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Model Building: the integration of art and math January 3, 2011

Posted by mareserinitatis in computers, electromagnetics, engineering, math.
Tags: emag, models, simulations
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As time goes on, I am really enjoying the trend toward more sophisticated computational tools. (Although I should also specify that I’m not crazy about the increasing prices…)

In elementary school, I learned to program in basic. I was using a TI computer hooked up to a TV. I had a tape recorder to save my programs. My first program was to make a ‘christmas card’ complete with blinking lights. This was an example program in the TI Basic text that came with the computer. I also very quickly learned the meaning of the word ‘debug’ because some of the flashing lights were floating above the Christmas tree rather than on it.

As I went through high school and then college, I picked up other variants of basic as well as ForTran and C. I found programming to be relatively boring, however, unless I got to do something related to graphics. Being able to create images, and better yet, make them move, made programming a lot of fun for me. I think my favorite formal programming experience was learning Logo, where I used it exclusively on old Apple IIs to draw pictures.

To be perfectly honest, however, drawing pictures doesn’t have the same fascination for me as it used to. I really enjoy it, but I like kicking it up a notch.

When I build my models for electromagnetic simulation, I start by creating a physical model. It’s drawing, but it’s mathematical. Items have to be a precise size, so more often than not I have to spend time doing some arithmetic to get things to fit together correctly. I draw shapes, but I may have to modify them using a mathematical relationship to the other objects.

More fun than drawing, however, are building models where you can change the dimensions of various objects. Take an interdigital capacitor, as an example:

There are a lot of things I might like to change if I were to model one. How long are the fingers? How wide? How much spacing between them? What thickness should the substrate be? Or superstrate? How about the metal?

An IDC is a simple example. When I model something that has several parts, I have to make sure that I create every part with a set of variables that will change the part dimensions if the model changes. This is where the math can be very fun. If I take my capacitor example above, I have two parts. If I change the finger lengths, I will have to change the position of one or both of the pieces that bridges all the fingers. The bridge piece will change length if I change the finger width. And if I change the gap, both the position and length will change.

Debugging these models can be fun, as well. I am often amused if I forget to apply a variable to a dimension that is supposed to change because the results will look very strange. If I don’t change the position of a bridge piece when I change the length of the fingers, it’s going to be a big mess. But it’s fun to see what the mess looks like.

Anyway, building models is a very fun aspect of my job, one that requires both math and a bit of artistry. It requires an eye for detail, because you need to make sure that everything lines up as it should be. The fact that I get to apply electromagnetics to it is a bonus.