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Wavelets in Packaging, Interconnects, and EMC In this chapter we will study multiconductor, multilayered transmission lines (MMTL) employing quasi-static, quasi-dynamic, and full-wave analyses. We extract from MMTL the distributed (parasitic) parameters in matrix form of the capacitance [C], inductance [L], resistance [R] and conductance [G], or the [Z ]-parameters, [Y ]-parameters, or more generally the scattering matrix [S]. MMTL systems are commonly found in high-speed, high-density digital electronics at the levels of individual chip carriers, printed circuit boards (PCBs), and more recently, multichip modules (MCMs). Previous methods for extraction of the distributed circuit parameters include the quasi-TEM solutions [1–5], and more. | Wavelets in Electromagnetics and Device Modeling. George W. Pan Copyright 2003 John Wiley Sons Inc. ISBN 0-471-41901-X CHAPTER NINE Wavelets in Packaging Interconnects and EMC In this chapter we will study multiconductor multilayered transmission lines MMTL employing quasi-static quasi-dynamic and full-wave analyses. We extract from MMTL the distributed parasitic parameters in matrix form of the capacitance C inductance L resistance A and conductance G or the Z -parameters L -parameters or more generally the scattering matrix S . MMTL systems are commonly found in high-speed high-density digital electronics at the levels of individual chip carriers printed circuit boards PCBs and more recently multichip modules MCMs . Previous methods for extraction of the distributed circuit parameters include the quasi-TEM solutions 1-5 and more rigorous techniques 6-9 . They also included full-wave analysis algorithms 10-15 . We begin with the quasi-static formulation QSF 1 which provides the parasitic capacitance C inductance L resistance A and conductance G . Due to the limitation of its assumptions the QSF results for L C A and G are independent of frequency values. This characteristic is accurate only under special circumstances. The comparison of the QSF solution with the full-wave finite element method FEM data indicates that the capacitance C values from the QSF are accurate to at least 50 GHz 16 while the L and A may have large errors. For most practical applications conductance G is negligibly small. Therefore in the quasi-static formulations of Sections 9.1 and 9.2 we will focus mainly on capacitance extraction. In Section 9.3 we will introduce an intermediate formulation between that of the quasi-static and full-wave referred to as the quasi-dynamic formulation QDF . The QDF provides us with frequency-dependent parameters of the skin effect resistance and total internal plus external inductance. The comparison of the QDF with the FEM 17 and laboratory tests 18 reveals
