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AUGUST 2020 I DESIGN007 MAGAZINE 23 netic wave down by about half (Figure 2). But that all depends on the exact dielectric con- stant of the surrounding materials. For the top layer 1, the electromagnetic energy travels in a combination of prepreg, sol- der mask, and air (Figure 3). The effective Dk will be around 2.68 with a propagation speed of 1.83 x 10 8 m/s. For layer 4, there is a com- bination of prepreg and core with an effec- tive Dk of 4.03 and a speed of 1.49 x 10 8 m/s. This should be simulated by a field solver, as it depends on the combination of materials and their Dks, order, and thickness. From this, one can see that the propagation speed of the elec- tromagnetic energy is always faster on the outer microstrip layers than the inner stripline layers. At high frequencies, short traces (particu- larly stubs or unterminated traces) on a PCB can act as a monopole or loop antenna. Dif- ferential-mode radiation is the electromagnetic radiation caused by currents consisting of har- monic frequency components flowing in a loop in the PCB. The radiation is proportional to the current loop area and the square of the fre- quency of the signal. Common-mode radiation is the electromagnetic radiation caused by cur- rent flowing in an unterminated trace (or ter- minated with a high-input impedance device) and may require load terminating resistors to eliminate reflections. The radiation resembles that of a monopole antenna, and the magni- tude is proportional to the current per line length and frequency. Trace antennas form a monopole with a quarter wavelength (l/4) at the resonant fre- quency. Monopoles require a ground plane; this forms the other quarter wavelength to radiate efficiently, which is not desirable in this case. It functions as an open resona- tor, oscillating with standing waves along its length. The radiation pattern is practically omni-directional. Unfortunately, the high-frequency compo- nents of the fundamental (lowest frequency in a complex wave) radiate more readily because their shorter wavelengths are comparable to trace lengths, which act as antennas. Conse- quently, although the amplitude of the har- monic frequency components decreases as the frequency increases, the radiated frequency varies depending on the characteristics of the antennas/traces. At 2.45 GHz, an 18-mm trace on the outer, microstrip layers may radiate while on the inner stripline layers, 15 mm (600 mils) is suf- ficient. And as we increase the frequency to 10 GHz, the maximum length is just 3.75 mm (150 mils), which is incredibly short. Strip- line traces are embedded between two planes, which dramatically reduces radiation with the exception of the fringing fields from the edge of the board. However, the outer microstrip layers will radiate; hence critical, high-speed traces should be avoided on these layers. Since the wavelength of electromagnetic energy depends on the signal frequency and dielectric constant of the surrounding materi- als, a low Dk (circled in Figure 4) is preferred for high-speed design. Fortunately, low-loss materials generally have this characteristic. Figure 3: Comparison of Dk per layer and relative velocity.