Multiphase VRM Behavioral Modeling and Parameter Extraction for Power Integrity Analysis

Multiphase voltage regulator modules (VRMs) are widely used to meet the stringent power delivery requirements of modern integrated circuits. However, multiphase VRMs exhibit nonlinear behaviors, such as dynamic mode transitions and burst pulse-frequency-modulation (PFM) operation, which complicate power integrity (PI) analysis. To address this challenge, this paper proposes a behavioral model for multiphase VRMs. The proposed model transforms discrete PWM modulation and PFM operation into continuous averaged processes, while the mode transition logic and PFM control logic are implemented in Verilog-A for concise and flexible realization. To identify unknown parameters for modeling practical VRMs, an automatic parameter extraction method based on the nonlinear least squares (LSQ) optimization
is proposed. The proposed behavioral model and parameter extraction method are validated using a three-phase VRM, demonstrating accurate representation of both frequency-domain
and time-domain behaviors.