Phase Margin Estimation of Linear Voltage Regulator Using Noninvasive Stability Measurement and Optimized Regression

Abstract

Linear voltage regulator (LVR) instability due to sudden load current change can be compensated by connecting an output capacitor with specific equivalent series resistance (ESR) at its output terminal. In manufacturing, the optimum ESR range is characterized by the load transient tests for a range of load current and ESR values. Currently, the stability condition is determined by observing the output voltage oscillation counts. However, this process is less accurate and time-consuming. A more precise stability condition can be obtained by measuring the phase margin based on the frequency response. Yet, it needs to be conducted in an openloop condition, which is difficult for the LVR integrated circuit. Therefore, an approach is developed to noninvasively measure the phase margin in closed-loop conditions based on the LVR frequency response. Furthermore, five machine learning (ML) methods were proposed to solve the regression problem to estimate the phase margin for any operating points. Those ML methods are support vector machine, decision-tree, ensemble method, neural network, and Gaussian process regression. The inputs are load current and ESR, while the phase margin acts as the targets in the ML training. In addition, hyperparameters in each ML method are also optimized. Results showed that Gaussian process regression produces validation RMSE, MSE, MAE, and R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> of 0.1736, 0.0301, 0.0612, and 1.0000, respectively. The trained ML methods were then used to estimate the phase margin. To conclude, the phase margin in the LVR circuit can be effectively estimated without breaking the internal control loop.