LC Oscillator Simulation

Overview

The circuit consists of an inductor (L1) and a capacitor (C1) forming an LC oscillator. The capacitor stores energy in an electrostatic field, producing a potential voltage across its plates, while the inductor stores energy in an electromagnetic field.

Initially, the capacitor is charged to Ic = 5V. When the capacitor discharges through the inductor, energy oscillates between the capacitor and the inductor, generating a sinusoidal waveform.

Oscillation Frequency

The resonant frequency of the LC circuit is given by:

\[f_r = \frac{1}{2\pi\sqrt{LC}}\]

For this simulation:

  • Resonant Frequency: fr = 0.5 Hz

  • Time Period: T = 2 s

Circuit Diagram

The LC oscillator circuit is illustrated in the following diagram:

LC Oscillator Circuit Diagram

Simulation Code

The following Python script simulates the LC oscillator using the PyAMS library:

from pyams.lib import circuit
from pyams.models import Inductor, CapacitorIc
from math import pi

# Define components
L1 = Inductor("out","0")
C1 = CapacitorIc("out","0")

# Set component values
L1.L += 1/pi
C1.C += 1/pi
C1.Ic += 5  # Initial capacitor charge

# Create circuit and add elements
circuit = circuit()
circuit.addElements({'L1': L1, 'C1': C1})

# Set output for plotting
circuit.setOutPuts("out")

# Perform transient analysis
circuit.analysis(mode="tran", start=0, stop=6, step=0.05)
circuit.run()
circuit.plot()

Simulation Output

The simulation generates the following sinusoidal waveform:

LC Oscillator Output Waveform

Conclusion

The LC oscillator generates an AC waveform due to the continuous exchange of energy between the inductor and capacitor. The PyAMS simulation verifies this behavior by producing a sinusoidal voltage output over time.