SUPERPOSITION

WHAT IS SUPERPOSITION?

-is a another algorithm circuit analysis method, with a prescribed procedure, like the node voltage or loop current method

-it applies on;y in circuits with 2 or more independent sources.

The superposition procedure

1. make a partial circuit by choosing one source to keep and turning of all the other independent sources.

2. Solve this "partial circuit" for the quantities of interest. Use whatever techniques are applicable to the partial circuit.

3. Go back to the original and create another circuit by choosing another source to keep (different than the first one) and turning off all the other sources in the circuit.

4. Solve the second partial circuit for the quantities of interest.

5. Repeat the process until each independent source has been used in partial circuit

6. Sum up all the partial results to get total results for the quantities of interest 

If there are n independent sources in a circuit, then when using superposition, you would expect to solve n partial circuit and find n partial results for the whatever you are looking for 

Example of the superposition method

Consider the circuit below. It has one voltage source and one current source, and we are asked to find the voltage VR2.

1. Choose one source. It doesn't matter which, so start with the voltage source. Turn off the current source (make it open circuit) to create the first partial circuit.

2. Solve the partial circuit

3. Now turn off the voltage source (by using it out) and keeping the current source.

4. Solve the partial circuit

5. Sum the partial solution to get total solution:

     

MESH ANALYSIS

What is mesh analysis?

Branch
-This is a circuit elements that connected two nodes

Loop
-This a closed path in a circuit. A set of these loops are used to create constraint equations.


Mesh
-A loop passing though at least on branch
Basic rule: The sum of voltage around any loop must be Zero.(from KVL) 

Manual Mesh/Loop Analysis algorithm:

* Choose a conventional current flow

* Identify and Number Loops or meshes

* Apply KVL to identified mesh and formulate circuit equation

* Create Matrix system from KVL equation obtained

* Solve matrix for unknown Mesh Currents by using Cramer's rule

* Uses solved Mesh Currents to solve for the desired circuit entity

Example:

Consider this figure with the following Parameter:

V1 = 15 V

V2 = 7 V

R1 = 2

R2 = 20

R3 = 10

R4 = 5

R5 = 2

R6 = 2

Find current through R3 using mesh analysis method
solution:

-We can see that there are three closed paths (loop) where we can apply KVL in, Mesh 1,2 and 3 as shown in the figure
- We can now apply KVL around the Mesh remembering Passive Convention When defining Currents and Voltages 

WYE TO DELTA

WHAT IS DELTA-WYE?

DELTA -WYE - is a type of three phase electric power transformer design that employs delta-connected windings on its primary and wye/star connected windings on its secondary.

example:

to solve DELTA-WYE

to solve WYE-DELTA