{'fraction_non_alphanumeric': 0.01717967072297781, 'fraction_numerical': 0.0, 'mean_word_length': 5.442396313364055, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Localized Stability Checking and Design of IC Power Delivery With Distributed Voltage Regulators

Placing multiple voltage regulators onto the die is an effective way of enabling distributed on-chip voltage regulation and provides significant benefits in suppressing various types of power supply noise. However, the complex interactions between the active voltage regulators and the large passive subnetwork may render the complete power delivery network (PDN) unstable, leading to design failures. While traditional stability measures such as phase margin are not applicable to regulated PDNs that have a large number of loops, a brute-force analysis of network stability can be impractical due to the high complexity of a given PDN. We present a hybrid stability margin concept and the associated stability-checking method for PDNs with integrated linear low-dropout voltage regulators (LDOs). With theoretical rigor, the proposed approach is local in the sense that the stability of the entire network can be efficiently examined through a hybrid stability constraint that is defined locally for individual LDOs. In the same spirit, we propose a localized LDO design methodology that optimizes individual LDOs in a stand-alone manner while ensuring the network-level stability. Key circuit-level design considerations and tradeoffs involved in stability-ensuring LDO design are also discussed.