The move to higher levels of integration has increased the fraction of application-specific integrated circuit (ASIC) designs containing both analog and digital circuits. While the die area for the analog portion of these chips is modest, the design time is often significant. This has motivated the development of automated analog physical design tools for cell-level place-and-route and system-level signal-integrity-routing. To date, there is no tool that has specifically addressed the critical design task of synthesizing the power distribution for the analog portion of an analog or mixed-signal ASIC. This text describes algorithms for analog power distribution synthesis and demonstrates their effectivenes. Existing digital power bus synthesis algorithms have failed to address critical concerns for analog circuitry, thus yielding unacceptable results. These tools synthesize only the bus component of power distribution networks and only consider simplified DC aspects of macros and buses. This work addresses power distribution synthesis for mixed-signal integrated circuits. Several key challenges in power distribution design are identified and automated methods to overcome them are described. The text presents a formulation for the analog power distribution synthesis problem which synthesizes both the power busses power I/O cell assignment by evaluating DC, AC, and transient interaction between the macros, busses, chip substrate, and package. Furthermore, algorithms are introduced which simultaneously optimize power I/O cell assignment, macro cell substrate coupling, power bus topology selection and power bus sizing. The book should be of interest to CAD designers and researchers specializing in physical design, modelling and circuit synthesis.