Study on Design of Bend Differential-Paired Lines With Low Common-Mode Noise Using Topology Optimization

Common-mode (CM) noise is generated and radiated in bend differential-paired lines due to imbalance components resulting from the difference in length between the two signal lines. CM components are often compensated for such as by equal-length routing, but equal-length routing requires a large area, which hinders miniaturization. Aiming to design bend differential-paired lines with low CM noise by thinking outside the box, topology optimization is used, in which a structural optimization method with a high degree of freedom, is applied to the bending section in this paper. A Normalized Gaussian Network (NGnet) is used to represent the structure to enable a smooth representation, and the micro genetic algorithm $(\mu \mathrm{GA})$ is used as an optimization algorithm to search for solutions globally through the evaluation of a small number of individuals. In addition, it is examined how optimization results are affected by narrowing down the design target and by increasing the expressive power by changing the number of bases of NGnet. As a result of optimization, a structure with better performance is designed by narrowing down the design target to only the inner line and by increasing the number of cells in the design area. Furthermore, a design that has a high degree of freedom is possible by generating the initial structure randomly, indicating the possibility of better designs for differential-paired lines.