A Thermal Management Example (Part 2: When Datasheets Attack)

In part 1, the process of making basic thermal management calculations was described. This page builds on that discussion, and demonstrates the importance of such analyses as an inflation gauge for certain component specifications.

The previous example assumed use of an IRL3713PBF transistor (TO-220 package), HS278-ND heatsink, and BER183-ND thermal pad, and showed the calculation of device temperatures using (for sake of simplicity) an assumed 4 watts of electrical power dissipation in the device. Here, device characteristics and common design constraints are used as limiting criteria, and practical upper limits for the transistor’s current carrying capacity are derived for various application scenarios. These practical limits will be shown to be significantly less than the figures suggested by the datasheet, to an extent that may take the unwary by surprise.

Figure 1. The basic thermal model from part 1.

A Datasheet, Poised to Strike

Page 1 of the IRL3713 datasheet is excerpted in figure 2. In the “Absolute Maximum Ratings” table the ID rating, called “Continuous Drain Current” is the item of focus in this discussion. From a linguistic standpoint, it would be entirely reasonable to understand such a term to indicate the maximum amount of current that can be passed through the part via its drain terminal on a continuous basis. From a practical standpoint, such an understanding (though reasonable) would be violently incorrect.

Figure 2. Excerpt from the IRL3713 datasheet.

Two significant clues to this are offered: first is that two differing values for the ID rating are given, subject to differing temperature qualifications. That these values differ by about 35% should indicate that this qualification is of significant importance

Figure 3. Maximum drain current ratings differ based on temperature qualifications.

The second clue as to the specious nature of these ID ratings is that a reference to note image is present at every mention. The text of that note is found on the next-to-last page of the datasheet:

image Calculated continuous current based on maximum allowable junction temperature. Package limitation current is 75A

Stated more bluntly, this note says "The conductors connecting the active silicon in this part to the outside world are prone to failure at current levels upwards of 75A. The numbers shown only apply in an imaginary world where that’s not an issue.

So, not only do the “continuous drain current” ratings for the part differ dramatically based on a temperature condition, the lesser of the two ID ratings given on page 1 of the datasheet is still more than double the limiting value recommended to avoid having parts of the device melt. These are the warnings that the excerpt in figure 4, given a place of prominence at the top of page one is tantamount to a standing game of “two truths and a lie;” two of the values given are descriptions of actual device behavior or capability that can be taken more or less at face value for design purposes and demonstrated with no particular effort, whereas the third represents an idealized theoretical value that neglects directly relevant device limitations and cannot be approached, much less realized in practical settings.

Figure 4.

Understanding Their Tactics

So where does the first-page ID rating come from? Note 6 indicates that it’s “calculated” and “… based on maximum allowable junction temperature” which is 175°C according to the Absolute Maximum Ratings section. The 260A ID figure in the parametric table further mentions a case temperature condition, TC = 25°C. Those conditions fit neatly on either side of RϴJ-C in the thermal model used in part 1, and the datasheet gives a value for RϴJ-C as 0.45°/W. This makes it possible to calculate the amount of thermal power that would have to be dissipated in the device’s junction in order to heat its innards to 175°C when it’s mounting surface is maintained at 25°C, using a thermal model similar to the one used in part 1 and shown in figure 5.
Equation 1.

Figure 5. The typical thermal model used for determination of ID ratings. Indicated RϴJ-C value taken from IRL3713 datasheet, values for other parts will differ.

Since this is supposed to indicate a “continuous drain current,” that thermal power would come from the rated 260A of drain current flowing through the part’s on-state resistance, RDS(ON) . Rearranging the basic P=I2*R formula for power dissipation in a resistor, one can calculate the amount of resistance required to dissipate a given amount of power with some specified current flow:
Equation 2.

The 4.9 milliohm result is fairly close to the datasheet’s characterization of the part’s on-state resistance. Note however, that the datasheet characterizes RDS(ON) at a 25°C junction temperature; in the theoretical case being studied, the device’s junction is stated to be at a rather more toasty 175°C, which will have an effect on RDS(ON).

Figure 6. Datasheet excerpt characterizing on-state resistance of the FET in question

To account for this, one can consult figure 4 of the datasheet (excerpted here as figure 7, arrow added) which indicates that on-state resistances when the device’s innards are at 175°C will be about 1.6 times higher than what they’d be with the die at 25°C.

Dividing the 4.9 milliohms found earlier by this temperature factor of approximately 1.6, we arrive at a figure of 3.1 milliohms, which is within a rounding error of the 3 milliohm maximum RDS(ON) value that the datasheet offers for conditions of 25°C junction temperature and a gate-source voltage of 10V.

Figure 7. Datasheet figure characterizing change in on-state resistance vs. temperature.

The ‘Note 6’ in the datasheet indicates that the quoted ID figures are “calculated,” and the above process demonstrates (in reverse) how the ID figures in the datasheet are derived. Though called “Absolute Maximum Continuous Drain Current” by convention, in practice what this specification amounts to is a figure of merit that characterizes a device’s on-state resistance and package thermal performance in a combined fashion. As such, while it does have utility for comparing various devices, it’s not very useful for understanding their practical capacities.

