Trapezoid Current

Symbol

Information

A Trapezoidal Wave Current Source generates a current signal with a linear rise and fall, forming a trapezoidal waveform.

\[\begin{split}I(t) = \begin{cases} I_0 + I_{off}, & t \leq T_d \\ \frac{(I_1 - I_0)}{T_r} \cdot t + I_0 + I_{off}, & 0 \leq t \leq T_r \\ I_1 + I_{off}, & T_r \leq t \leq T_r + T_w \\ \frac{(I_0 - I_1)}{T_f} \cdot (t - T_r - T_w) + I_1 + I_{off}, & T_r + T_w \leq t \leq T_r + T_w + T_f \\ I_0 + I_{off}, & t > T_r + T_w + T_f \end{cases}\end{split}\]

Where:

• \(I_0\): Initial current

• \(I_1\): Peak current

• \(T_d\): Initial delay time

• \(T_r\): Rise time

• \(T_w\): Pulse width (high duration)

• \(T_f\): Fall time

• \(T\): Total period of the waveform

• \(I_{off}\): Offset current

Ports

• p: Positive terminal

• n: Negative terminal

Model

The TrapezoidCurrent model generates a trapezoidal current signal.

This model is useful for PWM-controlled current sources, transient simulations, and power electronics analysis.

Attributes:

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

• I0 (param): Initial current, default is 1 A.

• I1 (param): Peak current, default is 1 A.

• Td (param): Initial delay time, default is 0 sec.

• Tr (param): Rise time, default is 0 sec.

• Tw (param): Pulse-width (high duration), default is 0.05 sec.

• Tf (param): Fall time, default is 0 sec.

• T (param): Total period of the waveform, default is 0.1 sec.

• Ioff (param): Offset current, default is 0 A.

Methods:

analog(): Implements the trapezoidal current equation.

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

 # Trapezoidal Current Source Model
 class TrapezoidCurrent(model):
   """
   This class models a Trapezoidal Waveform Current Source.
   """

   def __init__(self, p, n):
       # Signal declaration
       self.I = signal('out', current, p, n)

       # Parameter declarations
       self.I0 = param(1.0, 'A', 'Initial current')
       self.I1 = param(1.0, 'A', 'Peak current')
       self.Td = param(0, 'Sec', 'Initial delay time')
       self.Tr = param(0, 'Sec', 'Rise time')
       self.Tw = param(0.05, 'Sec', 'Pulse-width')
       self.Tf = param(0, 'Sec', 'Fall time')
       self.T = param(0.1, 'Sec', 'Total period of the waveform')
       self.Ioff = param(0.0, 'A', 'Offset current')

   def analog(self):
       """Defines the trapezoidal waveform equation for current output."""
       t = time  # Get current simulation time

       # Before initial delay
       if t <= self.Td:
           self.I += self.I0 + self.Ioff
           return

       # Time within the current cycle
       cycle_time = (t - self.Td) % self.T

       # Rising edge: 0 → Tr
       if cycle_time <= self.Tr:
           slope = (self.I1 - self.I0) / self.Tr
           self.I += slope * cycle_time + self.I0 + self.Ioff

       # High state: Tr → (Tr + Tw)
       elif cycle_time <= (self.Tr + self.Tw):
           self.I += self.I1 + self.Ioff

       # Falling edge: (Tr + Tw) → (Tr + Tw + Tf)
       elif cycle_time <= (self.Tr + self.Tw + self.Tf):
           slope = (self.I0 - self.I1) / self.Tf
           self.I += slope * (cycle_time - self.Tr - self.Tw) + self.I1 + self.Ioff

       # Low state: After (Tr + Tw + Tf)
       else:
           self.I += self.I0 + self.Ioff

Command syntax

The syntax for defining a trapezoidal current source in a PyAMS simulation:

# Import the model
from pyams.models import TrapezoidCurrent

# Iname: is the name of the current source instance
# a, b: The connection points in the circuit
Iname = TrapezoidCurrent(a, b)