Relative Stability Analysis of Multi-Loop Low Dropout Regulators Using a Sub-Loop Superposition Method

Circuit designers favor open-loop stability analysis, which finds a breaking point in phase margin (PM) simulation. However, the conventional open-loop based method may not suit a multi-loop system that has multiple potential breaking points. It is unclear which breaking point is correct, or whether a correct breaking point exists. In this brief, we first define “relative stability” from the worst stable sub-system of the original closed-loop system, and use it as a “reference”. Then, we examine and discuss the limitations of the conventional open-loop based method for a multi-loop system. The conventional method only indicates the “absolute stability” if the system has no common touching point. Subsequently, we propose a Sub-loop Superposition method for such a system, analyzing the “relative stability” in an open-loop way. We use the proposed method in two multi-loop low dropout regulators. The obtained PMs match the “reference”, verifying the effectiveness of the proposed method.