Finding Thevenin Equiv for Circuit w/ R1, R2, R3, R4, R5

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In summary, the author is trying to find the thevenin equivalent for a circuit with parallel resistors and does not understand how to find the equivalent voltage source. The author then uses a simulation to calculate the equivalent resistance and finds that it is incorrect.
  • #1
DmytriE
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Hi All,

I am struggling to find the thevenin equivalent for the following circuit. I will leave out the values for the resistances because they don't really matter in this case. I'm looking for guidance on how to find the overall thevenin.

I know the R-Thevenin is the same as the R-equivalent for the circuit. So I approached the problem as I would to find the equivalent for any other circuit.

R1 is parallel with R2. So This new resistance would be (R1 * R2)/ (R1 + R2). Let's call this new resistance R12

This next part is where I get confused. I believe that R3, R12, and R5 are all in series with one another so you can add their resistances. and this new resistance would be in parallel with R4.

I then simulate the circuit using PSpice and I do not get the same answer as the simulation. Any help would be greatly appreciated!

https://docs.google.com/file/d/0B70IRvZhJgh0UDAxaWowN0tIYkU/edit?usp=sharing
 
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  • #2
I cannot access the shared circuit diagram I guess?
 
  • #3
Rudinhoob said:
I cannot access the shared circuit diagram I guess?

I have now fixed the problem. Everyone should be able to access it. Thanks for the heads up.
 
  • #4
Could you please show how your simulation and analytical solution differ?

Edit: Just a thought, but did you calculate the equivalent voltage source as well that's needed to form the complete Thévenin equivalent circuit?
 
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  • #5
Here are the values for each resistor:
R1: 5.6k, R2: 12k, R3: 2.2k, R4: 15k, R5: 1k
VDC: 12V

R1 || R2 = 3.818k
R3, R12, R5 are all in series: 7.018k
R3.12.5 || R4: 4.781k

https://docs.google.com/file/d/0B70IRvZhJgh0eTdxZ2ZVeS1aamc/edit?usp=sharing

RTh = Vin / I1
I1 = 935uA
RTh = 12V / 935uA = 12.830k

There is a discrepancy of approximately 2.5 - 3 times...
 
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  • #6
Very strange. You have done an admirable job of calculating the correct equivalent resistance (4.781K) and then for some reason you have ignored it and gone on to calculate an incorrect equivalent resistance. Why?
 
  • #7
If you want to use your simulation to check your calculation of the equivalent resistance then:

- The equivalent voltage, Vth, is equal to V_O when the output is an open circuit.

Thus Vth = 15e3*371.6e-6 V = 5.574 V.

- Rth = Vth/I_O when the output is a short circuit.

Thus, in your simulation, you need to short out R4 and measure the current through R3/R5. Vth divided by this current is your equivalent resistance.
 
  • #8
Thank you very much! I was having trouble understand how to find Vth. With your help and some help of my classmate I feel confident in finding VTh and RTh.
 

What is Thevenin's theorem and how does it apply to circuit analysis?

Thevenin's theorem is a technique used in circuit analysis to simplify complex circuits into equivalent circuits with a single voltage source and a single resistor. It states that any linear circuit can be reduced to a single voltage source and a single resistor connected in series, where the voltage source is called the Thevenin voltage and the resistor is called the Thevenin resistance.

What are the steps for finding the Thevenin equivalent for a circuit with multiple resistors (R1, R2, R3, R4, R5)?

The steps for finding the Thevenin equivalent for a circuit with multiple resistors are as follows:

  1. Disconnect all power sources in the circuit.
  2. Identify the load resistor (RL) and remove it from the circuit.
  3. Determine the open-circuit voltage (Voc) by finding the voltage across the load resistor terminals.
  4. Calculate the equivalent resistance (Req) of the circuit seen from the load resistor terminals by shorting all independent voltage sources and opening all independent current sources.
  5. The Thevenin voltage (Vth) is equal to the open-circuit voltage (Voc).
  6. The Thevenin resistance (Rth) is equal to the equivalent resistance (Req).

How do I calculate the Thevenin voltage and resistance for a circuit with dependent sources?

The process for calculating the Thevenin voltage and resistance for a circuit with dependent sources is the same as for a circuit with only independent sources. The only difference is that you must take into account the effects of the dependent sources when determining the open-circuit voltage and equivalent resistance. This can be done by using superposition or by applying the dependent source transformations.

What is the difference between Thevenin and Norton equivalents?

Thevenin and Norton equivalents are two different ways of representing a complex circuit with a single equivalent circuit. The main difference between them is that the Thevenin equivalent consists of a voltage source and a series resistor, while the Norton equivalent consists of a current source and a parallel resistor. They are mathematically equivalent and can be converted into one another using source transformations.

How do I use the Thevenin equivalent to analyze a circuit?

To use the Thevenin equivalent to analyze a circuit, you can replace the original circuit with the Thevenin equivalent circuit and then apply any circuit analysis techniques you are familiar with, such as Ohm's law, Kirchhoff's laws, or nodal and mesh analysis. This simplifies the circuit and makes it easier to calculate voltages, currents, and power dissipation in the circuit.

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