NonlinearResistor

A nonlinear resistor with a piecewise-linear current-voltage characteristic, commonly known as Chua's Resistor.

This component models a voltage-controlled nonlinear resistor where the current i is a function of the voltage v across its terminals. The current-voltage relationship is piecewise-linear, defined by three distinct regions: For voltages within the range [-Ve, Ve], the resistor has a conductance Ga. For voltages outside this range (v > Ve or v < -Ve), the resistor exhibits a different conductance Gb for the portion of the voltage exceeding +/-Ve. The mathematical relationship is:

$$i=\{\begin{array}{ll}Gb(v+Ve)-GaVe& \text{if }v<-Ve\\ Gav& \text{if }-Ve\le v\le Ve\\ Gb(v-Ve)+GaVe& \text{if }v>Ve\end{array}$$

This behavior is characteristic of the nonlinear resistor element in Chua's circuit.

This component extends from OnePort

Usage

ElectricalComponents.NonlinearResistor(Ga, Gb, Ve)

Parameters:

Name	Description	Units	Default value
Ga	Conductance in the central region (-Ve <= v <= Ve).	S
Gb	Conductance in the outer regions (v < -Ve or v > Ve).	S
Ve	Breakpoint voltage defining the boundaries of the different conductance regions.	V

Connectors

• p - This connector represents an electrical pin with voltage and current as the potential and flow variables, respectively. (Pin)

• n - This connector represents an electrical pin with voltage and current as the potential and flow variables, respectively. (Pin)

Variables

Name	Description	Units
v	Voltage across the component (between pin p and pin n).	V
i	Current flowing through the component (from pin p to pin n).	A

Behavior

$$\begin{array}{rl}v\left(t\right)& =\mathtt{p}\mathtt{.}\mathtt{v}\left(t\right)-\mathtt{n}\mathtt{.}\mathtt{v}\left(t\right)\\ i\left(t\right)& =\mathtt{p}\mathtt{.}\mathtt{i}\left(t\right)\\ \mathtt{n}\mathtt{.}\mathtt{i}\left(t\right)+\mathtt{p}\mathtt{.}\mathtt{i}\left(t\right)& =0\\ i\left(t\right)& =ifelse(v\left(t\right)<-\mathtt{Ve},-\mathtt{Ga}\mathtt{Ve}+\mathtt{Gb}(\mathtt{Ve}+v\left(t\right)),ifelse(v\left(t\right)>\mathtt{Ve},\mathtt{Ga}\mathtt{Ve}+\mathtt{Gb}(-\mathtt{Ve}+v\left(t\right)),\mathtt{Ga}v\left(t\right)))\end{array}$$

Source

"""
A nonlinear resistor with a piecewise-linear current-voltage characteristic, commonly known as Chua's Resistor.

This component models a voltage-controlled nonlinear resistor where the current `i` is a function of the voltage `v` across its terminals.
The current-voltage relationship is piecewise-linear, defined by three distinct regions:
For voltages within the range `[-Ve, Ve]`, the resistor has a conductance `Ga`.
For voltages outside this range (`v > Ve` or `v < -Ve`), the resistor exhibits a different conductance `Gb` for the portion of the voltage exceeding `+/-Ve`.
The mathematical relationship is:

math i = \begin{cases} Gb(v + Ve) - Ga Ve & \text{if } v < -Ve MarkdownAST.LineBreak()

Ga v & \text{if } -Ve \le v \le Ve MarkdownAST.LineBreak()

Gb(v - Ve) + Ga Ve & \text{if } v > Ve \end

This behavior is characteristic of the nonlinear resistor element in Chua's circuit.
"""
component NonlinearResistor
  extends OnePort
  "Conductance in the central region (`-Ve <= v <= Ve`)."
  parameter Ga::Conductance
  "Conductance in the outer regions (`v < -Ve` or `v > Ve`)."
  parameter Gb::Conductance
  "Breakpoint voltage defining the boundaries of the different conductance regions."
  parameter Ve::Voltage
relations
  i = ifelse(v < -Ve, Gb * (v + Ve) - Ga * Ve, ifelse(v > Ve, Gb * (v - Ve) + Ga * Ve, Ga * v))
metadata {
  "Dyad": {
    "labels": [{"label": "$(instance)", "x": 500, "y": 1100, "rot": 0}],
    "icons": {"default": "dyad://ElectricalComponents/NonlinearResistor.svg"}
  }
}
end

Flattened Source

"""
A nonlinear resistor with a piecewise-linear current-voltage characteristic, commonly known as Chua's Resistor.

This component models a voltage-controlled nonlinear resistor where the current `i` is a function of the voltage `v` across its terminals.
The current-voltage relationship is piecewise-linear, defined by three distinct regions:
For voltages within the range `[-Ve, Ve]`, the resistor has a conductance `Ga`.
For voltages outside this range (`v > Ve` or `v < -Ve`), the resistor exhibits a different conductance `Gb` for the portion of the voltage exceeding `+/-Ve`.
The mathematical relationship is:

math i = \begin{cases} Gb(v + Ve) - Ga Ve & \text{if } v < -Ve MarkdownAST.LineBreak()

Ga v & \text{if } -Ve \le v \le Ve MarkdownAST.LineBreak()

Gb(v - Ve) + Ga Ve & \text{if } v > Ve \end

This behavior is characteristic of the nonlinear resistor element in Chua's circuit.
"""
component NonlinearResistor
  "Positive electrical pin."
  p = Pin() {
    "Dyad": {
      "placement": {"icon": {"iconName": "pos", "x1": -50, "y1": 450, "x2": 50, "y2": 550}}
    }
  }
  "Negative electrical pin."
  n = Pin() {
    "Dyad": {
      "placement": {"icon": {"iconName": "neg", "x1": 950, "y1": 450, "x2": 1050, "y2": 550}}
    }
  }
  "Voltage across the component (between pin p and pin n)."
  variable v::Voltage
  "Current flowing through the component (from pin p to pin n)."
  variable i::Current
  "Conductance in the central region (`-Ve <= v <= Ve`)."
  parameter Ga::Conductance
  "Conductance in the outer regions (`v < -Ve` or `v > Ve`)."
  parameter Gb::Conductance
  "Breakpoint voltage defining the boundaries of the different conductance regions."
  parameter Ve::Voltage
relations
  v = p.v - n.v
  i = p.i
  p.i + n.i = 0
  i = ifelse(v < -Ve, Gb * (v + Ve) - Ga * Ve, ifelse(v > Ve, Gb * (v - Ve) + Ga * Ve, Ga * v))
metadata {
  "Dyad": {
    "labels": [{"label": "$(instance)", "x": 500, "y": 1100, "rot": 0}],
    "icons": {"default": "dyad://ElectricalComponents/NonlinearResistor.svg"}
  }
}
end

Test Cases

No test cases defined.

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