Different Types Of Network Analysis Theorems, Definition

Hello guys, welcome back to my blog. In this article, I will discuss the different types of network analysis theorems such as thevenin’s theorem, superposition theorem, Norton’s theorem, maximum power transfer theorem, reciprocity theorem, compensation theorem, millman’s theorem, Tellegen’s theorem, substitution theorem, miller’s theorem, etc.

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Network Analysis Theorems

01. Thevenin’s Theorem

It states that any linear network can be represented with an equivalent network that consists of only one voltage source in series with a resistor which is called “thevenin’s” equivalent circuit. The linear circuit may consist of independent sources or dependent sources or resistors.

The voltage source which will be present in Thevenin’s equivalent source is called “Thevenin’s voltage” and the resistor is called Thevenin’s equivalent resistor.

Steps in order to find the thevenin’s equivalent circuit

Modify the given circuit diagram by opening the terminals for which the Thevenin’s equivalent circuit is to be found.
Find the Thevenin’s voltage, Vth across the open terminals of the given circuit.
Then find the Thevenin’s resistance across the open terminals by eliminating the independent sources present in it.
At last draw Thevenin’s equivalent circuit by connecting Vth in series with Rth.

02. Superposition Theorem

This theorem helps to determine the current and voltage is present in a circuit that has multiple sources. It states that “ in any linear network which will be having a number of voltage or current sources and resistance, the current through any branch of the network is algebraic sum of the currents due to individual sources when acting independently.” This term can be used for both AC and DC circuits.

03. Norton’s Theorem

Norton theorem states that “in an any linear network which contains several energy sources and resistances can be replaced by only one constant current source in parallel with resistor”. This is similar to Thevenin’s theorem but here equivalent current values are determined.

04. Maximum Power Transfer Theorem

This theorem will explain the condition for the maximum power transfer to load under different circuit conditions. This theorem states that “ the power transfer by a source to a load will be maximum in a network when the load resistance is equal to the internal resistance of the source”. For AC circuits the load impendence must match with the source impedance for maximum power transfer, even if a load of operates at different power factors.

The maximum power transfer can be observed when thevenin’s resistance is equal to the load resistance. The best example of this theorem includes an audio system where the resistance of the speaker must be matched with an audio power amplifier to obtain maximum output.

05. Reciprocity Theorem

This theorem states that “ in any linear network the excitation source and its corresponding response can be interchanged”.

06. Compensation Theorem

In a bilateral active network if the amount of impedances is changed from given value to some other value, which carries a current of I. Then the resulting changes which occur in other branches are same as those that have been caused by the injection of the voltage source in the modified branch with a negative sign and changed impendence product.

07. Millman’s Theorem

It states that when any number of voltage sources with finite internal resistance is operating in parallel, will be replaced with a single voltage source in series with an equivalent impedance.

08. Tellegen’s Theorem

This theorem states that “the summation of instantaneous power in the circuit with n number of branches will be 0. This theorem is applicable to linear, non-linear network, passive, or active or hysteric or non-hysteric networks.

09. Substitution Theorem

This theorem states that any branch in the network will be substituted by a different branch without any disturbance to the current and voltage in entire network provided with a new branch that has the same set of terminal voltages and current similar to the original branch. It can be used in both linear and non-linear circuits.

10. Miller’s Theorem

This theorem states that “ in a linear circuit if a branch exists with impedance Z Which will be connected between 2 Nodes with the nodal voltages and this branch will be replaced by two branches, connecting the corresponding nodes to the ground by two impedances. It is a tool for designing modified additional electronic circuits by impedance.

These are the different network analysis theorems in circuit. I hope this article “network analysis theorems” may help you all a lot. Thank you for reading.

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