Total Pageviews

13/11/2011

Network Theorems

Superposition Theorem


The response in any element of linear, bilateral network containing more than one source is the sum of the response produced by the sources each acting independently.
The superposition principle is only applicable to linear networks and systems.
The superposition theorem does not apply to the power as power is proportional to square of the current which is not a linear function.
Steps:-
  1. Select a single source. Short the other voltage sources and open the current source, if internal impedance's are not known. If known than replace them by their internal impedance.
  2. Find out the current through or the voltage across the required element, due to the source under consideration.
  3. Repeat the above step for all the sources.
  4. Add all the individual effect produced by individual sources to obtain the total current in or voltage across the element.

Thevenin's Theorem

Any combination of linear bilateral circuit elements and active sources, regardless of the connection and complexity, connected to a given load Zmay be replaced by a single two terminal network consisting of a
Single voltage source of VTH and a single impedance Zeq in the series with the voltage source, across the two terminals of the load ZL.
Steps:-
1.       Remove the branch impedance, through which current is required to calculate.
2.       Calculate the voltage across the open circuited terminals. This voltage is Thevinin’s equivalent voltage VTH .
3.       Calculate the equivalent impedance Zeq as viewed through the two terminals of the branch from which current is to be calculated by removing that branch impedance and replacing all the independent sources by their internal impedance.
4.       The required current through the branch is given by, I = VTH / ZL + Zeq .

Norton’s Theorem

Any combination of linear bilateral circuit elements and active services regardless of the connection or complexity, connected to a given load ZL can be replaced by a simple two terminal network consisting of a single current source of IN and a single impedance Zeq in parallel with it, across the two terminals of the load ZL .
Steps:-
1.       Short the branch through which the current is to be calculated.
2.       Find out the current through this short circuited branch. This current is nothing but the Norton’s current IN.
3.       Calculate the equivalent impedance Zeq as viewed through the two terminals of interest by removing the branch impedance and making all the independent sources inacticve.
4.       The current through the branch of interest is  I = IN * Zeq / ZEQ + ZL.






No comments:

Post a Comment