Circuits and YOU!

I figured since the circuits im am going to be analyzing are going to keep getting more complicated i figured i'd share some tools i use to make sense out of complicated circuits. If you are familiar with KVL,KCL, mesh and nodal analysis, you can skip this post otherwise i hope to shed some light on some useful techniques. The math can get a little difficult but ill try to use as many steps as possible.

Kirchoff's Voltage Law:

Voltage is defined as the potential difference between two points due to an electric field, because of this field there is potential energy to do work (Voltage).  Like all other potential energy this one is also related to position or location. To help realize this we can use an analogy to gravity.

With gravity, potential energy is directly related to how high an object is, as you move an object higher it gains potential energy. However, if you take an object at some height, raise it up and bring it back to your starting position the potential energy is the same, despite the fact you had a gain in potential energy, you had the same amount in loses to return the object to the starting position. The net of this motion is NO change in potential energy.

Voltage works the same way. KVL states that if you have a circuit, and you go around a loop in that circuit, the net change in voltage is zero. We express this with the following formula:

Lets make use of this law, consider the following circuit

What we do is define some variables, we let the current in out circuit be denoted by I.

Here we sum all the voltage drops, because the voltage source provides a voltage and we are summing over the drops we make it negative. Of course due to Ohm's law (eqn 1) the voltage across the resistors is I times their resistance.

Mesh analysis:

If we take KVL one step further we can solve some pretty advanced problems involving many currents and resistors. Mesh analysis is all about taking the loops and assigning each of them their own current (called mesh currents) and we keep track of each current in each loop using KVL.

Ill try and make this as clear as possible, but unfortunately my paint skills are limited. Consider the following circuit with three mesh current, I1,I2 and I3. Each current is positive in the counter clockwise direction.

Phew! If you plug all the currents back in however, they all check out. The work looks alot more tedious than it actually is, Mesh analysis is a very useful way of making good use of KVL.

Kirchoff's Current Law:

The second most important law in EE is KCL or Kirchoff's Current Law. This law like KVL has an analogy in physics. Its very common knowledge that energy and mass are always conserved in a physical system, simply you cannot create or destroy energy (it can only be transferred one place to another). With circuits, we have conservation of charge or simply that the charge into a node has to leave that node. This can be expressed as:

Or that all the current into a node = 0 and all the current out of a node = 0 Consider the following:

KCL states that the current coming from the left of the node has to add up to the current going through both resistors, in this case its trivial, each resistor draws 100mA of current and I1 = 200mA and I2=I3=100mA.

Nodal Analysis:

Nodal Analysis is where we define each node in a circuit. With these definitions and KCL we can find all the node voltages and from there we can define the circuit. Lets take our previous example, instead of using mesh currents we use nodal analysis.

As we look at our drawing, we can make some pretty clear distinctions, V1 is 5V, V3 is 10V and the current through R3 is 5mA. Using KCL at V2 node we make the following conclusion.

You can see the power of nodal analysis, for this circuit it is much easier to do a nodal analysis than it is a mesh one.

Recap:

KVL is that the sum of the voltages in a loop must equal zero (Change in potential in a loop is zero)

KCL says that charge is conserved so, the current into a node must also exit that node.

Mesh analysis is an application of KVL where we define mesh currents and find them using KVL

Nodal analysis is an application of KCL where we define node voltages and use KCL to find the remaining variables.

With these tools in hand, you can analyze almost any electrical circuit, even if you cannot follow the math, having these principles in mind make circuitry more intuitive.

We will be continuing with op amp circuits in the next upcoming posts and then moving onto more advanced topics, if you would like to see a certain derivation or any specific topics email me at Jfkfhhfj@gmail.com