How to calculate the temperature rise of a component over time ? - Page 1
Forum section: electronics / projects

author: chipeater
author_rank: Contributor
timestamp: May 11, 2023, 04:27:44 pm
content: Hello,I want to use a linear regulator to supply a 12V load with an input voltage of 35V for only 150ms.Obviously, the problem of the temperature rise arises, I found a regulator (LT3086) that match my requirement but I don't know how to calculate the temperature after only 150ms.In steady state : 35-12 * 1.5 = 34.5Wwith Tja = 20°C/W : 715°C @ 25°C ambiant tempIf you know how to calculate, let me knowThank you very much

author: temperance
author_rank: Super Contributor
timestamp: May 11, 2023, 07:09:40 pm
content: And how long will the regulator be switched off after this 150ms event?From there you can calculate the duty cycle. From the duty cycle you can calculate average power. But that's not the hole story of course. During this 150ms transient, the device will heat up. How much depends on the thermal mass and material.To get you started:https://en.wikipedia.org/wiki/Heat_capacity

author: bdunham7
author_rank: Super Contributor
timestamp: May 11, 2023, 10:18:47 pm
content: Quote from: chipeater on May 11, 2023, 04:27:44 pmYou don't have enough information to calculate what you want because you don't know the thermal mass of the case nor have you even stated which case variety you will use. You also need to know how often you will be powering this up and if it is totally off between events. You mention "1.5" in your calculations, but you don't say whether that is your intended load current. If it is, then your pulse is a little over 5J, which is probably just fine for a TO-220 case provided it cools off between pulses. If you pulsed it once every 10 seconds, that would be about a half-watt continuous, well within the dissipation ability of a TO-220 tab without any additional heatsink.

author: Tomorokoshi
author_rank: Super Contributor
timestamp: May 12, 2023, 03:28:21 am
content: You need something known as the "thermal transient resistance". With a quick look I couldn't find it at Analog Devices. However, it's a TO-220, so let's select another TO-220 and use its data. Searching through Digi-Key finds this:https://www.digikey.com/en/products/detail/onsemi/MJE18002/662232In the datasheet Figure 20 is the Typical Thermal Response curve, where the dependent axis is the Thermal Transient Resistance.Using your data:34.5W peak power20 C/W thermal resistance150 ms single pulseWe index into the Single Pulse line at 150 ms, and read back the normalized thermal resistance of about 0.14.Then the calculation is:Tjunction = Ppeak * RthJC * 0.14 + 25C = 121.6CThis is just below the junction maximum, so it should be okay.Note that the actual transient response could be quite different, and it would be best to find one from Analog. However this should give a reasonable estimate.

author: bdunham7
author_rank: Super Contributor
timestamp: May 12, 2023, 04:08:14 am
content: Quote from: Tomorokoshi on May 12, 2023, 03:28:21 amThe lower axis of that chart seems to be marked in milliseconds, not seconds as you seem to imply. Is that wrong? It seems wrong to me.

author: srb1954
author_rank: Super Contributor
timestamp: May 12, 2023, 06:25:17 am
content: Quote from: bdunham7 on May 12, 2023, 04:08:14 amI agree. I think that the derating factor from that graph should be about 0.95.Also, the graph is for RthJCso I don't think it can reliably be applied for determining a derating factor for the RthJAfor a device in free air. In this case the transient thermal response of the device junction to case needs to be added on to the transient thermal response of the ultimate heat removal mechanism, whether it is the air or a separate heatsink.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: May 12, 2023, 07:55:10 am
content: ZthJC data are irrelevant here as heat is conducted from chip to tab in about 100ms, therefore heat capacity, and external heatsinking, must be considered.The best way to handle this is:1. Get additional data from LT, if they have any available at all. The downside is, their parts are quite expensive; the upside is, their support is generally available and helpful. Or at least, was, last I worked with them. (That may've changed in the intervening years, but Analog (who bought them out) have a similar reputation, so a change in service quality wouldn't likely be due to that.)2. Match as closely as possible, the test conditions provided. If SON/TSSOP, use the same footprint dimensions, thermal vias, ground plane, etc.; if D2PAK/TO-220, same thermal pour(s), vias, inner plane(s), etc. Specifically for TO-220, adequate heatsink bulk.3. If applicable, wire up a transient thermal model and simulate device Tj in SPICE. Or if sufficient data are provided, you can fit your own curve to it -- though it's a bit of a bother.Simulation is doubly valuable as thermal diffusion is -- as the name suggests, a diffusion effect, i.e. energy spreads out as sqrt(t), so it is not sufficient to say that a device can withstand a certain amount of energy regardless of pulse width (as a basic heat capacity argument would use). If the power is varying during the pulse, you really need to model both the pulse itself, and the device thermal impedance, at the same time, to get an accurate (say, better than 30%) estimate.If I shall read into the test conditions just a bit -- 35V and 150ms sounds an awful lot like load dump conditions. There are much cheaper solutions for that, as the output regulation doesn't need to be much. One can use better-documented MOSFETs (that is, with ZthJA data*), or depending on requirements, a cutoff (switched) or shunt (large TVS) type transient limiter instead.*Although last I looked, there were very few if any actually with this. Which is... kind of disturbing?Perhaps your entire 1.5A load doesn't need to be protected, either: motors, solenoids, etc. can withstand that just fine. If switched off, simply use devices rated for the peak (this is why 55V+ parts are common for 12V automotive applications). If switched on, double check that the peak load current won't blow the switches.Also, just to make this perfectly clear: pretty much every datasheet gives ZthJC. But being impedance to case, it levels out around 10-100ms (for DPAK to TO-220 scale devices), and doesn't take into account surrounding materials. You must have ZthJA, the thermal impedance including PCB and pours. For SMT types anyway. For THT, it's very likely the device can handle that much power continuously (a MOSFET anyway; a 3-terminal regulator, maybe not), and just needs to be joined to a heatsink thick enough to handle the energy. Which is really only a few grams of aluminum; a TO-220 itself is already much of the way there, most likely sufficient by itself, but you can basically thicken the tab if more energy is required.Tim

author: Tomorokoshi
author_rank: Super Contributor
timestamp: May 13, 2023, 04:11:11 am
content: Wow, how many ways can I get it wrong. I missed a few big details there.

