Network Theorems

Thevenin’s theorem

Any linear electrical network containing only voltage sources, current sources and resistances can be replaced at terminals A-B by an equivalent combination of a voltage source in a series connection with a resistance .

• the voltage obtained at terminals A-B of the network with the terminals A-B open circuited.
• the resistance that the circuit between A-B terminals would have if all the current and voltage sources are set to to provide 0 currents or voltages.

Note

If the terminals are short-cuited, the current flowing from A to B is .

Norton’s theorem

In a network made of linear time-invariant resistances, voltage sources and current sources, at a pair of terminals, it can be replaced by a current source and a resistor connected in parallel.

In AC circuits, this theorem can be applied to reactive elements as well.

• the current flowing between the terminals as the terminals are short circuited
• where is the voltage between the terminals with no load

Finding the Thevenin Resistance directly

When there are no dependent sources in a circuit, Thevenin Resistance can be found directly by setting all the sources to be 0

• A voltage source set to 0 is equivalent to a short circuit.
• A current source set to 0 is equivalent ot a open circuit.

Superstition theorem

In a linear network with several independent sources, any voltage or current in the circuit can be found as the algebraic sum of the corresponding values obtained by assuming only one source at a time, with all the other sources turned off.

Reciprocity theorem

Bilateral network

A circuit whose characteristics are the same when the direction of current through various elements. In a linear passive bilateral network, an excitation and its response can be interchanged.

Compensation theorem

In a linear, bilateral network, any element can be replaced by a voltage source of magnitude equal to the current passing through the element multiplied by the value of the element.

Maximum Power Transfer theorem

For maximum active power to be delivered to the load, load impedance must correspond to the conjucate of the source impedance.

Millmann’s theorem

Suppose there are number of admittances which share a point and the other ends are open.

Equivalent Generator theorem

An extension of Millmann’s theorem. A system of voltage sources operating in parallel may be replaced by a single voltage source in series with an equivalent impedance. This is also Thevenin’s theorem applied to generators in parallel.

Rosen’s theorem

Used to convert star connected network to mesh equivalent. External conditions will not be affected.

When , the conversion becomes quite simple as mentioned in S1.