Introduction to Circuits, Lumped Abstraction

 Engineering is the purposeful use of science.   We can take objects and measure the voltage across them and look at the resulting current through the elements.

Engineers layer the level of abstraction such that we can simplify what numbers are telling us. Laws of physics are an example.

Physical laws V = RI. Physics can replace lots of tables with a very simple statement. Similarly, there are Maxwell's equations, and these laws describe the properties of nature. It's really, really hard to just simply building things using Maxwell's equations. This means we simply just have to simplify things. We jump from Maxwell's Laws and define Capacitors, and so on.

Another abstract layer is the amplifier abstraction. How do we make the leap between laws of physics and the amplifier abstractions? The next abstraction is the Digital Abstraction, which are like combination Gates. After this is control logic, then the next abstraction is the clocked digital abstraction, where some notion of time is introduced into the system. After this is an Instruction Set Architecture, or ISA. x86 is an example of this Abstraction. The class takes up from physics all the way to analog and digital logic. 

After this is Language abstractions, Software Systems Abstractions (Operating Systems, etc.) Linux and Windows are a set of system laws, and it's all abstraction layers built on Nature. Using these, we can build very useful things, (video games, space shuttle).

An analog can take an amplifier and take an abstraction, and can make an op amp, then we can build interesting analog system components, which can be oscillators, filters, power supplies, etc. which pulled together can give the next sets of systems such as toasters, control systems for power plants, and ultimately money. 

We want to build interesting analog systems, and go to an interesting digital system component, and this gives you a feel for the space of EECS. 

We want to go from Maxwell's equations to very, very simple equations. 

Maxwell's equations are very complicated. Therefore, we take the easy way. 

To calculate the acceleration, I first ask for the mass of the object, then figure out a = f/m. Done, as simple as this. I could have done differential equations, but done. This process of simplification is called point-mass discretization. This is user analogy. 

We can simply replace the bulb with a discrete object called a resistor.

Now in the same manner replace the battery with a battery object and apply the voltage V and get the I as V/R in accordance to Ohm's law.

Our goal in life as engineers is to build interesting systems. See all I care about is building systems. Let's make assumption that all the systems I consider will have this stuff to be equivalent to 0. 

Discipline myself to only deal with those systems. We might be making a simplification here, and we give a name to this, and it is called a lumped matter discipline. 

This allows us to define a unique I for current.

Vab is defined when ∂Φb/∂t = 0. We can get a certain number of lumped objects, then a unit source will be a part of many lumped objects. The math that you have to analyze them is incredibly simple. 

The Resistor and Zener diode plots represent these respective functions. 

I and V curve is represented.

Too much of anything is bad for you. Abstractions only work if you are working with certain constraints. There are ranges in how physical elements can behave like ideal lumped elements. Lumped abstraction cannot predict the resistance of pickles. There are limits, and you can't predict everything. 

Once we build lumped elements, we can provide connections to circuits. Sum of the loops of circuit = 0, which is Kirchoff's voltage law, and the dV/dt = 0 in Kirchoff's current law.