NonlinearResistor Icon

`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:

\[i = \begin{cases} Gb(v + Ve) - Ga Ve & \text{if } v < -Ve \\ Ga v & \text{if } -Ve \le v \le Ve \\ Gb(v - Ve) + Ga Ve & \text{if } v > Ve \end{cases}\]

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

OnePort

Usage

NonlinearResistor(Ga, Gb, Ve)

Parameters:

Name	Description	Units
`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

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

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 \\
# Ga v & \text{if } -Ve \le v \le Ve \\
# Gb(v - Ve) + Ga Ve & \text{if } v > Ve
# \end{cases}
# ```
#
# 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 = if (v<-Ve) then (Gb*(v+Ve)-Ga*Ve) else if (v>Ve) then (Gb*(v-Ve)+Ga*Ve) else Ga*v
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 \\
# Ga v & \text{if } -Ve \le v \le Ve \\
# Gb(v - Ve) + Ga Ve & \text{if } v > Ve
# \end{cases}
# ```
#
# 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 = if (v<-Ve) then (Gb*(v+Ve)-Ga*Ve) else if (v>Ve) then (Gb*(v-Ve)+Ga*Ve) else Ga*v
metadata {}
end

Test Cases

No test cases defined.

Examples
Experiments
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