Circuit theory - Resistor function for dynamic non linear circuits

In summary, The conversation discusses Theorem 2 in a paper about dynamic non-linear circuit analysis. The theorem presents sufficient conditions for the existence of a network's "Resistor function," but the paper also mentions that conditions 1-3 are necessary. However, the speaker believes that this is incorrect and that only the first condition is necessary. They provide an example of a counterexample to support their belief. They seek input on this matter.
  • #1
cianfa72
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TL;DR Summary
About necessary conditions for the existence of "Resistor function" for a generic dynamic non linear network
Hi,

I'm reading the following paper (L. Chua) about the state-of-art of dynamic non linear circuit analysis -- Chua_Dynamic_Circuits

I've a doubt about Theorem 2 on section 3.2 On the Existence of the Resistor Function that establishes sufficient conditions for the existence of network "Resistor function". In the rest of the paper it is said that conditions 1-3 of Theorem 2 are actually necessary for the existence of the resistor function.

I believe it is incorrect because, as mentioned before in the paper, we can build counterexamples to show that is not the case (take for instance an a-dynamic non linear "resistor" having an i-v voltage-controlled characteristic described by a Lipschitz function). Actually the necessary condition should be just the first one.

What do you think about ?
 
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  • #2
Any help ? thanks
 

1. What is a resistor and how does it function in a circuit?

A resistor is an electronic component that limits the flow of current in a circuit. It is typically made of a material that offers resistance to the flow of electrons, such as carbon or metal. This resistance is measured in ohms (Ω) and is used to control the amount of current flowing through a circuit.

2. How do resistors behave in dynamic non-linear circuits?

In dynamic non-linear circuits, resistors do not behave in a linear manner as they do in simple circuits. This means that the relationship between voltage and current is not constant, and the resistance of the resistor may change depending on the current flowing through it. This can cause non-linear effects in the circuit, such as distortion or oscillation.

3. What factors affect the function of a resistor in a dynamic non-linear circuit?

The function of a resistor in a dynamic non-linear circuit can be affected by several factors, including the material and composition of the resistor, the amount of current flowing through it, and the temperature of the resistor. These factors can cause changes in the resistance and alter the behavior of the resistor in the circuit.

4. How do you calculate the resistance of a dynamic non-linear circuit?

Calculating the resistance of a dynamic non-linear circuit can be more complex than in a simple circuit, as it may vary depending on the current. In general, the resistance can be calculated by dividing the voltage across the resistor by the current flowing through it. However, this may not give an accurate representation of the resistance in a dynamic non-linear circuit.

5. How can the function of a resistor be optimized in a dynamic non-linear circuit?

To optimize the function of a resistor in a dynamic non-linear circuit, it is important to carefully select the type and value of the resistor based on the specific circuit requirements. Additionally, using multiple resistors in series or parallel can help to achieve the desired resistance and minimize non-linear effects. Simulation and testing can also be used to fine-tune the function of the resistor in the circuit.

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