Is there any algebraic proof for Thevenin's theorem?

[Benomatics]

Is there any algebraic proof for Thevenin's theorem?

 

[axmls]

Yes. Have you searched for it? https://en.wikipedia.org/wiki/Thévenin's_theorem

 

[Benomatics]

Wikipedia did not provide any algebraic proof, they only provided a statement and an examples, which is not clear

 

[anorlunda]

Wikipedia did not provide any algebraic proof, they only provided a statement and an examples, which is not clear

Yes, but the references in the Wikipedia article cite this

Johnson, D.H. (2003a). "Origins of the equivalent circuit concept: the voltage-source equivalent"(PDF).Proceedings of the IEEE91 (4): 636–640

http://www.ece.rice.edu/~dhj/paper1.pdf

 

[Benomatics]

I have checked that paper but there i can only see a statement of the theorem and a little introduction to what thevenin did then, though i they made reference to a circuit that proof the theorem, there is no algebraic or a more vigorous mathematical proof that shows that.

 

[meBigGuy]

http://www.ohio.edu/people/starzykj/network/Class/ee616/homework/equivalent%20circuits.pdf has a proof, but does not prove the superposition theorem.

https://www.quora.com/How-do-you-prove-Thevenins-theorem

http://nptel.ac.in/courses/108105053/pdf/L-08(GDR)(ET) ((EE)NPTEL).pdf section L8.5

Maybe think of it as a derivation rather than a proof.

 

[Benomatics]

I think that's a verification rather than a derivative, in a derivative you assume, you don't have to quote any part of the theorem until you completely derive it. However that was insightful, when i did derive it myself, i did not realize other people have verified it. and its only when you derive it that you will understand the shortcomings of the theorem, it will be very difficult to realize it when you only try verifying it. In verifying it i found out that only the voltage across the resistive circuit other than the equivalent circuit remains consistent with the original circuit, but the voltages across the resistors in the equivalent circuit, become inconsistent with the original circuit, hence for very complicated purely resistive circuits, it will be wrong to apply Thevenin, especially with circuits with more than 4 rows and colums of nodes

 

[NascentOxygen]

In verifying it i found out that only the voltage across the resistive circuit other than the equivalent circuit remains consistent with the original circuit, but the voltages across the resistors in the equivalent circuit, become inconsistent with the original circuit, hence for very complicated purely resistive circuits, it will be wrong to apply Thevenin, especially with circuits with more than 4 rows and colums of nodes

Are you saying you can devise a linear circuit to which Thévenin's Theorem does not apply?

 

[Benomatics]

Yes, i will upload it here as soon as i device it

 

[donpacino]

this should be interesting

 

[donpacino]

I think that's a verification rather than a derivative, in a derivative you assume, you don't have to quote any part of the theorem until you completely derive it. However that was insightful, when i did derive it myself, i did not realize other people have verified it. and its only when you derive it that you will understand the shortcomings of the theorem, it will be very difficult to realize it when you only try verifying it. In verifying it i found out that only the voltage across the resistive circuit other than the equivalent circuit remains consistent with the original circuit, but the voltages across the resistors in the equivalent circuit, become inconsistent with the original circuit, hence for very complicated purely resistive circuits, it will be wrong to apply Thevenin, especially with circuits with more than 4 rows and colums of nodes

the point of the thevenin circuit is that the load will see the same voltage and current. The voltage across the equivalent resistor means nothing

 

[anorlunda]

Interesting indeed. Can nonlinear behavior arise from linear components? I suspect not. But how to prove that is not obvious.

 

[meBigGuy]

It is impossible to create a 2 port network from fixed resistors, fixed voltage sources and fixed current sources that will not behave identically at the two ports as the thevenin equivalent for that network. Period. End of Issue.

but the voltages across the resistors in the equivalent circuit, become inconsistent with the original circuit,

Of course, because the circuit topology is different.

Comparing the behavior internally is irrelevant/meaningless. I'm not sure what you are even getting at with that. It only matters what happens at the two ports. Why do you care anything about the internal nodes?

 

[Benomatics]

I am not comparing it internally for no reason, you need to understand that by finding the equivalence circuit which is infact not equivalent to the actual circuit--it only tells you the equivalence of the circuit for a particular load--your new circuit would be misrepresenting the history of the circuit save one. It is best to explain a problem without including another problem. Imust say that at this point i must reveal the real purpose of this thread, i have been able to derive Thevenin's equation myself, by assuming i know nothing of it. I derived it using algebra and i published. The theorem might be useful but it actually assumes a false state to solve a problem. The other methods icluding Kirchoff solve circuit problems without assuming a false state. So many undergraduate studets find it hard to understand Thevenin, this is because if you present the equivalent circuit to me after applying Thevenin, i would find every other thing wrong except the load. The problem is find the voltage across a load. What you do is find another voltage inorder to get the voltage across the load, what you have done is create another problem, there was initially a voltage, hence it is almost irrelevant to find another one, Find the equivalent circuit for the problem below with R7 as the load below , i am sure you would opt for something else.

