Thevenin isolates nonlinear element

In summary, the conversation discusses finding the values for ##R_{TH}## and ##V_{TH}## in a circuit with resistors in parallel and a special element. The speaker is able to find ##R_{TH}## by treating the resistors as parallel, but is unsure how to find ##V_{TH}##. They suggest trying to find the overall current and using that to find the voltage, but this method does not yield the correct result. The other person notes that the result is also not dimensionally consistent and suggests breaking the circuit and finding the Thevenin equivalent to simplify the process.
  • #1
JessicaHelena
188
3
Homework Statement
If we want to study the behavior of a circuit with linear resistors, independent sources, and an unfamiliar, perhaps nonlinear, element, it is to our advantage to package up everything but the unfamiliar element into a Thevenin or Norton model, so we can concentrate on the interaction of this simply-characterized circuit with the unfamiliar element. For example, the circuit on the left of the diagram can be summarized, from the point of view of the unfamiliar element, by the circuit on the right. (Please refer to Fig 1.1)

Write the algebraic expressions for the Thevenin voltage and resistance.
Relevant Equations
V/I = R
I have no problem getting the ##R_{TH}## since from the special element's POV, the resistors are in parallel, and that's the answer.

However, I don't really understand how to get ##V_{TH}##.

Ignoring the special element, it seems that I have the resistors in series this time. But I'm not too sure how to move forward from there.
So going back to the resistors in parallel idea, I can get the overall current by doing ##i = V_s / R_{TH}##. Since the special element and ##R_p## are in parallel, multiplying ##i## by ##R_p## will give me the voltage, which gives me ##V_s(R_s + R_p)/(R_s R_p)##, which isn't quite right, apparently...
 

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  • #2
The equivalent voltage Vth is the voltage obtained at terminals A-B of the network with terminals A-B open in the original circuit. I note that your result is also not dimensionally consistent ( which is a crime where I live !)
 
  • #3
Note that ##R_p## and your mystery device are in parallel, so that you may swap their locations without altering the circuit.
1578761621945.png

Break the circuit where indicated and reduce what's to the left of the break to its Thevenin equivalent. You should be able to find the voltage A-B without too much difficulty :smile:
 
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1. What is Thevenin isolation in relation to nonlinear elements?

Thevenin isolation is a circuit analysis technique that simplifies a complex nonlinear element in a circuit into a linear equivalent circuit. This simplified circuit can then be used to analyze the behavior of the nonlinear element without changing the overall behavior of the circuit.

2. Why is Thevenin isolation important in circuit analysis?

Thevenin isolation is important because it allows us to analyze circuits with nonlinear elements using the familiar and well-understood principles of linear circuit analysis. This simplifies the process of circuit analysis and makes it easier to understand and design complex circuits.

3. How is Thevenin isolation performed?

Thevenin isolation is performed by first finding the Thevenin equivalent circuit of the entire circuit, which consists of a voltage source and a series resistance. Then, the nonlinear element is replaced with its linear equivalent, which is determined by measuring the voltage and current at the terminals of the nonlinear element under different operating conditions.

4. What are the limitations of Thevenin isolation?

Thevenin isolation is limited by the accuracy of the linear approximation of the nonlinear element. In some cases, the linear equivalent circuit may not accurately represent the behavior of the nonlinear element, leading to errors in the analysis. Additionally, Thevenin isolation is only applicable to circuits with a single nonlinear element.

5. Can Thevenin isolation be applied to all types of nonlinear elements?

No, Thevenin isolation is only applicable to certain types of nonlinear elements, such as diodes and transistors. It cannot be applied to nonlinear elements with complex or time-varying behaviors, such as capacitors and inductors. In these cases, other techniques, such as small-signal analysis, may be more suitable for circuit analysis.

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