To illustrate the point and demonstrate why the ID values shown are “calculated” rather than measured, consider what might be required to meet the TC = 25°C condition stipulated by the fine print. It was calculated above that 333 watts of thermal power need to be removed from the device, and the case temperature maintained at 25°C. Doing so requires heat transfer through the thermal interface between the transistor’s case and an attached heat sink, which the transistor’s datasheet suggests will have a thermal resistance of about 0.5°C/W, if a thermally-efficient but electrically non-insulating thermal grease is used.

Figure 8. Thermal model for the IRL3713 with rated continuous drain current, inclusive of elements neglected by the model used to establish its ID rating.

If that interface thermal resistance estimate is valid, the temperature difference across the thermal interface works out to be 333W * 0.5°C/W=166.5°C. Since the device’s case is to be maintained at 25°C, the temperature on the cold side of the interface works out to be 25°C-166.5°C= -141.5°C. To allow for the thermal resistance of a heat sink would require an ambient temperature colder than this, which suggests the use of liquid nitrogen (which boils at -196°C or 77°K) as a coolant. Though not the coldest, it’s usually the cheapest of the commonly available cryogens, and is less likely to result in inadvertent conversion to a high-temperature state upon evaporation than hydrogen or oxygen…

Given the available temperature difference that can be imposed across the heat sink and dividing by the amount of thermal power that must be transferred, one arrives at a figure for the maximum allowable thermal resistance of a heat sink: (196°C -141.5°C)/333W= 0.16°C/W. P/N 345-1173-ND (datasheet excerpted in figure 9, highlight added.) meets that requirement with forced convection in air, which the boiling action of evaporating liquid nitrogen might be expected to approximate. (More on this later, in Appendix B.)

Figure 9.

How to Stay Safe

This gives rise to a pertinent question: what if the application at hand can’t accommodate a four and a half pound (2kg) heat sink and a liquid nitrogen bath? What’s the part’s current carrying capacity under slightly more practical conditions? It depends on what those conditions are exactly; while the character of the part itself does set the general scale of what’s achievable, the portion of this potential that can be utilized is largely a question of thermal management, subject to the user’s application constraints and design choices. Some of the major considerations are are discussed below, and their effects on maximum permissible drain current are shown in figure 11.

Max junction temperature: From a reliability standpoint, operating a device at it’s rated Absolute Maximum Junction Temperature (175°C in this case) is not good practice. Aside from degradations in device characteristics that typically attend elevated temperature operation, higher maximum allowed temperatures usually translate into larger temperature changes as a system is turned on & off, experiences changes in load, etc. The resultant mechanical stresses within a device due to thermal expansion effects shorten service lives and increase the likelihood of random failures, to an increasing degree as the magnitude and rate of the temperature changes involved increase. Depending on other design considerations, allowing a 25°C margin to maximum rated junction temperature might be a reasonable to aggressive design choice. Because it also happens to be convenient for purposes of consulting the datasheet’s figure 4, a maximum junction temperature of 150°C (25°C less than the rated maximum of 175°C) will be used in some of the scenarios tabulated below.

Maximum ambient temperature: The temperature difference between an electronic device’s innards and and the environment in which it’s operating is the thing that drives heat transfer from one to the other; all else being equal, smaller temperature differences translate to less heat transfer and lower operational limits. Since a designer often doesn’t have direct control over the operating environment, this is frequently established via a design specification applied to the end product. A figure around 40°C (104°F) is common for office equipment, consumer goods, and similar items designed to be co-located with people. The “ambient” temperature for thermal modeling purposes however refers to the environment in which the modeled system exists; if that’s the inside of a poorly ventilated outer enclosure for example, the effective “ambient” temperature may well be higher. To be generous, the following scenarios assume that this is not the case, and assume a maximum 40°C ambient temperature.

Thermal interface: A broader discussion of thermal interface materials and their usage is available here, but one of the overarching themes is that if one needs a thermal interface to be electrically insulating also, there’s a thermal resistance penalty to be paid. The datasheet for the transistor being modeled suggests 0.5°C/W is a reasonable figure when an electrically non-insulating smear of thermal grease is used. In comparison, a reasonable figure for an electrically-insulating interface (discussed in part 1) is closer to 2.9°C/W. Both of these values are used in different scenarios in figure 11.

Device package type/mechanical design: Up to this point, the TO-220-packaged variant of the IRL3713 transistor has been assumed, in conjunction with the use of some specified heat sink. Other heat sinks than those mentioned are available with different thermal characteristics, all of which are application-dependent to some degree. The transistor itself is also available in a surface-mountable D2PAK package, which offers a significant tradeoff between ease and cost of manufacture against thermal performance. In addition to the heat sink used for example in part 1, the surface mount option as characterized by the manufacturer (total junction-ambient thermal resistance =40°C/W) is included in the following scenarios.

