Mesh conforming electro-thermal co-analysis with application to PCB power integrity

Modern design of Printed Circuit Boards (PCB) applies electric IR drop analysis in order to optimize the supply voltage margins for the ICs mounted on the board. The IR drop however is affected by the heat generation in the PCB due to the temperature dependency of the material conductivities. Both the electric power dissipation inside the IC's and the Joule losses in the copper contribute to the heat generation. The electric problem is coupled with the thermal problem and is to be solved in a co-analysis setup to obtain thermal aware IR drop values. This paper presents an electro-thermal co-analysis technology targeting PCB designers responsible for Power Integrity (PI). We deploy a finite element discretization technique to solve the coupled electro-thermal steady-state equations simultaneously. Our solution combines H(div) Whitney face elements with mesh conformity. That is, the mesh used in the electric domain is reused in the thermal domain preserving all geometrical details in both domains. The exchange of electric data (power loss) and thermal data (temperature) at the mesh level speeds up the design process and increases the accuracy of the simulations. The electro-thermal co-simulation technique is validated using a via test board and applied for a real DDR4 board to demonstrate the significance of thermal aware IR drop.