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How to compute capacitor lifetime in Python using UliEngineering

You can easily compute the expected lifetime of an electrolytic capacitor using the UliEngineering Python library:

capacitor_lifetime.py
from UliEngineering.Electronics.Capacitors import capacitor_lifetime

# Compute lifetime at 85°C for capacitor rated 2000h at 105°C
lifetime = capacitor_lifetime(2000.0, 105.0, 85.0)
print(f"Lifetime at 85°C (2000h@105°C): {lifetime:.0f} hours")

# Compute lifetime at 70°C for capacitor rated 2000h at 105°C
lifetime = capacitor_lifetime(2000.0, 105.0, 70.0)
print(f"Lifetime at 70°C (2000h@105°C): {lifetime:.0f} hours")

Example output

capacitor_lifetime_output.txt
Lifetime at 85°C (2000h@105°C): 8000 hours
Lifetime at 70°C (2000h@105°C): 32000 hours

The capacitor lifetime calculation estimates the expected operating life of an electrolytic capacitor based on its rated lifetime at a reference temperature and the actual operating temperature. This is essential for reliability engineering, determining maintenance intervals, and ensuring system longevity in power supply and filter applications.

capacitor lifetime plot.svg

The lifetime is computed using the Arrhenius-based formula: $L = L_0 \times 2^{\frac{T_0 - T}{10}}$, where $L$ is the lifetime at operating temperature $T$, $L_0$ is the rated lifetime at reference temperature $T_0$, and temperatures are in Celsius. This rule-of-thumb shows that capacitor lifetime approximately doubles for every 10°C decrease in operating temperature.

The plot above shows capacitor lifetime versus operating temperature on a logarithmic scale for a capacitor rated 2000 hours at 105°C. Notice the dramatic increase in lifetime as temperature decreases - a capacitor that lasts 2000 hours at 105°C will last approximately 8000 hours at 85°C and 32000 hours at 70°C. This demonstrates why proper cooling and temperature management are critical for capacitor reliability.

Plot generation script

plot_capacitor_lifetime.py
#!/usr/bin/env python3
import matplotlib.pyplot as plt
import numpy as np
import sys
sys.path.insert(0, '/home/uli/dev/UliEngineering')

from UliEngineering.Electronics.Capacitors import capacitor_lifetime

# Temperature range for plotting
T = np.linspace(40, 105, 100)  # 40°C to 105°C

# Create plot
plt.figure(figsize=(10, 6))

# Calculate lifetime for capacitor rated 2000h at 105°C
L0 = 2000.0  # Rated lifetime at reference temperature
T0 = 105.0  # Reference temperature

# Calculate lifetime using Arrhenius formula: L = L0 * 2^((T0 - T)/10)
L = L0 * 2 ** ((T0 - T) / 10)

plt.plot(T, L, color='blue', linewidth=2)
plt.xlabel('Operating Temperature (°C)', fontsize=12)
plt.ylabel('Lifetime (hours)', fontsize=12)
plt.title('Capacitor Lifetime vs Temperature (Rated 2000h at 105°C)', fontsize=14, fontweight='bold')
plt.grid(True, alpha=0.3)
plt.yscale('log')  # Log scale due to exponential relationship

# Mark reference temperature
plt.axvline(x=T0, color='red', linestyle='--', linewidth=2, label=f'Rated temperature ({T0}°C)')
plt.legend(loc='upper right', fontsize=10)

plt.tight_layout()
plt.savefig('capacitor_lifetime_plot.svg', format='svg', dpi=300)
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