ink microstrip lines on polyimide substrate. The main objective is building a model to simulate surface roughness of printed RF component based on experimental measurements and study its effect on RF performance. In this way, it can be used for different inks printed using different additive manufacturing techniques. We used the modified Morgan and Hammerstad equation and the compound model to determine frequency dependent values for effective layer thickness and conductivity for a screen-printed silver ink trace. The results were compared to the experimental measurements. A very good agreement is observed between S21 using our model and the experimental measurements. An RMSE of 13.1% is achieved between experimental measurement and the simulated data.