# Thevenin equivalent with dependent current source

#### Connor Spangler 1

Joined Sep 8, 2015
6
Hello all! I'm trying to figure out how to determine the Thevenin equivalent of the following circuit:

I believe I know that R_th is 75Kohm, however my attempts at finding the voltage across the dependent source have been fruitless. The current going through the resistor is the same as the dependent source provides (correct?) however equating R1 in terms of v and the dependent source revealed nothing to me. Should I convert the source into a Norton equivalent instead? Thank you in advance!

#### WBahn

Joined Mar 31, 2012
27,412
Why do you think that R_th is 75 kΩ?

Remember that when dealing with circuit having dependent source, you can't just zero out the all the sources -- you can only zero out the independent sources.

So you have basically two options:

1) Turn off all the independent sources and the apply a test source to the output and determine the response. Use that to find R_th.

or

2) Determine the open circuit voltage and the short circuit current at the output and use those to determine R_th.

#### Connor Spangler 1

Joined Sep 8, 2015
6
Why do you think that R_th is 75 kΩ?
2) Determine the open circuit voltage and the short circuit current at the output and use those to determine R_th.
This is what I want to do and what I don't know how to do. How do I go about determining the voltage across the dependent source, thus finding Voc?

#### Connor Spangler 1

Joined Sep 8, 2015
6
Any help at all here?

#### Jony130

Joined Feb 17, 2009
5,419
Vs = V + Vth and you need to solve the circuit by using circuit analysis.

#### Connor Spangler 1

Joined Sep 8, 2015
6
Vs = V + Vth and you need to solve the circuit by using circuit analysis.
Thank you but I've worked out up to that point already. What I can't figure out how to do is solve for this system of 3 different unknowns. How do I get Vth across this dependent current source?

#### Jony130

Joined Feb 17, 2009
5,419
So you do not know Vs value ??

#### Connor Spangler 1

Joined Sep 8, 2015
6

#### Jony130

Joined Feb 17, 2009
5,419
But still you can symbolically solve this circuit.

#### Connor Spangler 1

Joined Sep 8, 2015
6
That's fine and all but I can't for the life of me figure out how.

#### Jony130

Joined Feb 17, 2009
5,419
Write KCL for the output node
I1 - I2 = 0
And
I1 = (Vs - Vth)/R1; and I2 = gm*(Vs - Vth)
So we have
(Vs - Vth)/R1 - gm*(Vs - Vth) = 0 And now solve for Vth.