Thermal Time Constant

Formula

Description

The thermal time constant determines how quickly a component heats up or cools down, analogous to the RC electrical time constant. It equals the product of thermal capacitance (the ability to store heat) and thermal resistance (the opposition to heat flow). After one time constant, the temperature reaches 63.2% of its final steady-state value. Small components with low thermal mass (SMD resistors, small ICs) heat up in milliseconds, while large heatsinks may take minutes to reach thermal equilibrium. This is important for analyzing transient thermal behavior during power pulses.

Variables

• τ — Thermal time constant (s)
• Cth — Thermal capacitance (J/°C)
• Rth — Thermal resistance (°C/W)

Practical Notes

Thermal capacitance depends on mass and specific heat: Cth = m × cp. Copper has cp = 385 J/(kg·°C), aluminum 900 J/(kg·°C), silicon 700 J/(kg·°C). A TO-220 package has τ ≈ 1-5 seconds. An SOT-23 package has τ ≈ 10-50 ms. Transient thermal impedance curves in datasheets show how junction temperature evolves during power pulses.