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May 2014 • The PCB Design Magazine 41 TRANSMISSION LINES continues wave as the electromagnetic energy propagates in the dielectric material. So the dielectric material determines the ve- locity (v) of propagation of the electromagnetic energy: equation 1 Remember that c is the speed of light (in free space) and Er is the dielectric constant of the material (FR-4 is ~4.0). By contrast, the Er of air is 1. Therefore, the velocity of propaga- tion in FR-4 is about half the speed of light, or 6 inches per ns. The important concept is that it is the electromagnetic energy that propagates down the transmission line—not electron flow. Electrons flow at about 0.4 inches per second, a snail's pace in comparison. A transmission line can be represented by an infinite number of segments, incorporating series resistive (R) and inductive (L) elements with shunt capacitive (C) and conductive (G) elements, as in Figure 4. And because of the re- stricted velocity of propagation in the media, the signal does not know what the termination is at the end of the line. It can only see the im- pedance of the line. The impedance of the line can be represented by: equation 2 If we assume that the transmission line is lossless—which occurs at frequencies below a few hundred MHz—then the R (conductor loss) beyond design Figure 3: embedded microstrip, symmetric and dual asymmetric stripline configurations. Figure 4: Transmission line represented by a series of r-l-C-g elements.