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76 The PCB Design Magazine • July 2017 The capacitive and inductive properties of the transmission line do not, in themselves, absorb the high-frequency components of the signal but rather, the energy is reflected back to the source creating ringing and overshoot un- less absorbed by a source termination. To quantify the RF losses of a transmission line, one needs to consider the attenuation of each mechanism that can be broken down into at least four major components that are accu- mulated: metal loss, dielectric loss, conductivity of the dielectric and stray radiation. The flow of charge through a material causes energy dissipation. The loss in both microstrip (outer layer) and stripline (inner layer) con- ductors may be broken down into two compo- nents: DC and AC losses. DC, in this context, is anything below 1 MHz. Although DC losses are not generally applicable to high-speed design, resistive drops can encroach on logic threshold levels and noise margins of multi-drop systems such as long DDR3/4 address, command and control bus routing associated with SODIMM memory modules. However, on-board memory has typically less than three inches of signal length, and as such does not exhibit this issue. For a typical 5 mil-wide trace, of 1.4 mil thickness (1oz Cu), one inch in length, the re- sistance, in the signal path at DC, is typically 0.1 ohm/inch. The bulk resistivity of copper–and most other metals–is constant with frequency until frequencies near 100 GHz. However, it is the skin effect that imposes a frequency depen- dency on conductors as shown in Figure 2. AC—frequency-dependent—conductor losses can be resistive or inductive. At low fre- quencies, the resistance and inductance assume DC values, but as the frequency increases, the cross-sectional current distribution, in the trans- mission line and reference plane(s), becomes non-uniform and moves to the exterior of the conductor . The current is forced into the outer surface of the copper, due to the skin effect, dra - matically increasing loss. This redistribution of current causes the resistance to increase and the loop inductance per length to decrease. As fre- quency increases beyond 1GHz, the resistance continues to increase while the loop inductance reaches a limiting value—the external induc- tance. The higher the frequency, the greater the tendency for current to flow in the outer surface of the conductor . The AC resistance will remain approximately equal to the DC resistance until the frequency increases to a point where the skin depth is smaller than the conductor thickness. In a microstrip structure (Figure 3, left) the current (blue) will flow under the trace closest to the reference plane and only use the copper to the skin depth of the applicable frequency. However, in a stripline structure (right), the cur- rent will flow on both the top and bottom of TRANSMISSION LINE LOSSES Figure 2: Resistance vs. frequency (5 mil, 1 oz, 50 ohm trace). Figure 3: Skin depth of microstrip (left) and stripline (right) traces.