The simplest of compact thermal models (CTMs) is a one resistor type. Of these the most widely quoted is Theta_ja (ok, ok, and Theta_jma, more on that variant later). Knowing the power dissipation of the component as well as the ambient temperature is in theory all that is required to determine the junction temperature from the supplied Theta_ja resistance value. You would think so. Unfortunately the junction temperature answer would be wrong.
Maybe wrong is the wrong word. It would be right once, just as a stopped clock is right twice a day.
The method for the experimental derivation of Theta_ja is defined in the JEDEC standard JESD51-2 “Integrated Circuits Thermal Test Method Environment Conditions – Natural Convection (Still Air)”. Basically you put a package on a test board, secure it horizontally in a 1x1x1ft box, power it up and measure its junction temperature and the temperature of the ambient air in the box. With the power, Tjunction (Tj) and Tambient (Ta) you can work out Theta_ja = Tj-Ta/Power [degC/W]
For this specific package, a ceramic ball grid array, the resulting Theta_ja value is 12.2 degC/W. For every watt of heat dissipated, the junction temperature will rise 12.2 degC above the temperature of the air around the board.
Let’s now take this same package and place it in a more realistic operating environment. Still Ta is the same value, the same power is dissipated from the package, the PCB is horizontal but…
…it gets about twice as hot or in other words its Theta_ja about doubles. Turn that round and consider if you’d used Theta_ja to predict Tj your simulation would be about a factor of 2 out, somewhat outside ‘engineering accuracy’ constraints. It should be very obvious that the resistance will change due to other effects apart from the ambient temperature and power dissipation. In the above case the fact that there are lots of other dissipating components around will change things, the PCB stack-up is different etc.
The Theta_ja value is therefore not independent of the environment around the package. The Theta_ja value is only valid for the one environment that it was measured in. It is said to NOT be ‘boundary condition independent’ (BCI).
I’m going to put my hands up at this stage and confess to being a bit of a simulation bigot with a point to prove; don’t use Theta_ja for prediction. Of course it’s not as if JEDEC didn’t realise this. As is described in detail in JESD51-12 “Guidelines for Reporting and Using Electronic Package Thermal Information”:
“The θJA and θJMA values are sometime used to estimate how a package will perform in a specific
application. These estimates cannot be accurate because a standardized test condition cannot match
the user’s application condition. The reasons for this and how to deal with this situation have been
described in section 5.1.”
I’ve seen too often though the bad application of Theta_ja for prediction purposes to NOT say something about it in this blog. So what can it be used for? It’s a good parameter to compare packages with each other. Say you’ve got a package on a board, you know its operating temperature (and it’s just on the limit of Tj_max) but you’re thinking of replacing it with another component with better thermal efficiency as the power in your next design is about to go up 20%. You could use Theta_ja ratio comparisons between current and proposed packages to get a feel as to what the change will be in Tj for the new component. Sarang Shidore explains more here.
Ahh, I nearly forgot, Theta_jma. Very similar to Theta_ja in that it’s a resistance that (if you’ve forgotten already) should NOT be used for prediction purposes. Instead of characterising the thermal behaviour in a ‘natural convection’ type environment (i.e. no fans), Theta_jma is a set of resistance values at differing speeds of air as the air is blown/washes over the component. It too though suffers the same well, not faults, but considerations as Theta_ja.
In our continuing search for the grail of BCI CTMs I’ll move onto 2-R models next time.
For now “Remember remember the 5th of November the gun powder treason and plot, I know of no reason why the gun powder treason should ever be forgot”.
5th November 2009 Ross-on-Wye