Thermal Guide
Transient Thermal Design: Pulses, Duty Cycle, Thermal Impedance, and Validation
A pulsed device can pass an average-power check and still reach an excessive junction temperature during a burst. Track the heating history, the physical thermal path, and the model's time range.
17 min · Advanced · Updated October 16, 2026
Define the Pulse and the Temperature Node
Write down instantaneous real loss, pulse width, repetition interval, burst count, background power, and operating ambient. Specify whether the limit applies to junction, case, winding, PCB, heat sink, or enclosure. The Thermal Resistance & Temperature Rise Calculator gives the settled rise for a known path; it does not resolve a short pulse.
A MOSFET switching burst, motor startup, RF transmit duty cycle, and intermittent LED drive have different electrical loss profiles. Measure or model power at the device terminals before fitting thermal parameters. A current pulse is not automatically a constant-power pulse when voltage or resistance changes during the event.
One-Node Thermal RC Model
Formula reference
First-order thermal response
tau = Rtheta CthetaTss = Ta + P RthetaT(t) = Tss + (T0 - Tss) exp(-t/tau)At T0 = Ta: DeltaT(t) = P Rtheta [1 - exp(-t/tau)]Variable definitions
- Rtheta in K/W and Ctheta in J/K give tau in seconds
- Ta is the ambient or boundary temperature used for this model
- T0 is the temperature at the start of the power interval
- P is constant real heat input during the interval
The Thermal RC Time Constant Calculator computes a single heating or cooling interval, the time to a reachable target, and R or C from a required response. It is useful for a first pass when one thermal mass dominates over the time range of interest.
At one time constant a step has reached about 63.2% of its final change; at five, about 99.3%. This fraction applies to the change from the actual starting temperature toward the new steady state, not to absolute temperature.
Repeat Pulses Without Resetting Temperature
For a one-node model with pulse power P during ton and zero power during toff, define a = exp(-ton/tau) and b = exp(-toff/tau). If the temperature rise just before a pulse is xlow, the next peak is xhigh = P Rtheta + (xlow - P Rtheta)a. Cooling leaves the next xlow = b xhigh. At periodic steady state these two equations can be solved without simulating hundreds of cycles.
Formula reference
Periodic one-node rise above a fixed boundary
a = exp(-ton/tau); b = exp(-toff/tau)xpeak = P Rtheta (1 - a)/(1 - ab)xvalley = b xpeakxaverage = P Rtheta ton/(ton + toff)Variable definitions
- All temperatures are rises relative to the same fixed boundary
- The first three equations describe the periodic steady state
- Average rise follows average power only for this linear, fixed-parameter model
- A nonzero background power needs its own baseline or a piecewise solution
For Rtheta = 8 K/W, Ctheta = 25 J/K, P = 10 W, ton = 20 s, and toff = 80 s, tau = 200 s. The first pulse from ambient rises 7.613 K. Repetition reaches a peak rise of 19.348 K and a pre-pulse valley of 12.970 K; the long-term average rise is 16 K. Treating every cycle as a fresh start would underpredict the peak by more than half.
When One Time Constant Is Not Enough
A semiconductor die can heat quickly while the case, board, and enclosure remain cool. Datasheet transient thermal impedance Ztheta(t) captures the response at a declared junction-to-case or junction-to-ambient boundary. For an isolated power pulse, DeltaTj is approximately P times Ztheta at the pulse duration when the manufacturer's conditions and linearity assumptions apply.
| Data | Use | Boundary |
|---|---|---|
| RthetaJA | Settled junction-to-ambient screening | Depends on board, airflow, orientation, and enclosure |
| RthetaJC | Settled junction-to-case path | Add case-to-ambient model or measured case temperature |
| ZthetaJC(t) | Short junction-to-case pulse response | Not a complete ambient path |
| Foster RC fit | Compact fit to a measured Ztheta curve | Branches are mathematical, not physical layer temperatures |
| Cauer RC network | Layer-oriented thermal network | Needs a valid physical parameterization and boundaries |
The Thermal Resistance Network Calculator reduces steady paths. It does not derive a transient multi-node model from a datasheet curve. For repetitive semiconductor pulses, use manufacturer duty-cycle curves or superposition of step responses with the correct reference temperature and cooling history.
Connect Short Pulses to Long-Term Cooling
Pulse peaks and long-term averages constrain different parts of the structure. A short junction peak may be set by die and package impedance, while average power warms the board, sink, and enclosure. Use the Heat Sink Thermal Resistance Calculator for a steady cooling target after defining the sustained loss. Then recompute junction peak above the hot case or board boundary, not above a cold ambient that exists only at startup.
Interfaces and airflow can vary with pressure, mounting, dust, fan state, and ambient temperature. A lower nominal Rtheta does not prove a fast pulse response: the participating heat capacity and where the heat is generated also matter.
