# Need help on finding the Thevenin resistance with dependent source in AC analysis

#### rogerloh4.0

Joined Sep 26, 2012
10
Determine the Thevenin equivalent of the circuit in the attachment as seen from the terminals a-b.

Answer: $$Z_{Th}$$ = 4.473$$\angle-7.64^{\circ}$$Ω, $$V_{Th}=29.4\angle72.9^{\circ}$$V

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#### WBahn

Joined Mar 31, 2012
26,398
Determine the Thevenin equivalent of the circuit in the attachment as seen from the terminals a-b.

Answer: $$Z_{Th}$$ = 4.473$$\angle-7.64^{\circ}$$Ω, $$V_{Th}=29.4\angle72.9^{\circ}$$V

Why couldn't you solve the resistance? We aren't mind readers. Unless you give us some idea of what the problem you were having was, we are forced to guess where you might have been going wrong. It's like calling up an auto mechanic and saying, "My car isn't working. What's wrong with it?"

If you think you did it right, then at least tell us what you got.

Better yet, simply do what the posting guidelines in the Sticky say and post/describe your efforts so far and where they have led you.

If I had to guess (and that's exactly what I'm doing), I would surmise that you are trying to find the equivalent impedance by turning off all the sources, including the dependent ones, and thus seeing all four components in series and coming up with Zo=(12+j2)Ω.

What you need to do is zero all *independent* sources, apply a test voltage to the output terminals and determine the resulting current (or apply a test current and determine the voltage). Take the ratio to find Zo.

#### rogerloh4.0

Joined Sep 26, 2012
10
Why couldn't you solve the resistance? We aren't mind readers. Unless you give us some idea of what the problem you were having was, we are forced to guess where you might have been going wrong. It's like calling up an auto mechanic and saying, "My car isn't working. What's wrong with it?"

If you think you did it right, then at least tell us what you got.

Better yet, simply do what the posting guidelines in the Sticky say and post/describe your efforts so far and where they have led you.

If I had to guess (and that's exactly what I'm doing), I would surmise that you are trying to find the equivalent impedance by turning off all the sources, including the dependent ones, and thus seeing all four components in series and coming up with Zo=(12+j2)Ω.

What you need to do is zero all *independent* sources, apply a test voltage to the output terminals and determine the resulting current (or apply a test current and determine the voltage). Take the ratio to find Zo.
Oops, sorry about that, I'll put my work down here.
I turned off all the independent sources and leave the dependent ones on. I connect an independent current source of 5A at the terminal a-b. When that current flows through the 8 ohm-resistor and j4 ohm-inductor the dependent source is turned on and puts another 0.2*5*(8+j4) A into the current. But that will increase the Vo, which will increase the current through the dependent source. This is where I get stuck. I also tried using node method too, changing the independent current source at the terminal to an independent voltage source of 5 volts, setting the node in the bottom of the graph to ground, which gives me the equation, Vo/(8+j4)+0.2Vo=0, which gives me the Vo to be -0.3+j(1/20), but that's not correct either.

This is what I have done so far. Although none of them seems to get me anywhere near the answer.

#### WBahn

Joined Mar 31, 2012
26,398
Oops, sorry about that, I'll put my work down here.
I turned off all the independent sources and leave the dependent ones on. I connect an independent current source of 5A at the terminal a-b. When that current flows through the 8 ohm-resistor and j4 ohm-inductor the dependent source is turned on and puts another 0.2*5*(8+j4) A into the current. But that will increase the Vo, which will increase the current through the dependent source. This is where I get stuck. I also tried using node method too, changing the independent current source at the terminal to an independent voltage source of 5 volts, setting the node in the bottom of the graph to ground, which gives me the equation, Vo/(8+j4)+0.2Vo=0, which gives me the Vo to be -0.3+j(1/20), but that's not correct either.

This is what I have done so far. Although none of them seems to get me anywhere near the answer.
But yet you were able to find Vth when there was a 20A current source in a slightly different place. Why do you think you were able to solve that but not with it removed and a 5A applied between a and b? To be sure, a minor change in topology can have a significant effect on how easy the analysis is, but see if you can figure out how the change is making it hard for you, and you might gain some insight.

Consider the following:

With your test current source installed, you basically have two current sources in parallel feeding a series circuit.

Q1) In terms of the combined currents of the two sources, what is Vo?

Q2) In terms of Vo, what is the combined current of the two sources?

Q3) Can the two equations above be combined so as to eliminate Vo?

Q4) With Q3 in mind, what is the voltage across the test current source?

Q5) What is the equivalent impedance?

In terms of the total current

#### rogerloh4.0

Joined Sep 26, 2012
10
Thanks for the advice, I'll keep that in mind and try to solve the problem again. Wish me luck!

#### rogerloh4.0

Joined Sep 26, 2012
10
But yet you were able to find Vth when there was a 20A current source in a slightly different place. Why do you think you were able to solve that but not with it removed and a 5A applied between a and b? To be sure, a minor change in topology can have a significant effect on how easy the analysis is, but see if you can figure out how the change is making it hard for you, and you might gain some insight.

Consider the following:

With your test current source installed, you basically have two current sources in parallel feeding a series circuit.

Q1) In terms of the combined currents of the two sources, what is Vo?

Q2) In terms of Vo, what is the combined current of the two sources?

Q3) Can the two equations above be combined so as to eliminate Vo?

Q4) With Q3 in mind, what is the voltage across the test current source?

Q5) What is the equivalent impedance?

In terms of the total current
I used your advice and got an equivalent impedance that's fairly close to the answer, although both angle and radius are off by 0.01. Thanks again!

#### WBahn

Joined Mar 31, 2012
26,398
I used your advice and got an equivalent impedance that's fairly close to the answer, although both angle and radius are off by 0.01. Thanks again!
Congratulations! The difference is almost certainly jusr roundoff error (yours and/or the author's).