Plenary lecture IV: fuzzy techniques in optimization-based analog design
Authors: Gabriel Oltean
Venue: Proceedings of the 10th WSEAS International Conference on Automatic Control, Modelling & Simulation (2008)

The actual trends in VLSI technology are towards the integration of mixed analog-digital circuits as a complete system-on-a-chip. Most of the knowledge-intensive and challenging design effort spent in such systems design is due to the analog building blocks. System level analog design is a process largely dominated by heuristics. While in digital design functionality depends on discrete sequences of discrete signals, continuous sequences (waveforms) of continuous values encode the information we need to manipulate and use in the analog case. For this reason, any second-order physical effect may have a significant impact on function and performance of an analog circuit. Given a set of specification/requirements that describe the analog system to be realized, the selection of the optimal implementation comes mainly out of experience. The current number of analog designers cannot keep up with the demand for analog components. Together with the increasing complexity of the analog blocks, this situation has created an analog- design bottleneck. Consequently, the development of CAD tools that automate and speed up the design process of analogue portions of circuits and systems remains as an active research area in both industry and academia. Fuzzy techniques have been successfully applied in fields such as automatic control, data classification, decision analysis, expert systems, computer vision, multi-criteria evaluation, modeling, optimization, etc. Works showing the possibility of application of fuzzy logic in computer aided design of electronic circuits started to appear in late 1980s and early 1990s. An argument for fuzzy logic application in CAD is derived from the nature of the algorithm used for solving design problems. The majority of algorithms for design synthesis use heuristics that are based on human knowledge acquired through experience and understanding of problems. The natural language, a fuzzy logic language is the most convenient way to express such knowledge. Linguistic descriptions are usually given in fuzzy terms not only because this is the most common form of representation of human knowledge, but also because our knowledge about many aspects of the design is fuzzy. Linguistic information while not precise represents an important source of knowledge. Another important source of knowledge is numerical data. Fuzzy logic systems are appropriate in such situations because they are able to deal simultaneously with both types of information: linguistically and numerical. This paper presents some applications of fuzzy techniques in the design of analog modules. Our research direction turns into account the advantages of fuzzy techniques in the optimization-based analog circuit design field. All the phases of the optimization process (optimization problem formulation, optimization engine, and performance evaluation) involve fuzzy approaches. The multiobjective optimisation problem (MOP) formulation is accomplished in a flexible manner using fuzzy sets to fuzzify the design requirements. The unfulfilment degrees of the requirements (UDR) are used as a measure of objective achievements, getting this way the possibility to consider different degrees for requirement achievements and acceptability degrees for a particular solution. The heart of the optimization algorithm is the optimisation engine. It should provide a rapid convergence toward an optimal solution (ideally global optimum) carrying out the best modification in the design parameters in the iterative process of optimization. The paper proposes two optimization engines based on fuzzy inference systems. The first one, GGFO (Global Gradients Fuzzy Optimization) uses global qualitative dependencies (qualitative gradients) of the performance functions on the design parameters. For every design parameter a zero order Takagi-Sugeno fuzzy system compute a coefficient to modify it, depending on the unfulfilment degrees for all the requirements that depends on that design parameter. The second optimization engine, LGFO (Local Gradients Fuzzy Optimization) is based on local quantitative gradients. For each design requirement, a fuzzy inference system computes a partial coefficient to modify each design parameter, based on the UDR and on the weight of the parameter in the respective performance function. Using these partial coefficients, a final coefficient for modifying each design parameter is inferred. This fuzzy optimization engine acts as a human expert: 1) it is better to modify more the parameter with greater importance, 2) the parameter with lower importance is modified less or not at all, 3) the final modification of a parameter is a weighted sum of the partial modification (the weights being imposed by every objective function). This optimization engine, involving a gradient- like algorithm will provide a local noninferior solution. To obtain a more valuable solution, consisting in a Pareto local noninferior set (specific to MOP) we develop the LFGO optimization engine to use multiple search paths using the concept of population of solutions. In the optimization based analog design the iterative process needs a large number of circuit performance evaluations and this is the most time-consuming task. A very efficient way to reduce the time spent with these simulations is to build efficient models of circuit functions. In this paper, fuzzy systems are used to model each circuit performance, satisfying both main requirements for a model - accuracy and speed. Fuzzy systems are very useful to model the circuit performances because they implies just a few simple mathematical operation and can model any complex, multivariable and nonlinear function at any level of accuracy. These models are automatically built up using a set of input-output data and the ANFIS training procedure in Matlab. Each circuit performance function is modelled by a first order Takagi-Sugeno system, with the circuit parameters as inputs and the performance function as output. Finally, a CAD tool called FADO (Fuzzy Analog Design Optimization) was implemented in the Matlab environment. Using a user-friendly graphical interface, the user can design several basic analog modules. The above mentioned methods and procedures are validated by a large collection of experimental results. Basic analog modules, as common-emitter stage, simple transconductance operational amplifier and Miller operational transconductance amplifier was designed for several sets of design requirements with very good results.