Worked Checks
| Case | Calculation | Interpretation |
|---|---|---|
| One-node constant | 8 K/W × 25 J/K = 200 s | Rtheta Ctheta has units of seconds |
| First 20 s pulse | 80 K × (1 - exp(-20/200)) = 7.613 K | Starts from the selected boundary temperature |
| Periodic 20 s on / 80 s off | Peak 19.348 K; valley 12.970 K | Residual heating carries into later pulses |
| Average check | 10 W × 20% × 8 K/W = 16 K | Average rise is below the periodic peak |
| Time to 50°C rise | With initial rise 25 K and final rise 80 K: 121.23 s | Target must lie strictly between initial and final states |
| Junction-to-case pulse | 12 W × 2 K/W transient impedance = 24 K | Add the actual case temperature at the same time |
Design and Verification Workflow
| Step | Action | Evidence |
|---|---|---|
| 1 | Define the power waveform | Measure or bound pulse power, on-time, off-time, burst length, and steady background loss. |
| 2 | Choose thermal nodes | Identify junction, case, board, interface, sink, enclosure, and ambient reference points. |
| 3 | Obtain response data | Use measured Rtheta/Ctheta or a datasheet Ztheta(t) curve for the actual boundary condition. |
| 4 | Compute a single pulse | Start from the real initial temperature, then evaluate the step response at the pulse end. |
| 5 | Accumulate repeated pulses | Carry the residual rise through each off interval; solve a periodic peak when duty is stable. |
| 6 | Check long-term heat | Use average real power and complete steady-state paths for case, board, sink, and enclosure temperature. |
| 7 | Review limits | Compare transient junction peak, case temperature, SOA, derating, and fault duration at worst credible conditions. |
| 8 | Correlate hardware | Measure pulse power and thermal response; adjust the model before relying on calculated margin. |
Common Mistakes
- Using average power as the only peak-temperature check.
- Resetting every repeated pulse to ambient.
- Using RthetaJA as a short-pulse Ztheta curve.
- Applying junction-to-case impedance without a case-temperature boundary.
- Mixing °C absolute temperature with K temperature rise.
- Assuming one RC pair represents die, package, board, and enclosure at every time scale.
- Ignoring background loss during nominal off-time.
- Applying a constant-power formula to a changing electrical waveform.
- Ignoring hot-condition power and cooling changes.
- Reading a duty-cycle curve without its pulse width and boundary conditions.
- Treating a mathematical Foster branch as a physical layer temperature.
- Validating only settled surface temperature while missing junction peaks.
Scope Boundary
This guide owns pulse history, periodic peak and valley estimation, datasheet thermal-impedance interpretation, and transient verification. The Electronics Thermal Design Guide owns the complete steady thermal path, interfaces, convection, and enclosure. The one-node pulse equations are engineering estimates; critical junction limits need manufacturer data and validation at the real operating boundary.
Support reference
FAQ
What is a thermal time constant?
For a one-node model, the time constant is thermal resistance multiplied by thermal capacitance: tau = Rtheta Ctheta. It describes the exponential response to a power step.
Can average power alone predict peak temperature?
No. Average power sets the long-term average rise for a linear model, but peak temperature also depends on pulse duration, repetition period, thermal impedance, and residual heat before each pulse.
How do I estimate temperature after a power step?
For constant ambient and parameters, T(t) = Tss + (T0 - Tss) exp(-t/tau), with Tss = Ta + P Rtheta.
Why is a single RC model sometimes inaccurate?
A package, die, board, interface, sink, and enclosure have multiple heat capacities and paths. One exponential may not describe both microsecond pulses and long-term heating.
What is transient thermal impedance?
Ztheta(t) is the temperature rise per unit power for a stated transient and thermal boundary condition. Datasheet curves often describe a multi-time-constant device response.
Does the device cool to ambient between pulses?
Only if the off-time is long relative to the relevant time constants. At shorter off-times, the next pulse starts from a nonzero temperature rise.
How do I use a junction-to-case thermal impedance curve?
Multiply pulse power by ZthetaJC at the pulse duration for that junction-to-case boundary, then add the modeled case temperature. Do not treat ZthetaJC as a complete junction-to-ambient path.
Can I use the same model at every ambient temperature?
Only when temperature-dependent losses, thermal properties, cooling, and device limits remain within the model's characterized range. Recheck hot operating corners.
How should a pulse model be verified?
Capture real power waveforms, ambient and case conditions, pulse spacing, and temperature at suitable locations. Compare heating and cooling curves over both short and long times, then retain margin for uncertainty.
Summary
Start with the real loss waveform and initial thermal condition. Use a one-node RC model only over a time range it represents, carry residual heat between pulses, and compare the resulting peak with transient impedance and long-term cooling limits. Measure the assembled product before relying on calculated margin.