Negative Resistance

Symbol

Information

A negative resistance component exhibits an inverse voltage-current relationship compared to conventional resistors. Instead of an increase in voltage causing an increase in current, a negative resistor decreases current as voltage increases in certain operating ranges.

The model follows a piecewise-defined conductance function, where the behavior changes based on a threshold voltage (Ve).

The mathematical formulation is:

\[\begin{split}I = \begin{cases} G_b \cdot (V + V_e) - G_a \cdot V_e, & \text{if } V < -V_e \\ G_b \cdot (V - V_e) + G_a \cdot V_e, & \text{if } V > V_e \\ G_a \cdot V, & \text{otherwise} \end{cases}\end{split}\]

Where:

\(I\) is the current through the negative resistance (A)
\(V\) is the voltage across the component (V)
\(G_b\), \(G_a\) are conductance multipliers (1/Ω)
\(V_e\) is the threshold voltage (V)

Ports

p: Positive terminal
n: Negative terminal

Model

The Negative Resistance model represents a nonlinear voltage-dependent conductance.

The current-voltage relationship depends on a threshold voltage (Ve), beyond which different conductance multipliers (Ga, Gb) define the current response.

Attributes:

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

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

Gb (param): Conductance multiplier in 1/Ω, default is -1.0.

Ga (param): Conductance multiplier in 1/Ω, default is -1.0.

Ve (param): Threshold voltage (V), default is 1.0V.

Methods:

analog(): Implements the piecewise function governing the current behavior.

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

class NegativeResistance(model):
    """
    Negative Resistance Model
    Implements a voltage-dependent conductance with nonlinear behavior.
    """

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

        # Parameter declarations
        self.Gb = param(-1.0, '1/Ω', 'Conductance multiplier')
        self.Ga = param(-1.0, '1/Ω', 'Conductance multiplier')
        self.Ve = param(1.0, 'V', 'Voltage')

    def analog(self):
        """Defines the current-voltage relationship for negative resistance."""
        if self.V < -self.Ve:
            self.I += self.Gb * (self.V + self.Ve) - self.Ga * self.Ve
        elif self.V > self.Ve:
            self.I += self.Gb * (self.V - self.Ve) + self.Ga * self.Ve
        else:
            self.I += self.Ga * self.V

Command syntax

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

# Import the model
from pyams.models import NegativeResistance

# Rneg: is the name of the Negative Resistance instance
# p, n: The connection points in the circuit
Rneg = NegativeResistance(p, n)