The topic of network theorems is an essential part of circuit analysis. There are many theorems, and hence they have been divided into two groups, essential theorems and other theorems.
Network theorems are useful in simplifying analysis of some circuits. But the more useful aspect of network theorems is the insight it provides into the properties and behaviour of circuits.
Mesh analysis and nodal analysis are general techniques of analysis. They can be called as the universal techniques within the context of circuit analysis. On the other hand, the network theorems are not as versatile, but the merit of theorems is in the insight they offer into the behaviour and properties of circuits.
Theorems have been into two groups, essential theorems and other theorems. Superposition theorem, Thevenin's theorem, Norton's Theorem, maximum power transfer theorem and Tellegen's theorem are considered to be essential theorems, and there are five more theorems in the other group. It is to be noted that grouping of theorems is somewhat arbitrary.
Superposition theorem is the foremost among the theorems, since the entire analysis of linear circuits is founded on principle of superposition. It is not normally easy or handy to use superposition theorem to analyze circuits. But it defines what constitutes a linear circuit. The page on superposition theorem is detailed and explains this theorem and its application in depth.
This theorem is the most popular among theorems. Its proof is based on superposition theorem. It is widely used, especially to analyze electronic circuits. The insight this theorem offers is important. This theorem states that a linear circuit containing independent sources, dependent sources and passive elements can be replaced by a model containing a voltage source and an equivalent resistance. The page on Thevenin's theorem is detailed, containing quite a few worked examples.
This theorem is the dual of Thevenin's theorem. This theorem states that a linear circuit containing independent sources, dependent sources and passive elements can be replaced by a model containing a current source and an equivalent resistance.
This theorem enables us to find the condition for maximum power transfer to the load. The application of this theorem to dc circuits is considered here. We shall study later how this theorem can be applied to ac circuits. This theorem has limited scope, as explained in the page on this theorem.
The last theorem in the group of essential theorems is Tellegen's theorem. This theorem results from the Kirchoffs Laws. We had a brief look at this theorem in the earlier lecture on Kirchoffs laws. We will re-visit this topic again. This theorem is useful in verifying the solution of a problem. Verification of solution is important, and most of the solutions will contain a section called the verification.
The first theorem from the other group to be considered is the Reciprocity Theorem. This theorem reveals one of the important properties of passive network. When the topic of two-port networks is described, we will see how this theorem applies to different descriptions of two port networks.
The second theorem to be considered is the Compensation Theorem. This theorem is useful to study the behavior of circuits when there is an incremental change in the value of a component.
The third theorem to be considered is the Substitution Theorem. This theorem states that it is valid to replace one component by another type of component. It is useful in some problems. It will be stated when we make use of this theorem.
The fourth theorem to be considered is Millers Theorem. This theorem is useful for applying to electronic circuits that have a gain.
The fifth theorem to be considered is Millmans Theorem. This theorem is not well known and is not mentioned in many text books. This theorem is useful for a particular type of circuits. It is worth learning this theorem. We use nodal analysis for application of this theorem.
The list of theorems described has been stated in this page. Detailed description of each of these theorems is provided in the relevant page.