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28 The PCB Design Magazine • February 2015 feature coulmn In my December 2013 column, I discussed "rooting out the root cause" and how some- times, the real root cause is hidden when dig- ging for the solution to a problem. In that column, I described how sometimes in an at- tempt to better correlate measured with mod- elled impedance, fabricators were tempted to "goal seek" the dielectric constant to reduce the gap between predicted and measured im- pedance. To cite a common English saying, "There is an elephant in the room," (i.e., something else that is contributing to the error that should be obvious but has perhaps been overlooked). And why is that? Well, maybe the elephant has been in the room for a while, but it started young and has now grown to a size that cannot be ignored. What is that elephant I am referring to, you ask? DC and AC resistance of the trace is a good pos- sible candidate for an answer here, something that started very small and has grown gradually and perhaps imperceptibly, until now it is often too big to ignore. Thinking back to first principles, when de- signers think of the impedance of a transmis- sion line, it has long been commonplace to ig- nore the losses. So, look at a lossless line where: And this is true enough in many cases where the copper is thick enough and the PCB trace by Martyn gaudion POlAr INsTruMeNTs THE PULSE I 3 : Incident, Instantaneous, Impedance