Permittivity Simulation
Mathematical models that describe the frequency-dependent behavior of dielectric constant and loss tangent ensure that signal integrity simulations remain causal across wide frequency ranges. The djordjevic-sarkar model approximates these changes by using an infinite distribution of relaxation times to represent the polarization behavior of the material. This formulation ensures that the simulated propagation delay and dispersion of high-speed digital signals match physical measurements.
Causality Requirement
High-speed digital signals contain frequency components that span from direct current to several gigahertz, requiring models that obey the Kramers-Kronig relations. Applying the djordjevic-sarkar model allows simulator software to calculate a continuous permittivity profile that prevents non-physical, non-causal responses in the time-domain. If a simple constant permittivity value is used instead, the simulation exhibits fictitious signal rise-time distortions and incorrect propagation velocities.
This model requires only a few inputs, such as permittivity and loss tangent at a single reference frequency, to extrapolate the material properties across the entire spectrum. This simplicity makes it a standard choice in commercial electromagnetic field solvers for printed circuit board design.
Design Application
Signal integrity engineers rely on this modeling approach to design transmission lines with predictable impedance and minimal phase distortion. Using these causal material models reduces the risk of discrepancy between the simulated eye diagrams and the oscilloscope measurements on the physical proto-boards. This accuracy is essential for validating high-speed serial links operating above ten gigabits per second.
