Network theorems

NETWORK THEOREMS

There are many theorems available for analysing d.c and a.c circuits this theorems help us to apply the fundamental network theorems to variety of dc and ac networks.so this chapter will explaining the superposition,thevnin ,Norton,maximum power transfer and reciprocity theorems.

superposition theorem:

This theorems applicable for linear and bilateral network.

so what is linear and bilateral theorems...
linear network:

a circuit parameters i.e.element like resistances, inductance and capacitance's are always constant irrespective of the change in time, voltage temperature etc..,is known as linear network.the ohm's law can be applied to such network.the mathematical equations of such network can be obtained by using the law of superposition.

Bilateral network:

A circuit characteristics behaviour is same irrespective of the direction of current through various elements of it is called bilateral network.best ex. of this network is resistance  .

statement of superposition theorem:

If the internal impedances of the sources are the unknown the independent voltage sources must be replaced by short circuit while the independent current sources must be replaced by an open circuit.

If the dependent current and voltage sources present in the circuit then such dependent sources should not replaced by open and short circuit and must be kept as it is.

This type of theorem is also known superposition principle.

applying superposition theorem step by step procedure:

step-1:
First you should select in which single sources acting alone for this circuit.

from this circuit having two voltage sources i.e B1and B2.then I want to select the B1 sources. so voltage source B2 is getting short and current sources is open if present in the circuit.

 let us considered 7v is short circuit.

step-2

Find the current through the or the voltage across the required element,due to the source under the consideration using a suitable network simplification technique.

let us cosidered the 7v considered.so 28v voltage sources getting short.

step 3:

Repeat the above two steps for all the sources.

step 4:

add all the individual effects produced by individual sources,obtain the total current in or voltage across the element.

Thevnin theorem:

Any combination of linear bilateral circuits elements and active sources regardless of the connection or complexity,connected to a given in load ZL  . The vth is the open circuit voltage is measured at the two terminals of interest with load impedance ZL is removed.This voltage is called thevnin equivalent voltage.

The Zeq equivalent impedance of the given network as viewed through the terminals wher ZL is connected with ZL is removed and all the active sources replaced by internal impedance.

If the internal impedance are not known the independent voltage sources are to be replaced by short circuit while the independent current sources must be replaced by open circuit.

steps to applying thevnin's theorems:

step 1

remove the branch impedance through which current is required to be calculated.

step 2

calculated the voltage across these open circuit terminals by using any of the network simplification techniques.this voltage is thevnin's equivalent voltage Vth.

step 3

calculated the equivalent impedance Zeq as viewed through the two terminals of the branch which current is to be calculated by removing that branch impedance and replacing all the independent sources by their internal impedance.

step 4

draw the thevnin's equivalent showing the voltage soruces Vth with the impedance Zeq in series with it,across the terminals of the branch through in which current is to be calculated.reconnected the branch impedance now.let it ZL

the required current through the branch is given by 

                          I=Vth/(ZL+Zeq)

after conversion of thevnins theorem,