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)