Fifteen Eighty Four

One of the reasons people like science and engineering is because of the joy of discovering things about the world around us. The more scientifically inclined are curious about nature and what surrounds us, and often wonder why things are the way they are. People that are more oriented towards engineering often ask how one might improve the quality of life and make the world better, from a practical point of view. Oftentimes, it is beneficial to first get an idea of the solution by estimating various effects through simple mathematical modeling.

In my recent book, “Fast Techniques for Integrated Circuit Design”, I outline a methodology (or algorithm if you will) to approach such estimation calculations systematically. I call it Estimation Analysis, which is not an entirely new idea. In the hallways of science and engineering departments, similar methods are often referred to as hand calculations or back of the envelope calculations, but I define it a bit more formally in four steps:

• Simplification– This is often the most difficult step, because it attempts to get to the core of how the system works.
• Solve – Solve the problem. If step (1) is executed properly, this will be fairly easy.
• Verification – Here we verify that the model in step (1) is reasonable, for example, by checking extreme cases, measurements, simulations, and perhaps exact calculations. If something is wrong, we go back to step (1).
• Evaluate – In this step, we analyze what the solution means.

Figure 1 Estimation Analysis flow graph

It is often easy to forget the verification step, and if one misses this and runs off in the wrong direction, it will cause some real problems at a later stage.
The reader no doubt realizes these steps are applicable to most scientific endeavors. Personally, I encountered this approach in the class “Order of Magnitude Physics”, at Caltech. Here, the professors had the students estimate the amount of rubber in the air from cars on LA’s freeways or estimate the growth of a straw of grass in a week with a given precipitation and sunlight. These kinds of questions might seem a little pointless, but the general idea of the class was to get to the core of the problem by thinking about the root cause and to come up with a simple model and estimate of the correct answer. I and many with me in the class were totally fascinated by this approach. In my engineering endeavors, I have strived to understand the projects I have been working on following these principles, and they have served me well. I am certainly not alone in this way of looking at design work and I have met many practicing engineers and academics that are very good at similar thinking. It is very satisfactory to be able to explain a certain behavior with a simple mathematical model, rather than resort to simulators.

The principles as they stand are fairly general and in the book I go through many specific examples from a deliberately wide range of circuit design topics, just to illustrate the methodology. Some calculations are very well known and some perhaps less so.

It is my hope that the book and its examples will inspire the reader to pursue his or her projects doing Estimation Analysis.

Further Reading

VIDEO:  Mikael Sahrling discusses Fast Techniques for Integrated Circuit Design on the Cambridge Core blog

Fast Techniques for Integrated Circuit Design by Mikael Sahrling. Published August 2019.