Thevenin equivalent of a network

[bishshoy007]

Homework Statement

The question is to find the Thevenin equivalent of the network across the terminals a,b.
The circuit is as follows:--

The solution is Z_th = 12.166 angle(136.3*)ohm and V_th = 7.35 angle(72.9*)
I can find out the V_th, that's easy. But I can get the Z_th right coz there is the dependent source. Please help ! I have tried almost 50 times, with different methods.

Homework Equations

The two basic laws (comon everyone knows this):--

Kirchoffs' Voltage law = sum of voltages in a loop = 0
Kirchoffs' node law = sum of current through a node = 0

The Attempt at a Solution

First I have lumped all series reactances.
At node 1 :--
5 + 0.2V₀ = -V₀/(8+4j)
Solving V₀ = -16.22 - 2.7j

Now writing the KVL for the loop :--
V_th + V₀ - (4 - 2j)*0.2-V₀ = 0
Solving we get V_th = 2.16 + 7.027j = 7.35 angle(72.89*)

For the Z_th I have tried solving by adding a dummy current source at the terminals a,b. It didnt work. Then i tried adding a voltage source across the (8 + 4j) impdedance. Still I couldn't get the answer correct.

 

[CEL]

You can calculate the Norton current In.
Zth = Vth/In.

 

[bishshoy007]

Yes I haven't tried that. But still I would like to have the thevenin voltage. Any mind helping me, with the solution.

 

[CEL]

There is a typo in the equation of the loop, otherwise it is correct. I have not checked your calculations.

The equation should be

Vth + Vo - (4-2j)*0.2*Vo = 0

You have posted:

Vth + Vo - (4-2j)*0.2-Vo = 0

 

[bishshoy007]

Thanks buddy. It works like a charm.