Network Theorems

Superposition theorem

In a network of linear circuit having more than one source, the current which flows at any point is algebraic/phasor sum of all currents which would flow at that point if each source was considered separately and all other sources are replaced by their internal impedances. The Superposition theorem cannot be applied to an electric circuit with a non linear resistance.

Thevenin's Theorem

Thevenin's theorem states that it is possible to simplify any linear circuit having multiple resistances and voltage sources to single voltage sources in series with the equivalent resistance of the circuit connected across the load no matter how complex is the circuit. The advantage of Thevenin's theorem is that it makes the solution of the complicated circuits quite easy.

Norton's Theorem

It is similar to that of Thevenin's theorem. It states that it is possible to simplify any linear complex circuit having numerous number of source and resistances to a single current source with equivalent resistance of the circuit connected in parallel across the load.

Maximum Power Transfer theorem

A resistive load, served through a resistive network, will abstract maximum power when the load resistance value is the same as the resistance, "viewed by the load as it looks back into the network."

Millman's theorem

Millman's theorem is the combination of Thevenin's and Norton's theorem. It states that number of voltage or current source can be combined into a single voltage or current source. The circuits having only two terminals point between which any number of parallel branches may be connected can be easily simplified by using this theorem.

Tellegen's theorem

According to this theorem the summation of instantaneous powers for the n-branches in an electric network is always zero. If there are n elements in any network; i₁,i₂,i₃...i_n are respective instantaneous currents flowing through these elements satisfying Kirchhoff's current law and v₁,v₂,v₃....v_n are the respective instantaneous voltages across these elements satisfying Kirchhoff's voltage law, then

where v_k is the instantaneous voltage across k_th element and i_k is the instantaneous current flowing through this element. This theorem is applicable to a very general class of lumped networks composed of elements that are linear or non linear, active or passive, time invariant or variant.

Note:- This are just introduction to this theorem and their statements, they will be described in detail in upcoming post.