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Design, Models, and Simulations

Knowledge MatrixDesign, if you are lucky, is based upon some calculations developed from a model of the thing you are attempting to design and construct. Often, as we have seen with the sheet metal brake project you are not lucky and we are left “flying by the seat of our pants.” Other times we know the general equation, but we don’t know that materials we are working with. An example of that case is the understanding of the popsickle crane forces, but we had no idea of the strength of the glue or the strength of popsicle sticks.  I describe that has a case of knowing what you don’t know.

I have taught the general theory about Bipolar Junction Transistors, and Field Effect Transistors and I considered diving into looking at some datasheets.  However, I think it would be very helpful if first we do some talking about models for these devices.   Eventually we will get to computer simulations of these, but it is my sincere belief that pencil and paper models are much more helpful at the start so you have a very good idea of what to expect before you start running computer models and simulations.

Tonight I will do a little talking about models and simulations.  So what is a model?  That is actually not an easy thing to define, but I am going to do my best after reading several definitions to prepare for this.   One kind of model is a scaled representation of a physical object.  Usually it is smaller scale, but we have all seen those double-helix models of DNA molecules.  In that case the model is much bigger than the real thing.   Many of us spent our youths putting together plastic models of airplanes, ships, and automobiles.  We could not afford the real thing so we put together a small-scale representation of it.

Another kind of model is an idealized representation of how things operate in real life.  That is very much where we are heading in this.  However, it is helpful to realize we are running models in our heads continuously and often we do not even know it.  In our day-to-day existence we often predict things and react accordingly.  For example, if I am walking down the street and have a big grin on my face, I predict that many people will return the smile.  Sometimes, my model fails me and someone will say “Wipe that smirk off your face.”  If that happens a lot I could end up getting depressed because the world no-longer meets my beliefs.  Psychologists have even given this a title, “cognitive dissonance” or in my terminology: “This just ain’t making sense”.  At that time I have two choices.  Either I ignore the real facts, or change my beliefs and expectations.  I call the second of those two choices, “modify my model”.

Ok, now that I went off track it is time to get back to the issue at hand.  (Believe it or not… it is related.)  Scientific models are based upon taking data and then trying to fit some understanding to fit that data.   Usually this is written in some type of mathematical  formula.  The important thing to understand here is the equations were created originally from data.  Once the equation has been created, parts of the new data is ran through the equation and the answer from the equation is compared with the other part of the data.   The difference between the predicted and the actual is the error in the model.  Sometimes this error is known to exist, but the model is “close enough”.

An example, of that kind of model is a road down the side of a mountain near here.   A sign on the road warns truck drivers 6% grade.  That would mean the elevation drops 6 ft for each 100 ft travelled.  The road actually has some curves and some places where it levels out for a short distance.  In other words, the 6% grade is an approximation.  In this case, the approximation is close enough.  Drivers are not really going to be concerned about the actual drop in elevation, but the warning is good to let people know they better slow down while they have the chance.

Often, as time goes on,  the sources of the error are better understood and the model is improved and the error becomes less. Sometimes, the improvement in the model is really good, but it is complicated.  It is too complicated to do with simple hand calculations and computers must be used to run the model.  When a computer is used to perform the calculations, it is called a simulation.  These simulations are ran using known data and the outcome is compared to known results to determine the accuracy of the simulation.   This works well for something such as electronics where tests and real data can be relatively quickly determined.   It does not work so good for slowly and gradually changing data such as weather, climate, and financial models.   (That is especially the case when money and politics is involved… which can be another whole model… but we are NOT going to go there.)

If the simulation varies wildly from the actual results there is a new set of problems to have to deal with.   First, it could be simply a problem with the model in the program.  Second, it could be a problem with the data being fed to the computer or a classic case of Garbage In – Garbage Out.

I have purposefully kept this discussion broad and general to this point to show how these concepts apply to a lot more than just designing things and specifically electrical and electronic things.  We have actually done a lot of work with models in previous blog posts.   Specifically the whole series on Op-Amps and the Thermistor circuit. The op-amp is relatively easy compared to transistors because the designer of the op-amp as done much of the work for us.  Things will be a little more complicated now, but not a lot.   We will baby step through it like we always do.


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