Rate of Temperature rise of heatsink

When designing for thermal requirements, thermal data relates to the steady state final value. e.g. the junction temp of a MOSFET will eventually (theoretically) reach 305degC when dissipating 100 Watts with a 2degC/W heat-sink (Ta 25degC, Rth-jc 0.4degC/W and Rth-cs of 0.4degC/w). Clearly this Tj will kill the device...

I am designing a circuit that will dissipate power starting at a max of 200W and linearly decaying to 0W over 10 seconds. (Discharging a bank 20F 10V suppercaps). The duty cycle is extremely low.. at least 5 min in-between.. I want to get away with using the smallest heat-sink possible. How can I easily calculate the rate of temperature rise of the system.. that way I can map the max MOSFET Power dissipation (Pd) in accordance with the the thermal derating constant to achieve the fastest discharge for a given heat-sink capacity.

(e.g. A MOSFET with a Pd of 375W @ Tc 25degC mounted to a small heat-sink (6degC/W) could probably dissipate 200W for a couple seconds until the heat-sink capacity was such that the Tc gets to the point where the device is limited to Pd = 200W due to thermal derating.. How many seconds does it take? )

I understand that a 3D FEA software package would be desirable but sadly I don't have one Are there any other tricks to give me a ball park starting point to give me a better idea of where to start with a prototype?

You could start with the specific heat of aluminium, which is 0.91 Kj/Kg/degrees Kelvin.

You are going to be dumping all the charge held in the capacitor into a mass of aluminium. So you calculate the number of Joules of energy, where Joules = 1/2CV squared.

If its 20 Farads charged to 10 volts, that would be 20Farads x 1/2 x 10v x 10v = 1,000 Joules.

Then you work out what might be a suitable safe temperature rise from that.

This is for a true "heat sink". It has nothing to do with time or heat radiation. It could be a solid cube of aluminium.

The heat dissipation is something entirely different, and will determine how quickly it cools for another "shot",

You are essentially asking about heat capacity of the heat sinks. In the 100 ms to low seconds range, it's also a problem of thermal time constants because the transistor package and heatsink don't heat up uniformly.

You find thermal models for power transistors from many manufacturers, usually allowing SPICE simulation of an equivalent electrical circuit. You can add heat sink thermal capacity (derived fro elementary material data) to the simulation, or make a simple 1D transport model if distributed heat sink time constants matter.

Thanks for the comments they lead me to the following.. very crude, but am I on the right track for a basic approximation?

1. Specific heat of aluminium = 913J/Kg.K
2. Energy to be dissipated = 1000J
3. Heat energy = mass x specific heat capacity x temperature change

for a 50degC rise in temp of the aluminium (I'll assume a solid block) the following amount of material is required..

mass = 1000J/(913*50) = 22 grams (not much!)

Area under the power curve is energy so the approximate temp rise each second for a 22g block of aluminium.. (???)

in the first second approx. 200J of heat energy is transferred to the block:

200/(0.022*913) = 10degC (Ta + 10 = Tt = 30degC)

the second second approx. 150J of heat energy is transferred to the block:

150/(0.022*913) = 7.5degC (Tt + 7.5 = 37.5degC)

etc...

I should be able to work backwards through the various thermal resistances to then estimate the junction temp... I'll prototype it and see how well this idea approximates the real thing.. Although I fear my simplistic idea assumes the heat energy is distributed uniformly, and as FvM points out this is not the case.. There will be a thermal gradient throughout the aluminium... which will determine the rate at which the heat energy is distributed throughout, which is the more complex part of the equation that I've conveniently left out and hope to determine with a few actual measurements

Yes, that is it.
Its a big heat reservoir to absorb the short thermal "hit"

This may require some testing and measurement and a bit of fine tuning.
If thermal gradients are a problem, copper is much nicer than aluminium, and a copper/aluminium sandwich can sometimes be a good solution.

Then you can work on heat radiation/dissipation which will slowly cool it back down to the starting condition in whatever time is available before the next discharge.

Its then a case of looking at available heat sinks that fulfil the minimum volume/surface area requirement.

