MathBench

Heat Sink Calculator

Work the semiconductor thermal path the way it is actually designed: solve for the largest sink-to-ambient resistance that keeps the junction under its target, or take a catalogue sink and find the junction temperature and margin it gives you. Case and sink temperatures, the derating headroom and the interface material are all shown separately, in degrees Celsius and °C/W.

The device

The thermal path

Result

—

The resistance network

How this calculator works

A semiconductor does not have a temperature; it has a chain of them — silicon to package, package to sink through the joint, sink to air. Each step resists the flow, and the resistances add in series like electrical ones: heat flow is the current, temperature the voltage.

Junction to case comes from the datasheet; only a different part changes it. JEDEC's JESD51-1 defines it as the resistance from the working part of the device to the outside surface of the package nearest the die, measured with that surface properly heat sunk — in practice clamped to a temperature-controlled copper cold plate, so essentially all the heat is forced through one face.

Case to sink is the joint you build, and the one people get wrong. Two machined surfaces touch across a small fraction of their apparent area, so the interface material fills the voids; its resistance depends on the material, the bond line thickness and, heavily, the mounting pressure. The presets here are measured TO-220 values from the onsemi applications laboratory and from Henkel's published data, not estimates. The Interface material tab computes the same joint from thickness, conductivity and area, beside those measured values.

Sink to ambient is the heat sink's catalogue rating, published as °C/W or as a rise at a stated power — divide the rise by the watts. Those ratings assume vertical fins in unobstructed still air, which is not what happens inside most enclosures.

The formula

The series network, junction to ambient:
    T_j = T_a + P × (R_jc + R_cs + R_sa)

Solved for the sink you need:
    R_sa(max) = (T_j(target) − T_a) ÷ P − R_jc − R_cs

Node temperatures:
    T_s = T_a + P × R_sa            heat sink base
    T_c = T_s + P × R_cs            package mounting surface
    T_j = T_c + P × R_jc            the silicon

Power the assembly can carry:
    P(max) = (T_j(limit) − T_a) ÷ (R_jc + R_cs + R_sa)

Optional parallel board path:
    T_j = T_a + P × [ R_ja × R_x ÷ (R_ja + R_x) ],  R_x = R_jc + R_cs + R_sa

Bulk resistance of an interface material:
    R_cs = t ÷ (k × A)              t = bond line, k = conductivity, A = area

The series form is Equation 5 of Texas Instruments application note SPRA953, which states it as the proper use of junction-to-case resistance when an efficient heat sink is attached. Equation 6 adds the option offered here: a packaged device also sheds heat through its leads into the board, so its junction-to-ambient path runs in parallel with the sink path. TI attaches a condition — it is the more accurate form only if the junction-to-ambient resistance is known for your system, and a datasheet figure from a JEDEC coupon is not. Leaving it out is conservative: ignoring a parallel path can only overestimate the junction. Equation 7, the interface relation, says outright that it neglects the contact resistance between the mating surfaces.

Bulk conductivities for grease and air are the reciprocals of the thermal resistivities quoted in onsemi AN1040 — 60 °C·in/W for joint compound and 1200 °C·in/W for air, which work out to 0.656 and 0.033 W/m·K. That twenty-to-one ratio is why the interface material exists.

Worked example

A TO-220 MOSFET dissipating 5 W in a warm box, the calculator's default. An onsemi FQP30N06L: 1.90 °C/W junction to case, a 175 °C limit, 45 °C air, a bare greased joint at 1.0 °C/W, and a 125 °C junction target — 50 °C of margin against the rating.

  1. Temperature available: 125 − 45 = 80 °C of rise
  2. Total path allowed: 80 ÷ 5 W = 16 °C/W
  3. Subtract what you cannot change: 16 − 1.90 − 1.00 = 13.1 °C/W, the largest sink that works
  4. Sink temperature: 45 + 5 × 13.1 = 110.5 °C
  5. Case: 110.5 + 5 × 1.00 = 115.5 °C; junction 115.5 + 5 × 1.90 = 125 °C as intended
  6. The sink carries 65.5 °C of the 80 °C rise — 81.9 percent of the resistance, against 6.3 for the joint and 11.9 for the package

Now take that 13.1 °C/W to a catalogue. A Wakefield-Vette 637-10ABEP, a 1 inch board-level extrusion, is rated at a 76 °C rise at 6 W in natural convection — 76 ÷ 6 = 12.67 °C/W, just inside the budget. Check a sink with its rounded 12.7 °C/W:

  1. Total path: 1.90 + 1.00 + 12.7 = 15.6 °C/W
  2. Junction: 45 + 5 × 15.6 = 123 °C, 2 °C under the target and 52 °C under the 175 °C limit
  3. Sink 108.5 °C, case 113.5 °C — hot enough that nothing else should touch either
  4. The assembly uses 60 percent of the 130 °C between 45 °C air and the junction limit
  5. It could carry 5.128 W at the 125 °C target, or 8.333 W before the junction reaches 175 °C

Two degrees of margin is thin: the sink that just fits on paper fails when the enclosure air climbs. The next size up, the 1.5 inch 637-15ABEP at 65 °C per 6 W or 10.83 °C/W, brings the junction down about 9 °C for a few cents and half an inch of height.

