Capacitor with initial voltage

Symbol

Information

A capacitor is a passive electrical component that stores electrical energy in an electric field. The current flowing through a capacitor is proportional to the rate of change of voltage across it:

\[I = C \cdot \frac{dV}{dt}\]

This model also accounts for an initial charge (Ic), meaning the capacitor can start with a predefined voltage at time t=0.

Where:

• \(I\) is the current through the capacitor (Amperes)

• \(V\) is the voltage across the capacitor (Volts)

• \(C\) is the capacitance (Farads, F)

• \(t\) is time (seconds)

Ports

• p: Positive terminal

• n: Negative terminal

Symbol description

Field	Value
Symbol.name	CapacitorIc
Symbol.file	CapacitorIc.sym
Symbol.directory	Basic
Symbol.referance	C
Model.name	CapacitorIc
Model.file	CapacitorIC.py

Model

The CapacitorIc model simulates a capacitor with an initial charge.

This model represents a capacitor where the current is proportional to the rate of voltage change across it, also considering an initial charge.

Attributes:

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

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

• C (param): Capacitance value in Farads (F), default is 1.0 µF.

• Ic (param): Initial charge in Volts (V), default is 0V.

Methods:

analog(): Defines the capacitor behavior using the differential equation:

\[I = C \cdot \frac{dV}{dt}, \quad \text{for } V(0) = I_c\]

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

class CapacitorIc(model):
    """
    Capacitor model based on I = C * dV/dt with an initial charge.
    """

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

        # Parameter declarations
        self.C = param(1.0e-6, 'F', 'Capacitor value')
        self.Ic = param(0, 'V', 'Initial charge')

    def analog(self):
        """Defines the capacitor’s current-voltage relationship with initial charge"""
        self.I += self.C * ddt(self.V, self.Ic)

Command syntax

The syntax for defining a capacitor in a PyAMS simulation:

# Import the model
from pyams.models import CapacitorIc

# Cname: is the name of the capacitor instance
# p, n: The connection points in the circuit
Cname = CapacitorIc(p, n)