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44 The PCB Design Magazine • May 2017 of current causes the resistance per length to increase and the loop inductance per length to decrease. As frequency increases beyond 1 GHz, the resistance continues to increase while the loop inductance reaches a limiting value. The higher the frequency, the greater the tendency for current to flow in the outer surface of the conductor. The skin depth is given by: where δ is the skin depth in microns, f is the fre- quency in MHz, µ is the magnetic permeability (4 p x 10 -7 H/m) and s is the copper conductiv- ity, typically (5.6 x 10 7 S/m). Looking at this equation, it is apparent that skin depth decreases with increased frequency. Figure 2 shows the skin depth compared to fre- quency. At low frequency (1 MHz), the skin depth is 66 um but this decreases to 0.66 µm at 10 GHz. Above 1 GHz, only the very outer surface of the plane conducts the current. The red horizontal lines represent the plane copper weight and thickness. This shows that at about 30 MHz, a signal traveling in a ½oz (17.78 µm) copper plane would not use the entire plane cross-section but rather the skin effect would be- gin to have an impact. This implies that at high frequencies, the thickness of the copper plane is irrelevant; ½ oz and 3 oz copper will have the same surface conduction area and hence will only transfer the same amount of current. As seen in Figure 3, the return current dis- tribution, in the plane surface of a microstrip configuration, is reduced as the distance to the center of the trace increases. Here we see a bal- ance of two opposing forces: • Too narrow a distribution increases inductance as narrow traces have more inductance than broad ones • Too broad a distribution increases inductance by increasing the loop area So, there is a sweet spot where the total en- ergy stored in the electromagnetic (EM) field surrounding the trace is optimized. Crosstalk between two or more conductors depends on their mutual inductance and mutual capaci- tance. The inductance plays the major role in this coupling. The signal return currents will generate EM fields. Those EM fields, in turn, in- duce voltages (crosstalk) into other signals. It can be seen in Figure 4 that the differen- tial impedance or the coupling of two parallel traces, levels off at 100 ohms above 12 mils trace clearance (blue curve). This is simulated quickly by multiple passes of the field solver. All other factors being equal, the differential impedance will always be 100 ohms regardless of increased spacing. This also represents the point at which crosstalk (coupling) begins. This curve provides a clear map of the design space and efficiently defines the stackup configuration for single end - ed and coupled pairs. In this case, once the sepa- ration is less than 12 mils, the two traces begin to couple and transfer electromagnetic energy. THE DARK SIDE – RETURN OF THE SIGNAL Figure 2: Skin depth (um) vs. frequency (MHz). Figure 3: Microstrip return current density.