THEVENIN EQUIVALENT CIRCUITS WITH DEPENDENT SOURCES

Thevenin's Equivalent circuits with dependent sources

Procedures in Solving Thevenin's Theorem with dependent sources:

1. Determine Vth the usual way

2. Determine Zth

3. Remove all independent sources

4. Place an assumed value of voltage at the open circuit

5. Determine the current supplied by the assumed voltage source

6. Solve for the Zth using the formula where Zth=Vo/Io

Example:

Find the thevenin equivalent of the circuit in the figure below as seen from therminals a-b.

To find Vth we apply KCL at node 1 in the figure below

15=Io+ O.5Io  => Io=10A

Applying KVL to the loop on the right-hand side in the figure above we obtain

-Io(2-j4)+0.5Io(4+j3) + Vth=0

or

Vth=10(2-j4) - 5(4+j3) = -j55

Vth= 55angle -90 V

To Obtain Zth, we remove the independent source. Due to the presence of the dependent current source, we connect a 3-A current source (3 is an arbitrary value chosen for convenience here, a number divisible by the sum of currents leaving the node) to terminals a-b as shown in figure b at the node, KCL gives

3=Io+0.5Io  =>  Io=2A

Applying KVL to the outer loop in figure b gives

Vs=Io(4+j3+2-j4)=2(6-j)

The Thevenin impedance is

Zth= Vs/Is =2(6-j)/3 =4-j0.6667 ohms