The discharge method hasn't been yet mentioned. Can be constant R, constant I or constant P.

FvM said:

The discharge method hasn't been yet mentioned. Can be constant R, constant I or constant P.

Click to expand...

I have done similar attempts to calculate thermal dynamics but I found an experiment more real.

Using a power resistor ( a car headlight bulb) I heated the volume and measured temperature rise over time. I used several heat-sinking methods and over several hours I was able to get enough data.
The real system then operated safely even when the ambient temperature rose.

For power levels like yours there are also commercial liquid coolers sold for computer processors. They allow to cool a small volume by dissipating heat elsewhere. You can also try heat pipes, commercial models available.

That is a very interesting idea...

Very slowly ramping up the gate voltage could spread out an otherwise pretty explosive heat release, and go towards reduce the thermal gradient.
Obviously the total energy transfer is not going to be diminished, but it could reduce the peak thermal stress considerably..

Results are in... I used a small grid array heat-sink which weighed approx. 35g (I don't have the RJsa value). I haven't got a plot unfortunately as I was using an thermal imaging camera.. But.. I modified the circuit a little so that the sense resistor shared some of the power (40W). The max case temp was 92degC at about 7 seconds and at this temp the device is derated to 145W.. so I think i'm safe.

This is the circuit I used..



and some of the simulated results which are quite accurate..






My aim was to discharge the caps to 0V (or very close) without having to use an external power source.. only what was available from the supercap.. however this proved to be a little difficult as you need some volts to maintain Vgs.. and BJTs only get down to .6V. this circuit works well... but only if the super caps are charged to a level above Vgs.. blocking diode D1 and storage cap C1 hold the initial voltage of the super cap so as to power the discharge circuit as the super cap voltage drops. I could probably reduce the sense resistor value and dissipate more power in the MOSFET and achieve a more constant and quicker discharge... but that was the only big resistor I had . But I fear this circuit will need one of those little 12-23A 12V remote batteries to ensure supercaps below 6V discharge... Unless anyone has any other bright ideas?

Thanks for the tips and tricks all... much appreciated.

An old-fashioned JFET will conduct down to bias=0V. (You shut them completely off by making the bias voltage cross zero and go into the opposite polarity.)

However a normal JFET probably would not withstand the power levels you're talking about.

Anyway they are no longer in plentiful supply.

Or, perhaps a depletion-mode mosfet, although I'm not sure they're easily available either.

Although knowing of their existence, I've never actually used a depletion mode MOSFET... (they tended to skip over them in favor of enhancement types during my time!) but after a quick look into them they're a handy part for analog electronics... IXYS seem to have the biggest ones... It appears depletion mode MOSFETs are limited in max Id due to their inherent high Rds-on. That said, their biggest device is still capable of 20A which is about what I want my discharge rate to be... although $25 a pop.. some good app notes from IXYS on the subject.. https://www.ixys.com/documents/appnotes/ixan0063.pdf

I would be concerned about the thermal insulation and losses in the Supercap.

Won't the Mosfet die early due to "thermal fatigue"? It heats and part of it expands then it cools and contracts. Over and over until something (a bonding wire inside?) breaks.
If you keep it from getting very hot then it will last MUCH longer.

A $2 MOSFET is cheap compared to repairing blown tracks or parts on an expensive 16 layer PCB after a technician drops a screw in the guts during disassembley or servicing! The duty cycle will be extremely low and i need to keep it as small as possible.

A technician prepared one earlier for us...

If you can charge up the mosfet gate capacitance while you still have sufficient voltage, and if that voltage can then be maintained by isolating the gate, it should be able to discharge right down to zero.

Something that pulses the gate up to a suitable voltage, then isolates itself through a diode should keep the mosfet turned hard on.

Gate capacitance by itself may not be enough, but that is the general idea.

@ thunderDan, very good design, you obviously know what you are doing, )

Thanks Orson Cart for the inspiring compliment. My first boss lived and breathed BJTs... it kind of rubbed off on me (and SPICE simulators!) but I owe a lot to the knowledge and willingness of the engineers that support edaboard.com. There's a wealth of information on here and it's a valuable resource that's usually my first port of call.