Olivier Maurice

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 0.1xa0MHz to 8xa0GHz. 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.

Electromagnetic game modeling through Tensor Analysis of Networks and Game Theory

A complex system involves events coming from natural behaviors. Whatever is the complicated face of machines, they are still far from the complexity of natural systems. Currently, economy is one of the rare science trying to find out some ways to model human behavior. These attempts involve game theory and psychology. Our purpose is to develop a formalism able to take in charge both game and hardware modeling. We first present the Tensorial Analysis of Networks, used for the material part of the system. Then, we detail the mathematical objects defined in order to describe the evolution of the system and its gaming side. To illustrate the discussion we consider the case of a drone whose electronic can be disturbed by a radar field, but this drone must fly as near as possible close to this radar.

Analysis of multilayer interconnects distributed energy-per-bit and power integrity with Kron-Branin formalism

With the increase of the operation speed and the miniaturization, the power consumption assessment of multilayer printed circuit board (PCB) becomes a crucial task during the design phase. More accurate power integrity (PI) analysis is necessary for the complex multilayer PCB. An unfamiliar modelling of static and dynamic power distributed through a four-layer interconnect structure is introduced in this paper. The modelling concept is based on the Kron-Branin (KB) formalism. The different steps of the proposed KB modelling are described with the consideration of the RLC equivalent model and its equivalent graph topology. The KB model efficiency is validated with the static and dynamic powers distributed through the multilayer structure by considering 20 ns duration and 0.5 ns rise/fall time a pulse signal. The computed energy-per-bit and average powers are compared with simulations from a commercial 3D EM computational tool.