Superposition Theorem:
- The principle of superposition is applicable only for linear systems.
- A linear element is one that satisfies the principle of superposition and homogeneity.
- The excitation is the current, and the response is the voltage v, When the element is subjected to a current i1, it provides a response v1, furthermore, when the element is subjected to a current i2, it provides a response v2.
- If the principle of superposition is true, then the excitation i1 + i2 must produce a response v1 + v2.
- If the element is subjected to an excitation ki where k is a constant multiplier, then if principle of homogeneity is true, the response of the element must be kv.
- The statement of the Theorem states that:
In any linear circuit containing multiple independent sources, the current or voltage at any point in the network may be calculated as algebraic sum of the individual contributions of each source acting alone.
- When determining the contribution due to a particular independent source, we disable all the remaining independent sources.
- That is, all the remaining voltage sources are made zero by replacing them with short circuits, and all remaining current sources are made zero by replacing
them with open circuits. - It cannot be used to determine power because power is a nonlinear function i.e. Power is proportional to square of current or voltage.
- While applying for AC, all the multiple sources should have same frequency.
Thevenin Theorem:
- The main objective of Thevenin theorem is to reduce some portion of a circuit to an equivalent source and a single element.
- This reduced equivalent circuit connected to the remaining part of the circuit will allow us to find the desired current or voltage.
- The Thevenin theorem may be stated as follows:
The current flowing through a load resistance RL connected across any two terminals A and B of a linear, active bilateral network is given by Voc/(Ri+RL) where Voc is the open circuit voltage (i.e. voltage across the two terminals when RL is removed) and Ri is the internal resistance of the network as viewed back into the open circuited network from terminals A and B with all voltage sources replaced by their internal resistance (if any) and current sources by infinite resistance.
Norton theorem:
- An American engineer, E.L. Norton at Bell Telephone Laboratories, proposed a theorem similar to Thevenin theorem.
- Norton theorem states that:
A linear two terminal network can be replaced by an equivalent circuit consisting of a current source iN in parallel with resistor RN , where iN is the short circuit current through the terminals and RN is the input or equivalent resistance at the terminals when the independent sources are turned off.
If you do not wish to turn off the independent sources, then RN is the ratio of open circuit voltage to short circuit current at the terminal pair.
Maximum Power Transfer Theorem:
The maximum power transfer theorem states that the maximum power delivered by a source represented by its Thevenin equivalent circuit is attained when the load RL is equal to the Thevenin resistance Rt.
- This theorem can be applied for AC circuits also.
- Maximum average power can be delivered to Load if Load Resistance is complex conjugate of Thevenin equivalent.
Millman’s Theorem:
- It can be stated either in terms of voltage sources or current sources or both.
- This Theorem is a combination of Thevenin and Norton theorems.
- It is used for finding the common voltage across any network which contains a number of parallel voltage sources as shown in Figure.
Millman theorem states that if n number of generators having generated emfs E1, E2,… En and internal impedances Z1, Z2, … Zn are connected in parallel, then the emfs and impedances can be combined to give a single equivalent emf of E with an internal impedance of equivalent value Z.
