NDSU
December 31, 2012
Thevenin Equivalent with Dependent Sources
The trick with finding an Thevenin equivalent circuit is to apply the same test to the Thevenin equivalent and the
original circuit. The results should be the same.
If you have a dependent source, the Thevenin resistance can be difficult to find. In that case, it sometimes helps to
Apply a 1V input and measure the current, or
Apply a 1A input and measure the voltage.
For example, find the Thevenin equivalent for the following circuit:
2k
Rth
Vout
Ib
1V
+
-
5k
30k
200Ib
1k
Vth
+
-
Recall that since the two circuits are equivalent, any test you run on the circuit to the right to find Rth and Vth
should generate the same results as the circuit on the left.
Let's start with the open-circuit voltage. To find Vth for the circuit to the right, open up the output and measure the
voltage. This open-circuit voltage will be Vth. Do the same thing to the circuit on the left.
There is only one unknown voltage (at Vout), so you need to solve one equation for one unknown. Summing the
current from Vout to zero gives:
 V out −1V  − 200  1V−V out  +  V out  = 0
 2k 
 2k   1k 
Note that -200Ib is used rather than +200Ib since I'm summing the current from the node.
This results in
V out = 0.9901V
This is the open-circuit voltage, so it's also the Thevenin equivalent voltage.
Next, let's find the Thevenin resistance. If you turn off the voltage and current sources, the dependent current
source is still there. It's not obvious what the resistance looking in is.
So, let's apply a 1V source at the output and compute the current the circuit takes. The resistance will then be
determined from V = IR.
NDSU
December 31, 2012
2k
I1
I3
I2
Ib
0V
+
-
30k
5k
200Ib
1k
Iin
+
-
1V
(test voltage)
The current from the 1V source is
I in = I 1 + I 2 + I 3
1V 
 1V   1V 
I in =  2kΩ
 + 200  2kΩ  +  3kΩ 
Note that the middle term has a double negative. Ib = -I1. I2 = -200Ib. The net is I2 = +200I1.
I in = 0.1008A
A 1V source results in 0.1008A, meaning the resistance looking in is
V = IR
R=
V
I
=
1V
0.1008A
= 9.917Ω
The above circuit has the following Thevening equivalent:
9.917
0.9901V
+
-