Lossy Transmission Lines

At high speed of actual digital devices, interconnects behave as lossy Transmission Lines (TLs) in which the effects of losses can seriously degrade Signal Integrity (SI) quality. Accurate and efficient simulation techniques are needed during design and verification to ensure that TLs do not affect correct operation. For this reason, the problem of considering losses in simulating TLs has come to prominence.

In this chapter, lossy line fundamental parameters are introduced and their effect on signal propagation is discussed. The reflection mechanism due to losses along interconnects such as PCB traces or cables is described by the segmentation approach based on the decomposition of the line into a series cascade of elementary circuit cells. Each cell includes an impedance, representing the effects of losses, and a lossless transmission line whose parameters are the nominal characteristic impedance and delay time associated with the corresponding lossless line segment. Losses due to skin, proximity, and dielectric effects are introduced, and the frequency range where they become significant is discussed. Closed-form expressions for calculating these losses are given, including the proximity effect which cannot be directly computed. A coefficient Kp is introduced into the skin-effect expression to take account of the proximity effect. This coefficient can be derived by using full-wave codes or analytically considering the procedure outlined in Appendix ...

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