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|Debye Model Fitting for Time-Domain Modeling of Lossy Dielectrics|
|Keywords: debye model, materials characterization, loss tangent|
|Accurate modeling of lossy dielectrics is becoming increasingly important as the signal edge rates get faster. Dielectrics used in packages and PCBs tend to have a constant loss tangent over the frequency range of interest. This implies a conductance increasing almost linearly with frequency, whereas the skin-effect resistance has a sqrt(f) dependency. Substrate losses become the dominating cause for attenuation already below 1GHz for common off-chip interconnects. There are many approaches for extraction of material properties, such as resonator or propagation-constant based methods. These methods provide the dielectric constant and loss tangent at discrete frequency points. This is not sufficient for signal integrity analysis, which requires time-domain models or circuit models that can be simulated in SPICE, to represent the lossy dielectric. The multi-pole Debye model is the most commonly applied lossy dielectric model in signal integrity analysis. Hence, it is critical to be able to fit a Debye model to extracted dielectric constant and loss tangent. Current methodologies, however, do not go much beyond manual fitting of the model, or using general-purpose heuristic methods such as genetic algorithms. Note that standard macromodeling or vector fitting algorithms are appropriate for RLC networks, hence do not necessarily guarantee a Debye model, which can be considered to be an RC network. In this paper, we will show a systematic procedure for fitting a Debye model to tabulated data of dielectric constant and loss tangent at discrete frequency points. Our approach is based on generation of a guaranteed passive RC macromodel, satisfying Kronig-Kramers relations for complex permittivity. We believe the results of this paper will be very useful in generating accurate models for transmission lines, power delivery networks, and other packaging structures for signal integrity analysis.|
|A. Ege Engin, Assistant Professor
San Diego State University
San Diego, CA