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Design of power delivery system has great influence on the power management in many-core processor systems. Moving voltage regulators from off-chip to on-chip gains more and more interest in the power delivery system design, because it is able to provide fine-grained dynamic voltage scaling. Previous works are proposed to implement power efficient on-chip voltage regulators. It is important to analyze the characteristics of the entire power delivery system to explore the tradeoff between the promising properties and costs of employing on-chip voltage regulators, especially the on-chip buck converters. In this paper, we present a novel analysis and design optimization platform of power delivery system called power supply on-chip (PowerSoC). It employs an analytical model to provide an accurate and fast evaluation of important characteristics, e.g., power efficiency, output stability, and dynamic voltage scaling, for the entire power delivery system consisting of on-chip/off-chip buck converters and power delivery network. Based on our model, geometric programming is utilized to find the optimal design for different power delivery systems and explore the tradeoff of using on-chip converters. Compared with SPICE simulations, our model achieves a simulation time reduction of six to seven orders of magnitude within 5% model error for the characteristic evaluation of different power delivery systems. By using PowerSoC, various architectures of power delivery systems are optimized for power efficiency under constraints of output stability, area, etc. Simulation results show that the hybrid architecture, consisting of both on-chip and off-chip converters, achieves 1.0% power efficiency improvement and 66.4% area reduction of converters, compared to the conventional design. We conclude the hybrid architecture has potential for efficient dynamic voltage scaling, small area, and the adaptability of the change of power delivery network parasitic, but careful account for the overhead of on-chip converters is needed. [ABSTRACT FROM PUBLISHER]