Representing analog circuits for optimization: an old debate
If you are going to analyze and optimize an analog circuit, you have to represent it in some form that makes analysis possible. And as the implementation gets more and more complex—because of tiny process geometries, huge variations and crummy transistors, for example—the choice of a medium for representing the design becomes a critical decision. But for as long as I can remember there has been a debate among designers over just what that form ought to be.
One camp I would call the intuitive school. These people—of whom I am in awe, by the way, much as I am in awe of a musician who can sight-read new material and play it on a woodwind—have an intuitive grasp of how a circuit will behave, just from looking at the schematic and the device sizing data. They can often get so clear a picture of the circuit behavior in this way that they can do sensitivity analysis and optimization by a few recursive estimates. But I understand that this technique is getting harder as geometries shrink.
Another camp I would call the computer faithful. These people learned analog design in the days when SPICE was the new wonder-tool, and they actually seem to think of circuits not as physical entities, but as SPICE models. It’s just that the physical embodiments are much harder to modify than the models. In this case, analysis and optimization seem to be a matter of lots of SPICE runs coupled with ingenious experiment design and clever sampling techniques to avoid a full Monte-Carlo analysis.
Finally, there are the mathematicians. I have a certain sympathy for this school, since the only things I learned about analog design at university were in automatic controls and systems synthesis courses, where circuits were not things, they were transfer functions in the log(s) plane. Or, across the campus in another building, they were linear differential equations that could be solved either analytically or on an analog computer. (No, we did not use a steam-driven generator to power the computer. Stop that.)
For the most part, analog designers I have met in industry seem to fit into one of the first two stereotypes. But there has been one notable exception. The folks, such as Mar Hershenson, who started Barcelona Design were very much of the mathematical school. Their initial concept at Barcelona was that if you modeled an entire class of analog circuits with similar functionality as a set of equations, you could apply formal optimization techniques to the equations and produce a highly-tuned implementation of the circuit to fit any set of constraints you wished.
According to Hershenson, this actually worked quite well. But deriving the equations from a base circuit topology was a very specialized task, and so it turned out that Barcelona had to do the base designs for you, and then let you do the optimization. That was just the opposite from the way most designers—especially the intuitives—wanted to work. They wanted to define the circuit, and let Barcelona’s tool do the optimization. So Barcelona went away.
But the idea—and much of the team’s core–survived, and reappeared in the form of Sabio Labs. This time the idea was to extract the mathematical expression from the customer’s design, and then use the mathematics to perform optimizations. This worked well enough that Magma bought the company in April of 2008, and integrated the Sabio tool into the Titan analog/mixed-signal design environment.
In its integrated form, the tool can extract a process-independent mathematical representation—based on, but not exactly like, the Matlab format—from either a schematic or a GDSII layout automatically. The tool also takes in a design-requirements file that captures constraints not deducible from the design data. It also absorbs process models for the target process, and produces an optimized design in the target process.
Hershenson says that the use of a process-independent mathematical representation of the design has a number of benefits. For one, it allows analytical optimization of the design rather than trial-and-error. For another, the models at this level are fast enough to analyze that designers can use them to explore the solution space, not just to drill down on one idea. And also, Hershenson—ever the mathematician—says that having a mathematical representation gives designers another independent way of looking at the design. Often reality checks and tests of simple assertions are easy in the mathematics even after they have become very difficult at an intuitive level.
The three design styles live on. I wouldn’t expect any skilled analog designer to convert from one style to another. They seem to be as innate as left- or right-handedness. But it does appear that as we move deeper into the realm of the sub-65nm, mathematics may reassert itself as a valuable—if not as the only viable—way of looking at complex analog designs.
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