NETWORK THEOREMS

1. Superposition Theorem

The current through, or voltage across, an element in a network is equal to the algebraic sum of the currents or voltages produced independently by each source.

2. Thevenin’s Theorem

Any two-terminal dc network can be replaced by an equivalent circuit consisting of a voltage source and a series resistor.

3. Norton’s Theorem

Any two-terminal linear bilateral dc network can be replaced by an equivalent circuit consisting of a current and a parallel resistor

4. Maximum Power Transfer Theorem

A load will receive maximum power from a network when its total resistive value is exactly equal to the Thevenin resistance of the network applied to the load.  That is, R_L = R_Th

5. Millman’s Theorem

Any number of parallel voltage sources or series current sources can be reduced to one.

6. Substitution (or) Compensation Theorem

If the voltage across and the current through any branch of a dc bilateral network is known, this branch can be replaced by any combination of elements that will maintain the same voltage across and current through the chosen branch.

7. Reciprocity Theorem

The reciprocity theorem is applicable only to single-source networks and states the following:

                The current I in any branch of a network, due to a single voltage source E anywhere in the network, will equal the current through the branch in which the source was originally located if the source is placed in the branch in which the current I was originally measured.

 The location of the voltage source and the resulting current may be interchanged without a change in current. (Or)

For any linear bilateral passive network the ratio of response to excitation is constant even if response and excitation are interchanged.

8. Tellegan’s theorem

                In a network if KVL and KCL are satisfied then total power in the network is zero.

9. Miller’s theorem

                If there exists a branch with impedance Z, connecting two nodes with nodal voltages ­V₁ and V₂, we can replace this branch by two branches connecting the corresponding nodes to ground by impedances respectively Z/(1 − K) and KZ/(K − 1), where K = V₂/V₁.