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30 The PCB Design Magazine • February 2015 wide enough for the losses to be ignored. Also, from an instantaneous point of view, the L and C scale per unit length and the ratio of L/C is to all intents and purposes independent of length. However, when geometries shrink, character- istics that could be comfortably overlooked in larger dimensions can no longer be ignored and the uncomfortable fact that the equation for transmission lines approximates to: R is the resistance per unit length, a com- bination of the DC and AC resistance, and the G is the conductance per unit length. Unlike the L and C, unfortunately, the R and G can- not be seen as dimensionless and the R piles up along the trace whilst the G stays close to 0 and the two do not divide out. This means that the TDR trace shows the effect of trace resistance presenting an upward slope as ohm upon ohm of combined DC and AC resistance "pile up" on top of the instantaneous impedance. Without this knowledge, someone trying to analyze why the measured impedance is somewhat higher than the prediction may seek the source of error. The dimensions are hard to argue with if there is access to precision mi- crosections, especially if three or four sections are taken along the trace and all correlate. So, it may be deduced that, given the dimensions are known and provided the impedance mea- surement system is calibrated and air line veri- fied, that the only unknown is the dielectric constant. However, deducing (derived from the Latin ducere meaning to lead [1] ) is not fool- proof: deduction only works if you are certain of the facts. (For example, when you see a per- son crying, it's easy to deduce the person is sad. Unless they are happy, of course; sometimes happy people cry.) So deducing that an erro- neous Er value is the cause of poor measuring and modeling correlation could be challenged if new facts come to light. Sometimes the clue is in the numbers, and I have seen situations where the Er amount has to be "adjusted" to make the impedance correlate appears to defy the laws of physics: for example, when the Er is adjusted to a lower level than each of the pri - mary individual constituents of the base mate- rial. This should be a clue that something else is awry here; this is, as I mentioned earlier, the elephant in the room. In 2009 at DesignCon, Navarro, Chairet and Mayevskiy [2] proposed a technique to measure I 3 : InCIDEnT, InSTAnTAnEOUS, IMPEDAnCE continues the pulse Figure 1: Onset of dielectric loss.