Microstrip Phase Velocity Fundamentals across Multi Layer Glass Stackups
Microstrip phase velocity depends on outer layer inhomogeneous dielectric fields, glass reinforcement architecture, copper roughness, and lamination compression.
Svensson-Djordjevic Dispersion
Frequency Model
Mathematical framework for describing how the dielectric constant and loss tangent of a material change as a function of frequency ensures that high-speed signal simulations remain physically consistent. Svensson-Djordjevic dispersion uses a wideband Debye model to link the real and imaginary parts of the permittivity, preventing non-causal results in time-domain reflections. This model is particularly effective for FR-4 and similar glass-reinforced resins because it accounts for the multiple relaxation times of the complex polymer molecules.
Accurate modeling of this behavior is necessary for predicting the rise times and jitter in multi-gigabit data links.
Phase Consistency
Simulations that use a single, fixed value for the dielectric constant often produce errors where the signal appears to arrive before it was sent. Applying the Svensson-Djordjevic dispersion model ensures that the phase velocity and group velocity are calculated correctly across the entire frequency spectrum. This consistency is achieved by enforcing the Kramers-Kronig relations which state that the loss and the permittivity are fundamentally linked.
In high-speed serial interfaces like PCIe or Ethernet, this accuracy is required to match the simulated eye diagram with the actual measurements from the physical board. The model requires input at two or more frequencies to define the slope of the dispersion curve.
Material Characterization
Electronic design automation tools use this model to represent the substrate properties in the stackup manager. A practitioner provides the known dielectric constant at a reference frequency, usually 1 GHz, and the model extrapolates the values for the rest of the simulation range. This approach is more reliable than using a flat line which ignores the reality of how molecules react to alternating electric fields.
Verifying the model fit against laboratory measurements ensures that the final PCB will meet the stringent timing requirements of modern electronics.