Thevenins Theorem

Any combination of sinusoidal AC sources and impedances with two terminals can be replaced by a single voltage source e and a single series impedance z. The value of e is the open circuit voltage at the terminals, and the value of z is e divided by the current with the terminals short circuited. In this case, that impedance evaluation involves a series-parallel combination.

Using Thévenin's Theorem is especially advantageous when:

· we want to concentrate on a specific portion of a circuit. The rest of the circuit can be replaced by a simple Thévenin equivalent.

· we have to study the circuit with different load values at the terminals. Using the Thévenin equivalent we can avoid having to analyze the complex original circuit each time. 

We can calculate the Thévenin equivalent circuit in two steps:

1. Calculate ZTh. Set all sources to zero (replace voltage sources by short circuits and current sources by open circuits) and then find the total impedance between the two terminals.

2. Calculate VTh. Find the open circuit voltage between the terminals. 

Z1 = 2 + j3 

Z2 = z1 // -j

Zth = Z2 // 5+j4

Zth= 0.523 - j1.27 

Vth = ? 

= 5+j4 // -j 

Z1=0.147-j1.088

Vth = Z1 // 2+j3

Vth = -1.07 - j1.58V 

      

V_TH = -1.07 - j1.58 V = 1.91∠124° V; Z_TH =  0.523 - j1.27 W = 1.38∠-67.7° W