Electrical Engineering ⇒ Topic : Thevenins Theorem with sinusoidal excitations

Thevenin's Theorem 

Thevenin's theorem gives us a method for simplifying a given circuit. The Thevenin equivalent form of any complex impedance circuit consists of an equivalent voltage source V_Th, and an equivalent impedance Z_Th, arranged as shown in Fig. (a). The values of equivalent voltage and impedance depend on the values in the original circuit.

Though the Thevenin equivalent circuit is not the same as its original circuit, the output voltage and output current are the same in both cases. Here, the Thevenin voltage is equal to the open circuit voltage across the output terminals, and impedance is equal to the impedance seen into the network across the output terminals.

    Consider the circuit shown in Fig.(b).

Thevenin equivalent for the circuit shown in Fig.(b) between points A and B is found as follows.The voltage across points A and B is the Thevenin equivalent voltage. In the circuit shown in Fig. (b), the voltage across A and B is the same as the voltage across Z₂ because there is no current through Z₃.

                                                                           figure (a)

                                                                            figure (b)

The impedance between points A and B with the source replaced by short circuit is the Thevenin equivalent impedance. In Fig. (b), the impedance from A to B is Z₃ in series with the parallel combination of Z₁ and Z₂.

The Thevenin equivalent circuit is shown in Fig. (c).

Thevenin's theorem is especially useful in analyzing power systems and other circuits where load resistance/impedance is subject to change, and re-calculation of the circuit is necessary with each trial value of load resistance, to determine voltage across it and current through it. Many circuits are only linear over a certain range of values, thus Thevenin's equivalent is valid only within this linear range and may not be valid outside the range. The Thevenin's equivalent has an equivalent I-V characteristic only from the point of view of the load. Since power is not linearly dependent on voltage or current, the power dissipation of the Thevenin's equivalent is not identical to the power dissipation of the real system

                                                            figure (c)