Transient Thermal Impedance Calculator
Steady-state resistance is the wrong number for a pulsed load. Thermal mass rides out short pulses, so the peak junction temperature sits somewhere between the average-power rise and the full steady-state rise. This evaluates a Foster network, which is the form semiconductor datasheets publish their Zth curves in.
Choosing something to solve for makes Peak temperature rise an editable target and computes the chosen input from it.
Formula
| Ri, taui | resistance and time constant of Foster stage i |
| tp | pulse width (s) |
| T | repetition period (s) |
| Zth | transient thermal impedance (K/W) |
| D | duty cycle, tp/T |
What this model assumes, and where it stops
Assumptions
- A Foster network fitted to the datasheet Zth curve, driven by rectangular power pulses.
- Linear, temperature-independent thermal properties.
- Steady periodic state - the repetitive figure is the settled peak, not the first pulse.
- The reference temperature is held constant, whether that is case, board or ambient.
- Power is applied uniformly at the source with no internal distribution.
Limitations
- A Foster network is a curve fit, not a physical model. Its internal nodes have no physical meaning, you cannot break it apart to insert a heatsink partway, and it is only valid over the time range the curve was fitted to.
- Foster networks cannot be chained. Bolting a datasheet junction-to-case Foster network onto a heatsink Foster network gives a wrong answer; convert to a Cauer network first.
- Thermal conductivity and heat capacity both vary with temperature, and silicon conductivity falls as it heats, which this linear model does not capture.
- Real power pulses are not rectangular. A switching waveform with the same average and peak can produce a different junction temperature.
- The reference node is assumed fixed. If the heatsink itself heats up during a burst, the true peak is higher than this.
- Very short pulses probe the die itself, where the published Zth curve is often least accurate and most part-dependent.
When you need a 3D field solution instead
Closed-form models like the one above hold on idealised geometry. These are the cases where they stop being good enough and a full 3D electromagnetic and thermal solution is the only way to get a trustworthy answer:
- Anything where the reference temperature moves during the event, so the datasheet network no longer applies.
- Combining a device with its own mounting and heatsink, which needs a physical Cauer model rather than stacked Foster fits.
- Non-rectangular or irregular power profiles, such as a real switching or fault waveform.
- Several devices sharing a substrate, where their transients interact.
- Short-circuit and surge events, where temperature-dependent properties and local hot spots dominate.
Common questions
Why is the peak temperature lower than power times thermal resistance?
Because thermal mass rides out short pulses. The default case - 100 W pulses at 20% duty - peaks at 46% of the full steady-state rise: the impedance Zth at that pulse width, not the resistance Rth, is what the peak sees. Sizing a repetitive-pulse design on Rth alone can overestimate the peak by a factor of two or more.
What is the difference between single-pulse and repetitive Zth?
A single pulse starts from ambient, so only the pulse itself matters - the default case reaches 24% of the steady-state rise. A repetitive train ratchets upward until the average power sets a baseline and each pulse rides on top, landing at 46% here. Datasheet Zth charts plot exactly these two families; this page reproduces the calculation behind them from R and tau pairs.
When can I treat a pulsed load as DC?
When the pulse period is long against the dominant thermal time constant, each pulse reaches steady state and Rth is the right number. When the period is short against it, the device only sees the average power. The interesting - and dangerous - regime is in between, where neither simplification holds; that is the regime this calculator exists for.
References
- Foster & Cauer networks - Infineon AN2015-10, Thermal equivalent circuit models
- Incropera & DeWitt - Fundamentals of Heat and Mass Transfer, 6th ed., ch. 5 on transient conduction