 

[anorlunda]

I think you misunderstand the meaning of equivalent. The equivalent behaves the same as the original only from the point of view of the two external terminals.

In power systems analysis, I can make you an equivalent of Canada as seen from two terminals in Niagara. There is no claim that it models everything inside Canada. (Joke about Canada omitted :-)

 

[Benomatics]

I very much understand the meaning of the equivalent, it only means an equivalent circuit for the same voltage across the load, like i said earlier on i have an algebraic derivation for it. If you also say it behaves the same way as the original i would say that statement is not clear as thevenin;s voltage only assumes the same propery of the original voltage across that particular load, everywhere else its just inconsistent. The above question is just a simple example that i think you should solve using thevenin, i am now trying to derive aa more complex circuit with two or more voltages which would prove inapplicable with thevenin. I think i should have given this thread a different title "Shortcomings of Thevenin;s theorem". I hope you understand me

 

[anorlunda]

There is no "everywhere else". It is meaningful only at the terminals.

 

[Jony130]

All Thevenin's and Norton's theorems amount to is that, for a linear circuit, the relationship between the voltage across any two points in the circuit and the current through those same two points (those two points are the "terminals") has a linear relationship that can be written as:

Vx = Vth - Ix*Req

This is the "load line" for the circuit between those two terminals.

But this is exactly the same relationship that you get if you replace the circuit with a voltage source with an output of Vth in series with a resistance of value Req -- so these two circuits are equivalent as far as what happens between the two terminals.

 

[Benomatics]

Tnk God you now understand me, i am infact not saying Thevenin is wrong, he was rigt on point with his specifics, but it not that thevenin helps you to find voltage across the load directly, it rather finds another voltage.

 

[donpacino]

Tnk God you now understand me, i am infact not saying Thevenin is wrong, he was rigt on point with his specifics, but it not that thevenin helps you to find voltage across the load directly, it rather finds another voltage.

thats not correct. It does find the voltage across the load.

 

[Benomatics]

Well you are not getting me, you can only find the voltage across the load after finding Vth but Vth does not represent the voltage across the load according to Thevenin and from my derivation.

 

[donpacino]

Well you are not getting me, you can only find the voltage across the load after finding Vth but Vth does not represent the voltage across the load according to Thevenin and from my derivation.

vth is not the voltage across the load.
vth is the voltage across the load and the equivalent series resistance

 

[Benomatics]

thts true, but i insist that Thevenin's theorem on face of it solves the problem, as you now have to deal with the "equivalence circuit" circuit and the load circuit in series but deep inside it distorts the actual state of the circuit, it deletes the history of the circuit save one. the equivalent circuit

 

[donpacino]

thts true, but i insist that Thevenin's theorem on face of it solves the problem, as you now have to deal with the "equivalence circuit" circuit and the load circuit in series but deep inside it distorts the actual state of the circuit, it deletes the history of the circuit save one. the equivalent circuit

yes. that's the entire point of the thevenin equivalent circuit. if you thought otherwise, maybe you would have been better served asking for a more detailed view of what the thevenin equivalent circuit is and how it is used, as opposed to asking for a detailed proof.

 

[Benomatics]

Well like i said, the title of this thread should have been "the shortcomings of thevenin;s theorem", in truth actually i have derived it myself, without using any quotation from thevenin at any point, but i really wanted to know what people think about Thevenin. And i would like you to solve that question i uploaded using Thevenin

 

[donpacino]

Well like i said, the title of this thread should have been "the shortcomings of thevenin;s theorem", in truth actually i have derived it myself, without using any quotation from thevenin at any point, but i really wanted to know what people think about Thevenin. And i would like you to solve that question i uploaded using Thevenin

finding the voltage across the load using thevenin would produce a result no different from the result by any other method.

 

[Benomatics]

Well if one kind find an equivalent circuit, it will certainly not provide a different answer across that load, but if you cannot then its not useful
but like i said try solving the problem using Thevenin

 

[The Electrician]

OK, here's the solution using Thevenin's theorem. First, remove R8 since it's shorted out anyway.

Remove R7, replace the voltage source V with a short, and calculate the equivalent resistance across the terminals where R7 was previously connected. This is just R3 in parallel with the other equivalent resistance around the loop below R3. This can all be done with simple series and parallel resistance formulas:

Now find the voltage across R3 using nodal analysis. The voltage source is given by V. We choose the left and right ends of R3 as our two nodes. Calculate the voltages there and take the difference to get the voltage across R3.

Now find the voltage across R7 using Rth and Vth in the usual way. R7 and Rth form a voltage divider so using the voltage divider formula, we get:

Now replace R7 in the original circuit and solve for the voltage across R7 with nodal analysis. We choose the left and right ends of R7 as our two nodes. Calculate the voltages there and take the difference to get the voltage across R7.

This is exactly the same thing we got using Thevenin's theorem.

QED.

 

[meBigGuy]

I'm going to say it again.

