Thevenin equivalent circuit with dependent source

In summary: Shorting the output simplifies the circuit because you know the current going through the output (and the load). Without shorting the output, you would have to find the current through each component, which is difficult.
  • #1
bnosam
148
0

Homework Statement


http://oi57.tinypic.com/263tqvr.jpg

I decided to try using mesh currents for thisFirst mesh is IA, second IB, third, ICSo I have the equations

IA = 500 μA

1310 IB + 100(IA - IB) = - 4*10-5V2

IC = -80IBAre these equations correct so far? I get the feeling they're not
 
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  • #2
Your second equation is not right given the current directions in the components in the loop. Consider the directions of the potential drops caused by each current in the components.

You should define your objective before starting to write equations. What is the goal of solving your loop equations? Are you heading for the Thevenin voltage or Thevenin resistance at this point?
 
  • #3
I'm solving for voltage at this point so I can find the thevenin voltage.

For the second equation would it be:

1310 IB + 100(IB - IA) = -4*10-5 V2

Or did you mean I have the sign for V2 wrong
 
  • #4
bnosam said:
I'm solving for voltage at this point so I can find the thevenin voltage.

For the second equation would it be:

1310 IB + 100(IB - IA) = -4*10-5 V2

Or did you mean I have the sign for V2 wrong
No, your equation looks okay now. I was worried about the sign of the term for for the 100 Ω resistor. Keep going :)
 
  • #5
1410 IB - 5000*10-6 = -4*10-5

So now I need an equation for V2:

(-80IB )*(50000)
= -4 000 000 IBso i plug it into the equation:

1410 IB - 5000*10-6 = -4*10-5 *(4 000 000 IB)

IB = 4*10-6 I

Does my conclusion so far seem correct?

I appreciate your help :)
 
Last edited:
  • #6
bnosam said:
1410 IB - 5000*10-6 = -4*10-5
You seem to have lost an order of magnitude in the second term: 100 x 500 x 10-6 = 5 x 10-2 = 1/20 . You also dropped the v2 on the right hand side.
So now I need an equation for V2:

(-80IB )*(50000)
= -4 000 000 IB
Okay. Fix your second term above and re-solve.
 
  • #7
1410 IB - 50000*10-6 = -4*10-5 V2

V2 = (-80IB)(50000 Ω)

so IB = 4 * 10-5
 
  • #8
bnosam said:
1410 IB - 50000*10-6 = -4*10-5 V2

V2 = (-80IB)(50000 Ω)

so IB = 4 * 10-5
Looks good. So What's v2?
 
  • #9
V2 = - 160V
 
  • #10
bnosam said:
V2 = - 160V
Also looks good.

Now, how are you going to approach the Thevenin resistance?
 
  • #11
gneill said:
Also looks good.

Now, how are you going to approach the Thevenin resistance?
Hook up a test charge on the outside of the circuit to find that out?
 
  • #12
bnosam said:
Hook up a test charge on the outside of the circuit to find that out?
You mean a voltage source? Yes, I suppose that would work.

I have another suggestion though. Do you know the way Thevenin and Norton models are related? If you could determine the short circuit current (at the output) fairly easily, would that help?
 
  • #13
gneill said:
You mean a voltage source? Yes, I suppose that would work.

I have another suggestion though. Do you know the way Thevenin and Norton models are related? If you could determine the short circuit current (at the output) fairly easily, would that help?
Before dependent sources, the only way I've been shown how to do it was just by combining resistors. Then I was shown this whole Etest/Itest method and I have no idea how to grasp it really. I've had one example of it.
 
  • #14
Okay, very briefly:
The Thevenin and Norton resistances for a given circuit have the same value. The Norton current is the current that flows when the output is shorted. The Thevenin voltage is the open circuit voltage at the output. You should be able to show, using simple Norton and Thevenin models, that the Thevenin (or Norton) resistance is given by Vth/IN. That is, the open circuit voltage divided by the short circuit current.

You have already determined the open circuit voltage. If you can find the short circuit current then you'll be in good shape. How does shorting the output simplify the circuit?
 

Related to Thevenin equivalent circuit with dependent source

1. What is a Thevenin equivalent circuit with a dependent source?

A Thevenin equivalent circuit with a dependent source is a simplified representation of a complex circuit that contains a dependent source (such as a voltage-controlled voltage source or current-controlled current source). It is used to model the behavior of the original circuit and is often used in circuit analysis and design.

2. How is the Thevenin equivalent circuit with a dependent source calculated?

The Thevenin equivalent circuit with a dependent source is calculated by first finding the open-circuit voltage (VOC) and the short-circuit current (ISC) of the original circuit. Then, the equivalent voltage source (VTH) is equal to VOC and the equivalent resistance (RTH) is equal to VOC/ISC. The dependent source is then incorporated into the equivalent circuit using its controlling variable (such as a voltage or current).

3. What are the advantages of using a Thevenin equivalent circuit with a dependent source?

Using a Thevenin equivalent circuit with a dependent source can simplify complex circuits and make them easier to analyze and design. It also allows for the use of standard circuit analysis techniques, such as Ohm's law and Kirchhoff's laws. Additionally, it can provide insight into the behavior of the original circuit and help identify potential issues or improvements.

4. Can a Thevenin equivalent circuit with a dependent source be used for any type of circuit?

Yes, a Thevenin equivalent circuit with a dependent source can be used for any type of circuit, as long as it contains a dependent source. This includes circuits with resistors, capacitors, inductors, and other components. However, the resulting equivalent circuit may not always accurately model the behavior of the original circuit, so it is important to carefully consider the assumptions and limitations of the Thevenin equivalent circuit.

5. How can a Thevenin equivalent circuit with a dependent source be verified?

The validity of a Thevenin equivalent circuit with a dependent source can be verified by comparing its predictions to the behavior of the original circuit. This can be done by simulating the circuits using software or by performing experiments on physical circuits. If the results match closely, then the equivalent circuit can be considered valid for the given range of values of the dependent source's controlling variable.

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