This tutorial paper discusses an efficient approach that can be adopted to analyze complex analog circuits. The approach is specifically designed to show the graphical interdependencies between system nodes and variables and has been validated across multiple engineering disciplines. By utilizing this graphical approach, we reduce the dependency on circuit analysis techniques that often requires solving extensive systems of simultaneous equations as while effective, they become increasingly difficult and error-prone when applied to circuit with numerous voltage nodes. This paper presents an alternative approach that utilizes basic small-signal analysis principles, Gain Formula from control theory to derive the transfer functions of the circuit or its sub-circuits. The method simplifies the analysis process by directly providing closed-form expressions for the transfer function. This approach not only reduces the general difficulty of the circuit analysis but also minimizes the potential for algebraic mistakes, which are common when working with analytical techniques. Furthermore, it removes the guesswork typically involved in the simplification process found in many textbook examples, where assumptions or approximations are often employed to simplify complex circuits.

The rising demand for defect-free integrated circuits (ICs), especially in the mission-critical automotive industry, has stimulated the development of more efficient defect detection methods. Currently, defect testing methods for digital circuits are far more advanced than for analog circuits, largely due to the greater functional complexity of analog designs. However, in the automotive industry, almost 80% of IC failures stem from defects in analog circuits, creating an urgent need for robust and cost-effective defect detection techniques for analog and mixed-signal (AMS) circuits. This paper presents an all-digital defect detection approach for charge-pump phase-locked loops (CP-PLLs). The proposed Design for Test (DFT) strategy harnesses the robustness of digital control and monitoring circuits to improve detection accuracy, minimizing false failures. Through extensive transistor-level simulations, we demonstrate that the proposed method achieves a high defect coverage of over 97.5% with minimal chip area (< 0.1%) requirements for the BIST circuits.

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.

Backed by standards like ISO26262, achieving near 100% defect coverage is becoming a common reliability requirement in the ever-growing automotive industry. However, achieving high defect coverage in an analog circuit has been proven to be a difficult/expensive task even with sophisticated analog and digital testing circuitry. In this work, we present a simple design for testability (DfT) technique that achieves 98% defect coverage for operational amplifiers including Widlar current reference and biasing circuitry. Our robust testing method utilizes purely digital testing circuits and is extremely time-efficient reducing the test cost. The proposed method can be used both at production test and for on-line health monitoring post-deployment to detect zero-time and latent defects. Also, the digital nature of our method presents a way for defect localization through the recorded bit streams. In this work, we also introduce a simple method to detect defects in the Widlar current reference and the bias current circuit. We validate all our results using extensive transistor-level simulations in UMC65nm technology.