last time, we talked about theta-jb and psi-jb and how they are useful figures of merit for comparing the performance of different packages, especially in applications with no heatsink.

at that time we had also posed the question - is it then possible to predict the actual junction temperature in an application-specific environment (barring using a full blown detailed model representation of the package) in a cfd simulation?

we are now closer to answering this question. before we get there, however, let us recall the differences between detailed and compact models.

detailed and compact models: the difference

it is important to keep in mind that there is a clear distinction between a detailed model and a compact model. let us first understand the distinction.

a detailed model is a model that attempts to represent or reconstruct the physical geometry of a package to the extent feasible. thus the detailed model will physically always look similar to the actual package geometry.

a properly constructed detailed model is, almost by definition, boundary condition independent (bci); i.e. the model will predict the temperature of the various elements within the package (including junction, case, and leads) accurately regardless of the computational environment in which it is placed.

a compact model on the other hand is a behavioral, model, that aims to accurately predict the temperature of the package only at a few critical points - junction, case, and possibly leads. it cannot predict the temperature at any other part of the package.

most importantly, a compact model is not constructed by trying to mimic the geometry and material properties of the actual component. it is rather an abstraction of the response of a component to various boundary conditions.

one could argue that theta-ja is nothing but a compact model, and strictly speaking, one would be correct. theta-ja is an experimentally derived metric that could theoretically be used a predictive "model". however, we have already seen in previous articles that such single-parameter metrics are simply too inaccurate to be of use as predictive tools.

hence when we talk of compact models, we should narrow this term a little down to behavioral models that at least track the trends for junction and case temperatures. this would then exclude single-parameter metrics such as theta-ja or theta-jc, as these only capture one of the major thermal paths from the junction to the ambient.

the holy grail in compact modeling is when they are bci. a generalized approach for deriving bci models has been a major focus of research for the past decade or so. the non-proprietary delphi methodology, proposed by the publicly funded, delphi consortium is the approach that is gaining acceptance as the standard for generating bci compact models by the supplier community. it involves the derivation of multi-resistor compact models.

we shall talk about the delphi approach in greater detail in a future column.

however, although bci compact models are already available for some package styles in at least one prominent cfd software tool, there is an alternative approach that bridges the single-parameter world and the bci compact modeling world. that is the idea of two-resistor models.

fig. 1 - two-resistor and multi-resistor model topologies

the basis of two-resistor models

the theoretical basis for two-resistor models is the paper1 by jim andrews of motorola. he conceptualized the package as being made up of two thermal resistances - junction-to-case resistance (rjc) and junction-to-board (rjb) resistance.

he also showed that the junction temperature rise above ambient is approximately a linear function of the board temperature rise above ambient. this showed that a two-resistor model tracks the trend of the heat flow out of the junction fairly accurately.

the next major contribution in this area was from a landmark paper in 1999 by joiner & adams2. this was the first serious numerical and experimental investigation of the possibilities of using the two-resistor model to predict the performance of a package. the authors first defined a junction-to-board resistance based on measurements using a "ring cold plate" - this eventually was adopted by jedec as the theta-jb standard (refer to my previous column).

they then defined the two-resistor model as a combination of theta-jc and theta-jb. five different packages were considered - 164 fc-pbga, 256 pbga, 272 pbga, 144 tqfp, and 32 soj - and theta-jc and theta-jb were obtained using experimental measurements.

next, using a commercial cfd tool, they simulated the detailed models of these packages and compared the junction temperature and flux results to the predictions of the corresponding two-resistor models. the comparisons were done on two standard jedec boards - 2s2p and 1s0p under natural and forced convection environments.

the results showed that the two-resistor model predicted the junction temperature to within 30% in all cases. the predictions were better for 2s2p boards - not surprising, as the theta-jb standard utilizes this board.

this paper was followed up by a number of studies of the performance of two-resistor models for various packages3,4,5. some of these studies also considered heatsink applications, something joiner & adams had not examined. the conclusions seem to confirm the 30% figure for the upper bound of the error of a two-resistor model in predicting junction temperature.

using two-resistor models in simulation tools

a maximum error of 30% for junction temperature may seem significant, and it is. still, it is worth remembering that in many cases the predictive error is less. also, even an error that seems that high can be useful if we know that it is bounded.

the problem with using single-parameter metrics such as theta-ja was always highly risky precisely because they appeared to be unbounded, or rather, the bound was too high for them to be of any practical use.

in the case of two-resistor models, this is not the case. the reason is that two-resistor models allow for two heat transfer paths - junction to the package top and junction to the package bottom. since the heat escaping from sides of a package in just about all applications is very small (just a few percent), this is a gross but complete description of the ways heat leaves the package.

the errors seen in the two-resistor model are due to lumping the various paths heat takes as it flows from the junction to the top (or bottom) of the package.

incidentally, it is important to note that the accuracy of prediction of the case temperature is likely to be worse than the junction temperature, especially in plastic or "glob-top" type of packages. this is because the mold compound surface has a significant gradient of temperature, and representing the top as a single node tends to average this temperature out.

it is advisable to use two-resistor models during the initial design phase to predict approximate values of junction temperature. since a two-resistor model almost always under-predicts the temperature, joiner & adams suggested adding a correction factor by increasing theta-jb by 25% to make the model more accurate. this is a valid suggestion, but some users may be uncomfortable adjusting theta-jb values.

two-resistor models will also produce high accuracy for parametrics. in other words, the difference in temperature between two variations in cooling solutions for the package will tend to be more accurately predicted than the absolute values of the temperatures.

next time we will take a look at some specific examples involving two-resistor models.

references

1. andrews, j.; "
2. joiner, b. & adams, v.; "measurement and simulation of junction to board thermal resistance and its application in thermal modeling"; proc. of semitherm 1999; san diego.
3. ewanich, j., shidore, s., pashaei-rad, s.; "numerical and experimental investigation of a tape ball grid array package"; semitherm xvi, march 2000, san jose, ca, usa
4. shidore, s, adams, v, lee, t; " a study of compact thermal model topologies in cfd for a flip chip plastic ball grid array package"; itherm 2000 may 2000 - las vegas, nevada.
5. xu, w., shidore, s., gauche, p.; " creation and validation of a two-resistor compact model of a plastic quad flat pack (pqfp) using cfd"; hd-international 2000 conference denver, co, usa.

about sarang shidore:

sarang shidore obtained engineering degrees from iit madras (india), texas a & m university (college station), and university of texas (austin). he worked at flomerics inc. in various roles in engineering and product management with a special focus on package-level thermal modeling and analysis, a field in which he has authored several papers and articles.

in addition, he worked for mentor graphics as product marketing manager and for several years as a consultant for various organizations. he is currently a visiting scholar at the lbj school of public affairs at the university of texas focused on energy and climate policy and future strategies.