Thevenin equivalent of a network

AI Thread Summary
The discussion revolves around finding the Thevenin equivalent of a circuit across terminals a and b, where the calculated Thevenin voltage (Vth) is 7.35 angle(72.9°) volts. The main challenge lies in determining the Thevenin impedance (Zth) due to the presence of a dependent source, which has led to multiple unsuccessful attempts by the poster. The poster initially used Kirchhoff's laws to derive the voltage but struggled with the impedance calculation, even after trying various methods, including adding dummy sources. A correction to the loop equation was provided, which helped resolve the issue with the calculations. The conversation highlights the importance of accurate equations in circuit analysis for obtaining correct results.
bishshoy007
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Homework Statement



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

The solution is Zth = 12.166 angle(136.3*)ohm and Vth = 7.35 angle(72.9*)
I can find out the Vth, that's easy. But I can get the Zth 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



k9yk9s.jpg

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 :--
Vth + V0 - (4 - 2j)*0.2-V0 = 0
Solving we get Vth = 2.16 + 7.027j = 7.35 angle(72.89*)

For the Zth 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.
 
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You can calculate the Norton current In.
Zth = Vth/In.
 
Yes I haven't tried that. But still I would like to have the thevenin voltage. Any mind helping me, with the solution.
 
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
 
Thanks buddy. It works like a charm.
 

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