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14 The PCB Design Magazine • August 2014 dielectric material. It is the dielectric material that determines the velocity (v) of propagation of the electromagnetic energy: equation 1 Keep in mind 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 by comparison. The electrical properties of a dielectric mate- rial can be described by two terms: 1. The dielectric constant or relative permit- tivity (Er or Dk) is the ratio of the amount of electrical energy stored in a material by an ap- plied voltage. It describes how the material in- creases the capacitance and decreases the speed in the material. 2. The dielectric loss or dissipation factor/ loss tangent (Df) is a parameter of a dielectric material that quantifies its inherent dissipation of electromagnetic energy. Dielectric constant and dielectric loss are not a function of the geometry of the transmis- sion line—they are a function of the dielectric material in which the signal propagates, their distribution in the PCB stackup, and the ap- plied frequency. These mechanisms contribute to the frequency dependent loss and to degrade the speed of the signal. The signal quality trans- mitted through the medium, and picked up at the receiver, will be affected by any impedance discontinuities and by the losses of the dielec- tric materials. The glass epoxy material (FR-4) commonly used for PCBs has negligible loss for digital applications below 1 GHz. But, at higher frequencies the loss is of greater concern. So if you have a fast rise/fall time, high fre- quency signal, then the wave needs to propa- gate at higher speed and therefore the Er needs to be low to enable this. If a material with a high dielectric constant is placed in an electric field, the magnitude of that field will be measurably reduced within the volume of the dielectric. Therefore, a lower Er is desirable for high-speed design. It is best to use the value of the dielectric constant applicable at the highest frequency of interest. For digital signals, the highest frequen- cy of interest (f) depends on the rise/fall time (Tr) and is approximated by: equation 2 Therefore, for a 1-ns rise time signal, the fre- quency of interest will be 500MHz. But then, the maximum bandwidth also needs to consider the 3 rd or 5 th harmonic of the fundamental—1.5 GHz to 2.5 GHz—in this case. The bandwidth is an indication of the highest data rate that can be transmitted by an interconnect. So for a 1 ns rise time signal, we should look at about a 2 GHz material. Also of importance is the glass transition temperature (T g ), which is the point at which a glassy solid changes to an amorphous resin/ epoxy. If the reflow temperature exceeds the T g for an extended period, the material rapidly ex- pands in the Z-axis. Plus, mechanical material Figure 1: simulated signal propagating through a curved waveguide 2 . beyond design MATERIAL SELECTIoN FoR DIGITAL DESIGN continues