author: bdunham7
author_rank: Super Contributor
timestamp: May 13, 2023, 05:12:34 am
content: Quote from: Tomorokoshi on May 13, 2023, 04:11:11 amHmmm. Misread one parameter by 1000x, apply the resulting derating factor in reverse and you still get a plausible answer! There's probably a lesson in there somewhere but I've no idea what it is. I didn't see how the problem could be solved without knowing how much metal is in the tab.

author: bdunham7
author_rank: Super Contributor
timestamp: May 13, 2023, 05:44:17 am
content: Quote from: T3sl4co1l on May 12, 2023, 07:55:10 amThe device obviously can't take the same amount of energy in a very short pulse because the heat can't get out of the junction fast enough. However, 150ms is a fairly long time and I was just figuring that with ~35W and 3C/W Tjto case, as long as the tab stayed under 45C then Tjwouldn't exceed 150C because that works for steady state and thus it should be OK with anything less than forever. Obviously that's a 'safe' estimate as there can be some heat in transition at the end of the pulse and if the tab goes over 45C after the power is off there's still no problem. So the only question is if the tab will stay cool for long enough and for that we need to know if the tab is one of those thin ones or a nice thick chunk of aluminum.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: May 13, 2023, 03:57:57 pm
content: Quote from: bdunham7 on May 13, 2023, 05:44:17 amExactly.Would be nice to have (or assume e.g. by way of heat capacity --> thermal capacitance) a ZthCA plot, and some way to interface the two -- but as far as I know there isn't such a method, at least not a simple (geometrical?) one. One again could curve-fit an RC circuit, and connect that in series with another, but that's a somewhat nontrivial process.Tim

author: mawyatt
author_rank: Super Contributor
timestamp: May 13, 2023, 04:16:25 pm
content: Way back quite a bit of effort went into thermally modeling devices on a silicon chip, this became even more complex as one had to consider the effects of local (on chip) heat sources and sinks and their relative proximity as well as how the chip is mounted, the package details. Then how the package is mounted, heat sink details, the ambient conditions and so forth.Eventually a reliable proprietary thermal modeling simulation was developed that would show not only the steady state but thermal transient effects at each individual device within the chip. The thermal device models were complex as well with 2nd order thermal effects and non-linear time constants included. This was eventually ported to the Cadence time domain & AC simulator to allow studying thermal effects under waveform conditions, and required an enormous amount of computing horsepower, but with Multi-Multi Million $ chip designs at stake made the overall efforts worthwhile.Ironically the limited factor today is high density computing chips is thermal, and this alone limits the speeds!!Anyway, thermal modeling is a difficult and complex task for just steady state conditions, when one includes transient thermal conditions things get unwieldy quickly!!Best,

author: Siwastaja
author_rank: Super Contributor
timestamp: May 13, 2023, 04:31:22 pm
content: Thermal modelling is possible but difficult enough so that building a prototype and measuring is highly recommendable.

author: mawyatt
author_rank: Super Contributor
timestamp: May 13, 2023, 05:15:57 pm
content: Quote from: Siwastaja on May 13, 2023, 04:31:22 pmSo true, and a wise choice for a circuit designer.However, at the custom chip level where a process run, even a shared run, can cost many Millions $, and take 3~6 months this may not be economical nor schedule wise. Here one must rely on experience, knowledge, expertise, and the simulator, otherwise their career as a chip designer will be very short!!Best,

author: bdunham7
author_rank: Super Contributor
timestamp: May 13, 2023, 05:54:13 pm
content: Quote from: Siwastaja on May 13, 2023, 04:31:22 pmIndeed. Just for fun I tried this with some old regulators, a generic 7812 and an LM340T-12. The 7812 didn't work at all, perhaps I crossed a wire. For the LM340T-12, initial tests were promising and showed that when the regulator was hit with 35V driving an 8R load (pretty much exactly the OP's scenario) it went about 600ms before starting current foldback and apparently breaking into some bad oscillations. I added an input cap, but this didn't help and after a few tests, the LM340T-12 was toast as well. Perhaps a more careful experiment with a better layout is needed, but I'm out of scrap 12V regulators. The bottom line is that I don't think a single 150ms pulse per the OP's spec is going to thermally challenge a typical TO-220 linear regulator.

author: Kleinstein
author_rank: Super Contributor
timestamp: May 14, 2023, 07:33:40 am
content: Some regulators have an extra SOA protection. So at a high input voltage the maximum output current can be reduced even for short times.Otherwise the calculation with the "thermal transient resistance" is OK. That is exactly what this is about.Still the result with some 120 C is quite high and this would be quite some stress for the part. So ideally one would reduce the input voltage, e.g. with a zener diode in series.