Bridging the gap : an optimization-based framework for fast, simultaneous circuit & system design space exploration

Abstract

Design of modern mixed signal integrated circuits is becoming increasingly difficult. Continued MOSFET scaling is approaching the global power dissipation limits while increasing transistor variability, thus requiring careful allocation of power and area resources to achieve increasingly more aggressive performance specifications. In this tightly constrained environment traditional iterative system-to-circuit redesign loop, is becoming inefficient. With complex system architectures and circuit specifications approaching technological limits of the process employed, the designers have less room to margin for the overhead of strict system and circuit design interdependencies. Severely constrained modern mixed IC design can take many iterations to converge in such a design flow. This is an expensive and time consuming process. The situation is particularly acute in high-speed links. As an important building block of many systems (high speed I/O, on-chip communication, ...) power efficiency and area footprint are of utmost importance. Design of these systems is challenging in both system and circuit domain. On one hand system architectures are becoming increasingly complex to provide necessary performance increase. On the other, circuit implementation of these increasingly complicated systems is difficult to achieve under tight power and area budget. To bridge this gap between system and circuit design, we formulate a circuit-to-system optimization-driven framework. It is an equation-based description, powered by a human designer. Provided with equation-based model we use fast optimization tools to quickly scout the available design space. Presence of a designer in the flow is invaluable resource enabling significant saving by simplifying the models to capture only the relevant information and constraining the search space to areas where meaningful solutions might be expected to be found.

(cont) Thus, the computational effort overhead that plagues the simulation-based design space exploration and design optimization is greatly reduced. The flow is powered by a signomial optimization engine. The key challenge is to bring, from the modeling point of view, very different problems such as circuit design and system design into the realm of an optimization engine that can solve them jointly, thus breaking the re-design loop or at least cutting it shorter. Relying on signomial programming is necessary in order to accurately model all the necessary phenomenons that arise in electrical circuits and at system level. For example, defining regions of operation of transistors under polarization conditions can not be modeled accurately with simpler type of equations. Similarly, calculating the effect of filtering to a signal also requires possibility to handle signomial equations. Thus, signomial programming is necessary yet not fully explored and finding suitable formulation might take some experimenting as we will see in this thesis. Signomial programming, as a general non-convex optimization problem, is still an active research area. Most of the solutions proposed so far involve local convexification of the problem in addition to branch & bound type of search. Furthermore, most of the non-convex problems are solved for one particular system of equations, and general methodology that is reliable and efficient is not known. Thus, a big part the work to be presented in this thesis is detailing how to construct a system formulation that the optimization engine can solve efficiently and reliably. We tested different formulations and their performance measured in terms of parsing and solving speed and accuracy. From these tests we motivate and explain how a series of transformations we introduce improve our formulation and arrive to a well-behaved and reliable form. We show how to apply our design flow in high-speed link design.

(cont) By restructuring the traditional design flow we derive system and circuit abstractions. These sub-problems are interfaced through a set of well defined interface variables, which enables code level separation of problem descriptions, thus building a modular and easy to read and maintain system and circuit model. Finally we develop a set of scripts to automate formulating parametrized system level description. We explain how our transformations influence the speed of this process as well as the size of the model produced.