Toward automated reasoning for analog IC design by symbolic computation – A survey☆
Introduction
Analog integrated circuit (IC) design is a process of using a set of transistors to compose a circuit that implements certain mathematical function (like amplification, filtering, noise suppression, modulation, energy conversion, and tracking, etc.) [1], [2], [3], [4]. Transistors are nonlinear devices and only operate in certain biased regions. Hence, design to fix the biasing and sizing of all devices is nontrivial. Transistors in analog circuits cannot be treated as logical gates, rather their state exists in a high-dimensional continuous state space. Given design constraints, it is not feasible to use logical compilation to determine biasing and sizing of a circuit. The design details must be based on qualitative and quantitative analysis.
Since the co-operation of several transistors complicates the mathematical relations in a typical analog IC, analog designers have to derive the analytical results by going through lengthy hand analysis. Typically, designers do circuit transformation to simplify manual deduction. Simplified circuits can more easily exhibit design insight; designers can use that for circuit topology modification and functional redesign. Reasoning during the conceptual design stage is a very typical human behavior. There exist some reference design procedures for operational amplifier (opamp) circuits. But often designers would prefer to follow their own design steps. Innovation is more a matter of personalized thinking and reasoning. That is why analog IC design automation is much more difficult than logic circuits. Circuit-level knowledge and past design experience determine the success of a design.
However, as a matter of fact, analog IC design is not purely artistic work where no formal rules can be followed. Over the years, engineering in the field has reached such a maturity that systematic design formalisms do exist and most of them have been written in textbooks [1], [2], [3], [4]. So far students and engineers have been successfully trained by such formal design knowledge.
Unfortunately, the existence of formal design knowledge does not mean that computer-aided design tools can be developed accordingly. As many other science and technology fields, mechanisms for computer processing of human knowledge have not been well understood at all [5]. Even for domain-specific knowledge in analog IC, no formal computational paradigm exists for quantitative or qualitative processing. Although formalisms exist in textbooks, computer representation of such formalisms is unknown, not even mentioning the modeling of the human reasoning process in analog IC design.
Despite all the immaturities, we still would like ask a simpler question: Can we develop tools to help designers do reasoning? Reasoning is a knowledge-based inference process. If a computing machine is able to generate readable results that human designers can use to infer new design knowledge, we say that this is computer-aided reasoning (CAR). Further, we may let machine incorporate human knowledge on circuit in its generation process. That would create a human-machine co-working ecosystem, within which quite an amount of laborious analytical work can be left to machine, and human designers are liberated to devote more time to creative work.
Currently, this kind of computer-aided reasoning tool has not been in the mainstream yet in the analog IC domain. Because in the CAR environment human designers are expected to be involved in the design flow, such design automation tools only offer semi-automation assistance. But still, lots of challenges lie ahead.
The main goal of this survey is to go through the historical literature on analog IC design automation, expose the technical approaches, and comment on their limitations; then we introduce a symbolic computation approach to CAR. Section 2 is dedicated to a concise survey on the existing vast literature spanning over three decades of research on analog IC design automation. We shall cover representative knowledge-based tools in early times, optimization-based methods for analog synthesis, and more recently data mining approach to design knowledge discovery. Then in Section 3 we mainly discuss several necessary tool components that form the constitutive parts of CAR in an open tool environment. Interaction is a key feature of such tools, but should be based on the capability of automatic generation of readable objects. Such objects include reduced circuits and readable analytical formulas. To enable automatic generation, a powerful symbolic computation engine is needed. We then review in Section 4 the topological symbolic analysis method, graph-pair decision diagram (GPDD), that has been demonstrated by a variety of examples to be a powerful computation engine for the purpose of CAR. We also comment on the shortcomings we are facing currently and shed light on the potential progresses that can be made. In Section 5 we make an outline on the technical contents of CAR and list several recommendations on the tool development. Finally, we conclude the paper in Section 6.
Section snippets
Analog design automation – state-of-the-art
Design automation for the whole domain of analog IC design is an ambitious task. This survey would be focused on the narrower area of operational amplifier (opamp) design, including those transconductance amplifiers and other similar analog cells. The importance of opamp design in the whole discipline of analog IC design is unquestionable. Many textbooks on analog IC design cover a great deal of opamp design [1], [2], [3], [4], [6]. A number of research monographs were written solely for the
Interactive approach to knowledge generation and reasoning
The notion of knowledge-based synthesis was once the central focus of many works [78], [25], [27], [29]. Harjani el al. [26] observed that “good analog designers exhibit two characteristics. First, they are adept at choosing highly simplified models of devices and device interactions to guide their choices for tradeoffs. These models, though simple, are informed by detailed knowledge of how subtleties of the fabrication process and the desired performance parameters will interact in a specific
Design knowledge acquisition by symbolic computation
As we have mentioned many times, topological exploration is an important part of analog design automation. A unique feature in analog IC design is that on many occasions topology-based reasoning is more intuitive and handy than analytical reasoning. Also we know that poles and zeros of analog circuits can be topologically characterized by creating a condensed macromodel circuit first. Extracting design knowledge with a tool following a similar work flow is an appealing idea, but its computer
Framework of computer-aided reasoning
We devote this section to an outline of the framework of computer-aided reasoning, which summarizes all we have presented previously. A philosophical view point is that development of a symbolic analysis tool, as a complementary design aid to numerical simulation tools, should respect designers’ habit and tradition in their daily practice as much as possible. This is because the day of completely replacing human design effort by a CAD tool in the analog IC domain has not come yet and its
Conclusion
In this survey we have outlined the technical contents of a new notion of research called “computer-aided design reasoning” for analog ICs. After a thorough review on the existing literature on analog IC design automation from a multitude of aspects, we have summarized the critical defects in the proposed tools. The most critical missing link is related to the reasoning part which is a constituent element in the daily design practice of analog IC designers. Without offering partial or full
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