The efficient analysis of power grids is a crucial yet computationally challenging task in integrated circuit (IC) design, given the shrinking power supply voltage of ultra deep-submicron VLSI design. Different from the conventional modified nodal analysis technique, this paper introduces MAUnet, an innovative machine-learning model that redefines state-of-the-art full-chip static IR drop prediction. MAUnet ingeniously integrates multi-scale convolutional blocks, attention mechanisms, and U-Net architecture to optimize prediction accuracy. The multi-scale convolutional blocks significantly enhance feature extraction from image-based data, while the attention mechanism precisely identifies hotspot regions. The U-Net architecture, on the other hand, enables scalable image-to-image prediction applicable to circuits of any size. Uniquely, MAUnet also incorporates a pioneering fusion method that synergies both power grids and image-based data. Additionally, we introduce a low-rank approximation transfer learning technique to extend MAUnet's applicability to unseen test cases. Benchmark tests validate MAUnet's superior performance, achieving an average error of less than 6% relative to the average IR drop on three benchmarks. The performance enhancements offered by our proposed method are substantial, outperforming the current state-of-the-art method, IREDGe, by considerable margins of 29%, 65%, and 68% in three canonical benchmarks. Transfer learning is validated to enable model to achieve effective improvement on real circuit test cases. Compared to commercial tools, which often require hours to deliver results, the proposed method provides orders of magnitude speed-up with negligible error in practice.

A magnetic quasi-static (MQS) surface integral equation (SIE) formulation based on the cut set analysis (CSA) is proposed to extract parameters of interconnects in packages. The surface impedance approximation is used to describe the surface current caused by skin effect at high frequencies. To accurately model arbitrarily shaped structures, triangle meshes are selected to discretize surfaces of interconnects in the proposed formulation. After physically interpreting the discretized matrix equation as a circuit, the CSA is tailored to carefully apply the charge conservation condition. Triangles on each terminal are bounded together as a supernode to enforce currents flowing into/out interconnects. In addition, an efficient preconditioner and the pre-corrected Fast Fourier Transform (pFFT) are used to accelerate the convergence and matrix-vector product. Four numerical examples were carried out to validate the effectiveness by comparing it with the industrial solver. Our results show that the proposed formulation is accurate, efficient, and flexible to model complex interconnects at high frequencies.

Frequency-modulated continuous-wave (FMCW) radar plays a pivotal role in the field of remote sensing. In low-altitude environments, where unmanned aerial vehicle (UAV)-borne FMCW radars are increasingly used, mutual interference poses significant challenges to radar performance. In this article, a novel FMCW radar interference mitigation (RIM) method, termed as RIMformer, is proposed using an end-to-end transformer-based structure. In the RIMformer, a dual multihead self-attention mechanism is proposed to capture the correlations among the distinct distance elements of intermediate frequency (IF) signals. In addition, an improved convolutional block is integrated to harness the power of convolution for extracting local features. The architecture is designed to process time-domain IF signals in an end-to-end manner, thereby avoiding the need for additional manual data processing steps. The improved decoder structure ensures the parallelization of the network to increase its computational efficiency. Simulation and measurement experiments are carried out to validate the accuracy and effectiveness of the proposed method. Extensive simulations and empirical measurements demonstrate that RIMformer significantly improves interference mitigation and signal recovery, which advances the reliability and effectiveness of UAV-borne FMCW radars in complex environments.