Kron–Branin Modeling of Y-Y-Tree Interconnects for the PCB Signal Integrity Analysis

The signal distribution interconnect network modeling plays an important role during the digital/mixed printed circuit board (PCB) design. With the increase of the design complexity, the PCB interconnect modeling becomes a challenging task. This paper proposes an innovative circuit theory of the PCB electrical interconnects modeling based on the tensorial analysis of network (TAN). The model under study, fundamentally built with the Kron-Branin formalism, is applied to the asymmetrical 1:3 Y-Y-tree interconnects. This Kron-Branin method enables to establish quickly the tree interconnects equivalent model for the signal integrity (SI) analysis. An asymmetrical microstrip circuit was designed and fabricated to validate the developed TAN concept. The modeled, simulated, and measured S-parameters are in good agreement in the broad frequency band 0.1 MHz to 8 GHz. The electrical power budget distributed through the Y-Y-tree prototype in dc and in the considered entire frequency band was analyzed. Furthermore, the Kron-Branin model was also validated in the time domain with 1-Gb/s-rate 8-bits serial data and eye diagram analyses. This innovative formalism presents a considerably high computation speed and is beneficial for the SI analyses thanks to its adaptability to the complex system.