Transmission line models for lossy waveguide interconnections in VLSI

At high frequencies the waveguide nature of interconnections in VLSI circuits becomes important. Moreover, losses in interconnection are a major feature, not a perturbation. Here it is shown that even for such lossy waveguide structures an exactly equivalent transmission line can be found. Equations are given determining these transmission line parameters in terms of the waveguide propagation constant and complex average power, and also in terms of integrals over the electric and magnetic field varibles. The resulting , , and parameters differ from the usual static values when losses are important, and R is not restricted to the usual formula based upon a perturbation treatment of the skin effect. Consequently, semiconductor substrates can be treated. "Current" and "voltage" are found to have an abstract meaning in the equivalent transmission line. For a waveguide in a medium where conductivity and permittivity vary with position (such as a many-layered medium) an explicit formula relating "current" and "voltage" to weighted averages of transverse waveguide fields is given. A brief discussion of the reformulation of Thevenin equivalent circuit parameters in terms of reflection coefficients avoids terms such as "open circuit voltage" that are difficult to interpret for the equivalent transmission line. The framework presented allows construction of equivalent circuits for lossy waveguide interconnections, drivers, and terminations that provide correct spatial dependence in the direction of propagation and correct power relations despite the abstract nature of "current" and "voltage" in these lines.