Note
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Tunnel-diode oscillator
The negative resistance of the tunnel diode amplifies small voltages and damps large ones, so a tiny initial voltage grows into a self-sustained oscillation of fixed amplitude, the limit cycle of the van der Pol oscillator.
The model is created by name from the catalog with L = C = 1, alpha = gamma = 1, and the initial voltage 0.1, and
runs for 50 time units. The default blueprint shows the voltage and the current in one time series view.
import matplotlib.pyplot as plt
import numpy as np
from skcomplex.engine.runtime import Simulation
from skcomplex.engine.viz import RerunObserver
from skcomplex.models import create
MODEL = 'tunnel_diode_oscillator'
system = create(MODEL)
observer = RerunObserver(MODEL, save_path=f'{MODEL}.rrd', blueprint='default', interval=4)
simulation = Simulation(system, dt=0.05, observers=[observer]).check().prepare().run(until=50)
Open the recording in the Rerun viewer
One limit cycle
Runs started inside and outside should all converge on one closed orbit, whose voltage amplitude is close to
2 sqrt(alpha / (3 gamma)) = 1.15 for a weak nonlinearity and grows towards 2 as alpha becomes large.
fig, ax = plt.subplots(figsize=(6, 5))
for V0, i0 in [(0.1, 0.0), (2.0, 1.0), (-1.5, -1.5), (0.0, 2.5)]:
run = Simulation(create(MODEL, V=V0, i=i0), dt=0.05).check().prepare().run(until=50).trajectory_
ax.plot(run.values('circuit.V'), run.values('circuit.i'), linewidth=0.8)
ax.plot(V0, i0, 'o', color='gray', markersize=4)
trajectory = simulation.trajectory_
amplitude = np.abs(trajectory.values('circuit.V')[trajectory.times > 30]).max()
for side in (-1, 1):
ax.axvline(side * 2 * np.sqrt(1 / 3), color='black', linestyle='--', linewidth=0.8)
ax.set_xlabel('voltage V')
ax.set_ylabel('current i')
ax.set_title(f'Limit cycle of amplitude {amplitude:.2f}')
plt.show()
About the model
A tunnel-diode oscillator: an inductor and a capacitor in parallel with a negative-resistance diode.
References
- van der Pol 1926
- Trzaska 2023
Total running time of the script: ( 0 minutes 1.095 seconds)
Download Python source code: plot_tunnel_diode_oscillator.py
Download Jupyter notebook: plot_tunnel_diode_oscillator.ipynb