Matching Critical Analog Circuit Components Up To Third-Order Gradients for All Possible Exact Matching Ratios

This article presents a systematic approach to generate layouts for two devices, with an arbitrary integer ratio of device sizes, that cancels up to at least third-order gradient effects. A new analysis leads to mathematical constraints on 1-D layouts that meet the required integer ratio and cancel second-order gradients. From those layouts, we apply reflection and rotation symmetries to generate 2-D layouts that cancel higher-order gradients. We demonstrate our proposed methodology on current sense transistors interspersed in active power transistors. Legato electrothermal simulation show our proposed approach, respectively, improves worst-case matching accuracy about a factor of 9.9 and 7.15 when compared to a common centroid (CC) and interdigitated (ID) pattern in the presence of gradients effects. Furthermore, we discuss evaluation metrics that can be used to select one of multiple gradient canceling layouts for any fixed rectangular grid and device application.