Modeling and analysis of system stability in a distributed power delivery network with embedded digital linear regulators

On-chip power delivery networks (PDNs) for today's microprocessors and systems-on-chip (SoCs), which are characterized by dynamic supply voltage, many embedded integrated VRs (IVRs), lower decoupling-capacitor, high current ranges, multiple power modes and fast transient loads are designed to minimize AC load transients and supply noise. The close interaction of the VRs with the power grids create multiple feedback paths in the overall network, compromising the resultant phase margin and can even lead to system instabilities. The introduction of digital linear regulators operating in the low dropout (LDO) mode, with low power supply rejection, further exacerbates the problem. This paper provides a comprehensive methodology, based on Mason's Gain Formula applied to hybrid control, for modeling and analyzing distributed linear regulators and their interaction with the PDN.