THEVENIN'S AND NORTON'S THEOREM

THEVENIN'S  AND NORTON'S THEOREM

THEVENIN'S THEOREM

-Thevenin’s Theorem states that it is possible to simplify any linear circuit, no matter how complex, to an equivalent circuit with just a single voltage source and series resistance connected to a load. It is especially useful in analyzing power system and another circuits where one particular resistor in the circuit called the load resistor is subject to change and re-calculation of the circuit is necessary with each trial value of load resistance to determine voltage and current across it.

It is also states that the linear two terminal circuit can be replaced by an equivalent circuit consisting of a voltage source VTH in a series resistor RTH where Vth is the open circuit voltage at terminals and Rth is the input or total resistance at the terminals when the independent source are turn off.



There are two cases you need to consider in thevenin's:

Case 1: If the network has no dependent source therefore you need to turn off all independent source. Rth can be computed via parallel or series connection seen from the given.

Case 2: If the network has dependent source turn off all dependent source. Apply V0 at A-b and Also Io at A-b.


Thevenins Equivalent Circuit:

NORTON'S THEOREM

-Any collection of batteries and resistances with two terminals is electrically equivalent to an ideal current source i in parallel with a single resistor r. The value of r is the same as that in the Thevenin equivalent and the current i can be found by dividing the open circuit voltage by r.

Norton's Circuit

Norton's Equivalent Circuit:

SAMPLE PROBLEM:

LINEARITY PROPERTY, SUPERPOSITION AND SOURCE TRANSFORMATION

*LINEAR PROPERTY

-linear network consist of linear elements, linear dependent sources and linear independent sources.

It is state that the output of linear circuit is directly proportional to its input.

LINEAR SYSTEM HAVE TWO IMPORTANT AND USEFUL PROPERTIES:
-Superposition
-Homogeneity





*SUPERPOSITION
- Superposition states that the voltage across an element in linear circuit is the algebraic sum of the  voltages across that element due to each independent source acting alone.



WAYS OR TECHNIQUES IN SOLVING THIS CIRCUIT:

-Turn off, killed, inactive source:
-independent voltage source: 0 V (short circuit)
-independent current source: 0 A (open circuit)
-Dependent sources are left intact.

After you apply those techniques above, proceed to the steps in solving superposition.

STEPS TO APPLY THE PRINCIPLE:
1.Turn off all independent sources except one source. Find the output voltage or current due to that active source using mesh analysis or nodal analysis.

2.Repeat step 1 with other independent sources.
3.Find the total contribution by adding directly all of the contributions of independent sources.

In killing the independent sources, first you need to turn off all the sources(current and voltage) short the voltage source and open the current source and make their voltages and currents equal to zero.



SAMPLE OF A SUPERPOSITION CIRCUIT:

SAMPLE PROBLEM:

Find the voltage Vx using superposition

*SOURCE TRANSFORMATION
-Source transformation talks about simplifying a circuit especially with complicated or mixed sources. By transforming the voltage sources into current sources and current sources into voltage sources using ohms law V=IR.

Sample Problem :

(this sample problem is unfinish but we only post this sample in order to explain properly the transformation)

MESH ANALYSIS

Mesh Analysis

Mesh analysis is the method that is used to solve planar circuits for the currents at any place in the circuit. We first note that the mesh current method is only applicable for “planar” circuits.


Planar circuits have no crossing wires when drawn on a plane. Often, by redrawing a circuit which appears to be non-planar, you can determine that it is in fact, planar.


Mesh analysis works by arbitrarily assigning mesh currents in the essential meshes (also referred to as independent meshes). An essential mesh is a loop in the circuit that does not contain any other loop.


A mesh current is a current that loops around the essential mesh and the equations are set solved in terms of them. A mesh current may not correspond to any physically flowing

current, but the physical currents are easily found from them.

Mesh Analysis with Current Sources

In mesh analysis there are two cases we need to consider:


Case 1- A current sources exist only in one mesh

- Set the mesh currentt = current source


Case 2- A current source between two meshes are called

supermesh









A supermesh occurs when a current source is contained between two essential meshes. The circuit is first treated as if the current source is not there. This leads to one equation that incorporates two mesh currents. Once this equation is formed, an equation is needed that relates the two mesh currents with the current source. This will be an equation where the current source is equal to one of the mesh currents minus the other.

Mesh Analysis without Current Sources

1. Assign mesh currents to the meshes. Assume mesh current flows clockwise.






2.Apply KVL