Nonlinear Resistance

Symbol

Information

A nonlinear resistor is an electrical component whose current-voltage (I-V) relationship deviates from Ohm’s Law. Unlike a standard resistor where I = V/R, the current in a nonlinear resistor follows a nonlinear function of voltage.

This model is defined by:

\[I = \mu \cdot V \cdot (V^2 - 1)\]

Where:

• \(I\) is the current through the nonlinear resistor (A)

• \(V\) is the voltage across the nonlinear resistor (V)

• \(\mu\) is a scalar nonlinearity factor

Ports

• p: Positive terminal

• n: Negative terminal

Model

The Nonlinear Resistance model represents a voltage-dependent resistance.

The resistor exhibits a nonlinear behavior, meaning the current response is not directly proportional to the applied voltage.

Attributes:

• V (signal): Input voltage signal, defined between nodes (p, n).

• I (signal): Output current signal, defined between nodes (p, n).

• µ (param): Nonlinearity scalar (dimensionless), default is 1.0.

Methods:

analog(): Implements the nonlinear current-voltage function.

from pyams.lib import model, signal, param
from pyams.lib import voltage, current

class NonlinearResistance(model):
    """
    Nonlinear Resistance Model
    Defines a resistor with a nonlinear current-voltage relationship.
    """

    def __init__(self, p, n):
        # Signal declarations
        self.V = signal('in', voltage, p, n)
        self.I = signal('out', current, p, n)

        # Parameter declarations
        self.µ = param(1.0, ' ', 'Scalar of nonlinearity')

    def analog(self):
        """Defines the nonlinear current-voltage relationship."""
        self.I += self.µ * self.V * (self.V * self.V - 1)

Command syntax

The syntax for defining a Nonlinear Resistance model in a PyAMS simulation:

# Import the model
from pyams.models import NonlinearResistance

# Rnonlin: is the name of the nonlinear resistance instance
# p, n: The connection points in the circuit
Rnonlin = NonlinearResistance(p, n)