On the Interface material tab, a Bergquist Sil-Pad 1500 is 0.254 mm thick at 2.0 W/m·K; across a TO-220 tab of 111 mm² that is 0.000254 ÷ (2.0 × 0.000111) = 1.14 °C/W of bulk material, a 5.72 °C step at 5 W. Henkel measures the same pad on a real TO-220 at 2.68 °C/W — the missing 1.54 °C/W is contact resistance at the two faces.

Assumptions & tips

  • Use the ambient the sink sees, not room temperature. Air in a sealed box with a few tens of watts in it sits 20 to 30 °C above the room, and sizing to 25 °C then installing into 50 °C air fails silently — as a shortened life, not a dead board.
  • Catalogue sink ratings assume the ideal orientation. Lay that extrusion flat, crowd it behind a wall of electrolytics, or stack two, and the real resistance is higher than the sheet. Derate, or measure.
  • Torque the joint. Interface resistance is a strong function of pressure: onsemi's TO-220 data is taken at 8 inch-pounds, and the same Sil-Pad measures 3.54 °C/W at 10 psi against 2.22 °C/W at 200 psi. Too little torque throws that away; over-torquing a plastic package cracks the die.
  • Grease matters most where the surface is worst. On a flat metal-to-metal TO-220 joint it buys about 0.2 °C/W; with a hard, uneven mica washer it halves the resistance, 3.4 to 1.6. If you must isolate electrically, isolate and grease, or use a pad or phase change film.
  • A datasheet R_jc is usually a maximum, and R_sa is usually a typical. Mixing a worst-case package number with a best-case sink number and a nominal ambient gives an answer with no defined confidence. Pick worst-case or nominal, and be consistent.
  • Check the transient, then check the bench. This page solves the settled condition: a device that pulses hard exceeds it briefly, and one on a large sink takes many minutes to reach it, which is why a five-minute bench test passes a design that overheats after an hour. Then measure: a sink hotter than predicted means the rating or the ambient is wrong, and a case much hotter than the sink means the joint is.

Frequently asked questions

Can I just use the R-theta-JA number on the datasheet?

Only for comparing one package against another. Junction-to-ambient resistance is measured with the package soldered to a standard JEDEC test board in a still-air chamber, and Texas Instruments notes that in those tests 70 to 95 percent of the heat leaves through the board rather than the package. Your board is not that board and your enclosure is not that chamber. TI ranks the influences on R-theta-JA as PCB design strong at 100 percent, die or pad size strong at 50 percent, internal package geometry strong at 35 percent and altitude strong at 18 percent. Use R-theta-JC with a real heat sink resistance instead, which is what this calculator does.

How much does the mounting interface actually cost me?

More than most people expect on a small package. Measurements in the onsemi applications lab give a TO-220 tab bolted to a heat sink at 8 inch-pounds of torque 1.2 degrees C per watt dry, 1.0 with thermal grease, 1.6 through a 2 mil mica washer with grease, and 3.4 through the same mica washer dry. A dry mica joint on its own is nearly twice the junction-to-case resistance of a typical TO-220 MOSFET, so an electrically isolated device that skips the grease can throw away more temperature budget in the washer than in the silicon.

What junction temperature should I design to?

Below the datasheet maximum, with room for the ambient you have not thought of yet. Semiconductor field history quoted by onsemi shows the failure rate of most silicon devices falling roughly by half for a drop in junction temperature from 160 to 135 degrees C, and design guidelines for military power supplies impose a 110 degrees C ceiling. A 125 degrees C target against a 175 degrees C rating, the default on this page, leaves 50 degrees C for high line, a blocked vent, a hot day and part-to-part spread. Set the target yourself rather than sizing to the absolute maximum.

Does a fan really help enough to bother with?

Usually yes, and by roughly a factor of two on a small extrusion. The Wakefield-Vette 637-10ABEP board-level sink is rated 76 degrees C rise at 6 watts in still air, which is 12.67 degrees C per watt, and 5.8 degrees C per watt at 200 linear feet per minute of air. That is a 54 percent reduction from the same aluminium. The catch is that the number now depends on a fan you have to power, monitor and eventually replace, so many designers size the sink for natural convection and treat airflow as margin rather than as the design basis.

Why does the calculated interface resistance disagree with the pad datasheet?

