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MAY 2018 I DESIGN007 MAGAZINE 25 fiber glass. When a substrate of sparse fiber weaving is used, PCB traces could cross differ- ent regions of resin and fiber glass more fre- quently. As a result, the speed or propagation delay of the signal changes frequently along the trace from transmitting to receiving end. The relationship between them is governed by Equation 2 [9] . (Equation 2) Where: v = signal's speed on PCB (in unit inch/ns) c = speed of light (~12 inches/ns) D k = dielectric constant This scenario poses a great challenge to multi-gigabit differential signals. The homo- geneous substrate is the most desired ideal condition, where substrate segment of non- inverting signal has the same dielectric proper- ties as inverting signal. However, practically, depending on the fiber weave density, non- homogeneous substrate condition (i.e., when non-inverting signal is routed on fiber glass, while inverting signal crosses resin region or vice versa) is encountered. Due to the chang- ing propagation delay experienced by the inverting signal, the phase difference between non-inverting and inverting signals in common mode could be much less than 180 degrees at the receiving end. The large extent of skew or misalignment between the rising and fall- ing edges leads to the reduction of width and height of the eye diagram, equivalent to larger differential insertion loss. Ultimately, high bit error is experienced. Figure 4 depicts the simulated plot of dif- ferential insertion loss for fiber weave effect on differential microstrip signals 8 inches in length. When the non-homogeneous sub- strate segment increases from 5% to 20% of total channel length, the channel attenuation is increased in the range of 0.7dB and 4dB versus 100% homogeneous at 14GHz. Hence, substrate with denser fiber weave such as 3313 shall be used. C. Copper surface roughness Surface roughness of the copper for trace routing promotes its adhesion to the substrate during PCB fabrication. However, it is neces- sary to keep the roughness magnitude small. This is because the current of the signal tends to propagate more closely to the surface of the copper trace when the frequency of the sig- nal gets higher. Skin depth is the parameter that determines how extensive the current of signal travels with reference to the surface of the transmission channel. The relationship between skin depth and the signal frequency is governed by Equation 3 [10] . (Equation 3) σ = skin depth in unit um f = frequency of signal in unit MHz There are mainly two types of copper foil used for PCB fabrication, namely rolled copper and electrodeposited (ED) copper. Each type of copper foil has many variations that come with different typical surface roughness. For example, rolled annealed copper has rough- ness 0.3 um while high profile ED copper has roughness 2.2 um [11] . At a given skin depth, a larger magnitude of roughness causes more resistance to the signal propagation. Figure 5 depicts the simulated plot of dif- ferential insertion loss for conductor surface Figure 4: Simulated plot of differential insertion loss for fiber weave effect with Hyperlynx.