If you have a 2 terminal black box containing an arbitrary linear network and a 2 terminal black box containing the thevenin equiv. circuit, you could not tell which was which by measuring anything about the two terminals. The two terminals would behave EXACTLY the same for all arbitrary loads.

Do you completely accept the above?

What about that is ambiguous? In what way, from the 2 terminals, are the 2 boxes not exactly identical.

 

[meBigGuy]

Find the equivalent circuit for the problem below with R7 as the load below , i am sure you would opt for something else.

Draw the circuit as a 2 port network driving R7. Then, replace the two port network (not including R7) with the Thevenin Equivalent. You can thern set R7 to any value and the voltage and current will be the same in both circuits.

The thevenin equivalent seems like such a simple concept to me. Reduce any two port network to two components and it will behave exactly the same as the original circuit at ALL LOADS. Why are we having so much trouble talking about it.

You seem to think the thevenin equivalent can change with load. It cannot. One circuit must be exactly identical at ALL loads. The Thevenin equivalent is (MUST BE) computed without consideration of the load.

Is it possible that you are mistakenly trying to include the load resistor in the thevenin equivalent?

 

[Benomatics]

As i profread his solution to the circuit using Thevenin myself, i want to comment on your statement meBIgguy "you seem to think thevenin equivalent can change with load" Yes i think so if i change thel oad i am considering then i will have to devise a different equivalent circuit. An on your question, you thought wrongly, you can read my previous posts, i have never at anytime said the load was part of the equivalent circuit, i am not even saying obtainig the with Thevenin's voltage and Thevenin's resistance you are unable to find the voltage across the load, but i am saying it involves finding another voltage Vth from your original voltage. Y

 

[Benomatics]

Sorry i did not complete that, you might think i do not understand Thevenin's theorem, but infact i do and i have derived, it and if you wish to confirm, i have included the document in this post. Thevenin succesfully calculates the voltage across the load, though even for for more complex circuits you will rather opt for other theories. Technically Thevenin;s theorem creates another problem to solve a problem. Changing the circuit just to suit one particular load, but forgetting that you are at the same time rendering the other resistive components inconsistent in regards to properties with the original, for the solution to the problem, i willl get back to you on what i think about it, and i am preparing a different one this time with two or more voltage sources. However i am really enjoying the contribution here.Bye for now.

 

[Averagesupernova]

I didn't think Thevenin could be this irritating. Long long ago I had an instructor ask the class for several resistor values that we wanted to use in a network and a voltage for the voltage source. I don't remember what the network was in terms of arrangement but it doesn't matter. He drew this on the board and then drew several various load resistors that could be switched in. He asked the class to find the load current and voltage for each different load. We did. None of us had heard of Thevenin. In less than half the time it took us to solve for them he solved for all of them. The reason is he used Thevenin. He found the Thevenin voltage and Thevenin resistance and simply took the load and put in series with the Thevenin resistance and solved. The Thevenin voltage and resistance stayed the same for each different load. To be honest I haven't had a lot of use for it since then but I know the laws of physics haven't changed. It certainly does have its place though.
-

The theorem might be useful but it actually assumes a false state to solve a problem.

I suppose that is arguable but seriously we assume a lot of false states in engineering. As pointed out before, no one cares about what is going on inside the network, only at the port(s).

 

[donpacino]

Sorry i did not complete that, you might think i do not understand Thevenin's theorem, but infact i do and i have derived, it and if you wish to confirm, i have included the document in this post. Thevenin succesfully calculates the voltage across the load, though even for for more complex circuits you will rather opt for other theories. Technically Thevenin;s theorem creates another problem to solve a problem. Changing the circuit just to suit one particular load, but forgetting that you are at the same time rendering the other resistive components inconsistent in regards to properties with the original, for the solution to the problem, i willl get back to you on what i think about it, and i am preparing a different one this time with two or more voltage sources. However i am really enjoying the contribution here.Bye for now.

please see what me big guy said above... also thevenin is useful for evaluating how the load voltage ad current will change as the load changes.

 

[meBigGuy]

Thevenin turns out to be incredibly useful when you need a Thevenin Equivalent. Otherwise not so much.

I totally do not understand your fixation. Neither what you are fixated on, nor to what end. Thevenin is what it is.

Can you succinctly state your issue, and its practical application?

Changing the circuit just to suit one particular load, but forgetting that you are at the same time rendering the other resistive components inconsistent in regards to properties with the original, for the solution to the problem

I do not understand what you mean by this, nor its significance in a black boxed 2 port network. If you need the internal behavior to match some hidden goal, then Thevenin won't help. Exactly what are you trying to accomplish? You have not been unambiguous about your goals.

BTW: A more significant issue with a thevenin equivalent is that the temperature of the black box can be different between the original and the equivalent. That is why I have always said "behavior at the two ports" . That is all Thevenin is concerned with: "The behavior at the two ports". If you have other requirements, then you need some other solution. Your "other solution" will probably internally use Thevenin or some close derivative. But, WHO CARES?