Because the thickness-over-conductivity formula only counts the bulk material and ignores the two contact surfaces. Bergquist Sil-Pad 1500 is 0.254 mm thick with a conductivity of 2.0 W per metre-kelvin, which over a TO-220 tab of about 111 square millimetres works out to 1.14 degrees C per watt of bulk resistance, yet Henkel measures the assembled TO-220 joint at 2.68 degrees C per watt at 50 psi. The missing 1.54 degrees C per watt is contact resistance at the two faces. Prefer a measured joint value at your mounting pressure whenever the manufacturer publishes one.

Sources

  1. Semiconductor and IC Package Thermal Metrics (SPRA953D) — Darvin Edwards and Hiep Nguyen, Texas Instruments application note, December 2003, revised March 2024. ti.comEquation 5 is the series network this calculator solves, Equation 6 the optional parallel board path, and Equation 7 the bulk interface resistance used on the Interface material tab. Section 1 is the source of the warning that 70 to 95 percent of the heat in a JEDEC junction-to-ambient test leaves through the test board, and of the table ranking PCB design, die size, package geometry and altitude as influences on that figure.
  2. AN1040/D — Mounting Considerations For Power Semiconductors — Bill Roehr, onsemi, rev. 5, August 2021. onsemi.comTable 1 supplies the measured TO-220AB interface resistances at 8 inch-pounds of torque used as presets: 1.2 °C/W dry, 1.0 greased, 3.4 through a 2 mil mica washer dry and 1.6 with grease. The note is also the source of the 60 and 1200 °C·in/W thermal resistivities for joint compound and air, of the reliability statement that failure rates roughly halve between 160 and 135 °C, and of the 110 °C military design ceiling.
  3. JESD51-1, Integrated Circuits Thermal Measurement Method — Electrical Test Method (Single Semiconductor Device), with the companion documents JESD51-2 (natural convection, still air), JESD51-3 (low effective thermal conductivity test board), JESD51-6 (forced convection, moving air) and JESD51-7 (high effective thermal conductivity test board) — JEDEC Solid State Technology Association.The definition of junction-to-case resistance quoted on this page, and the standardised test boards and environments behind every datasheet thermal number. JEDEC distributes these documents free after registration; its site refuses automated requests, so no link is given rather than one that could not be verified.
  4. FQP30N06L N-Channel QFET MOSFET data sheet — onsemi (originally Fairchild Semiconductor), rev. C1, November 2013. onsemi.comThe default device: TO-220 package, 1.90 °C/W maximum junction-to-case resistance, 62.5 °C/W maximum junction-to-ambient, and a 175 °C maximum junction temperature.
  5. Board Level Power Semiconductor Heat Sinks — 626, 627, 637, 667 and 292 series — Wakefield-Vette catalogue pages 70–71. wakefieldthermal.comThe catalogue sinks in the worked example: the 637-10ABEP at a 76 °C rise per 6 W in natural convection, which is 12.67 °C/W, and 5.8 °C/W at 200 linear feet per minute; the 637-15ABEP at 65 °C per 6 W, or 10.83 °C/W.
  6. Technical Data Sheet — BERGQUIST SIL PAD TSP 1500 — Henkel, November 2018. henkel.comConductivity 2.0 W/m·K per ASTM D5470, total thickness 0.254 mm, thermal impedance 0.46 °C·in²/W at 50 psi, and TO-220 joint performance of 3.54 °C/W at 10 psi, 2.68 at 50 psi and 2.22 at 200 psi — the pressure-dependence quoted in the tips and the measured value the Interface material tab compares against.
  7. Technical Data Sheet — BERGQUIST HI FLOW THF 1500P — Henkel, April 2020. henkel.comThe phase change preset: conductivity 1.5 W/m·K, thermal impedance 0.20 °C·in²/W at 25 psi and a measured TO-220 resistance of 1.15 °C/W for the 0.001 inch film. Dividing impedance by measured resistance for this product and for the Sil-Pad gives 0.174 and 0.172 in², which is where the 111 mm² default contact area for a TO-220 tab comes from.
  8. Fundamentals of Heat and Mass Transfer, 8th edition — T. L. Bergman, A. S. Lavine, F. P. Incropera and D. P. DeWitt, Wiley. wiley.comThe thermal resistance analogy that lets conduction, contact and convection resistances be added in series and combined in parallel, and the treatment of thermal contact resistance between pressed surfaces that the interface presets illustrate.

  • dBm to Watts Calculator

    Convert between dBm and watts or milliwatts in either direction, with a common-values table.

  • VSWR Calculator

    Enter any one of VSWR, return loss, reflection coefficient, or mismatch loss to get the rest.

  • Coax Cable Loss Calculator

    Cable type, length, and frequency to dB loss and power delivered — RG and LMR presets included.

  • Microstrip Impedance Calculator

    Trace width, substrate height, and εr to Z₀ — or solve for the width that hits a target impedance.