Figure 11. This table shows results from basic thermal models as illustrated in part 1, for different application scenarios ranging from absurd (used in the derivation of rated drain current values) to convenient (surface mounting). It’s worth noting that even in the most aggressive of the practical design scenarios tabulated, the maximum permissible continuous drain current (ID) works out to less than a quarter of the headline value from page 1 of the datasheet. Using the surface-mount variant of the device under more conservative design conditions, the maximum permissible continuous drain current is approximately 10% of the advertised value.

Why Datasheets Hunt

The practice of characterizing the current-carrying capacity of devices such as the IRL3713 in impractical terms and calling the resultant figures by a name that doesn’t do well at signalling the fact may come across as being a bit disingenuous. At the least, it doesn’t make life any easier for the unwary or uninitiated. It is however, a situation that has developed over time and through consistency of practice.

The performance of early FETs in terms of both RDS(ON) and package thermal performance was poorer by a decimal place or two, and the currents and power dissipation levels involved were a decimal place or two smaller, as can be seen in the table of figure 12 for a FET from the late ‘90s. There was a need to communicate devices’ current carrying capacity, maximum junction temperature was typically the limiting concern, and some sort of standard conditions needed to be established to allow for meaningful comparison. Maintenance of the device’s case at room temperature (notionally 25°C) became that standard condition. Defining a case temperature is quite reasonable, from the standpoint of avoiding inclusion of an extra variable (an interface thermal resistance) in a product’s characterization. The 25°C number chosen might have even been reasonable too at some early point; with the earliest and most feeble devices, the condition might have been closely approximated by use of a large heat sink at room temperature.

The development of FET technology quickly eroded any direct relevance of drain current ratings based on a 25°C case temperature condition, however. By the time the PHP3055E was introduced for example, an oversized heat sink and a refrigerator would have been needed to achieve the advertised rating, for which thermal model results are shown tabulated in figure 12 under the same scenarios as used for the IRL3713 in figure 11. It’s worth noting that datasheets for many parts also include ID ratings based on higher case temperatures (such as 125°C) which are far closer to having direct application relevance.

Figure 12. Thermal model results for an older FET (a PHP3055E, Rev. 1 of the datasheet for which appears to date to 1997) using the same set of scenarios tabulated above for the IRL3713, which dates to around 2013. Note the ambient temperature figure of 3°C with which the manufacturer’s rated drain current could be realized given use of an oversized heat sink, and compare with the -196°C temperature needed to do the same for the IRL3713, according to the model used.

Information on earlier devices is relatively difficult to come by these days; the old databooks tend to get thrown away, and few suppliers bothered to create soft-copy datasheets for parts that were already end-of-life as the industry was migrating to online information transfer in the mid-late '90s.

The Moral of the Story

Were the content of this post to be condensed into a solitary nugget of insight, it might be this:

Do not presume that manufacturer’s current ratings are relevant to your application; evaluate all such things from a thermal management perspective in light of expected application conditions.

While low-voltage FETs like those used as examples here are likely the most eggregious offenders in terms of advertised values exceeding practical limitations, the principle applies to other product types as well. Discrete power semiconductors of all flavors are likely suspects, but current flows of all sorts that fall within rated limits can present unwelcome thermal surprises if left unevaluated. Stay alert–like other predatory creatures, datasheets prefer to attack when their targets are distracted…

Appendix A: Beware the Accomplice

As if thermal management for high-current devices themselves wasn’t bad enough, high-current applications also demand close attention to circuit board design, given the fact that copper is not a room-temperature superconductor. A one-inch length of half-inch wide PCB trace made of “heavy” 2 oz. copper (25x13mm, 70um thick, for the metric world) has an end-to end resistance of about half a milliohm. That would be seen as a very beefy trace and negligible resistance in a lot of applications, but the ~25A maximum drain current contemplated for a surface-mounted IRL3713 passing through it’s length would result in a power dissipation approaching a third of a watt, which one model for PCB trace heating suggests would cause in a temperature rise of about 20°C. Since surface-mounted parts use the PCB traces they’re attached to as a heat sink, that could result in the “ambient” temperature for the part being 20°C higher than expected if trace heating effects are neglected in one’s analyses. And what about that marquee 260A figure? Even with a 20oz (0.7mm) copper thickness, a half-inch wide, one-inch long PCB trace would dissipate over three watts when carrying such a current, suggesting a temperature rise upwards of 220°C. That liquid nitrogen bath might come in handy…

Figure 13. An approximation of what 1" total length of 1/2" wide trace (yellow region) between a D2PAK transistor and a set of high-current screw terminals might look like on a printed circuit board.

Appendix B: Cryogenics and Cocktail Napkins

Engineering folklore is filled with tales of calculations done on cocktail napkins or similar expedient materials(1)(2) during a moment of inspiration. Keen observers might note that the prospect of using a heatsink in a liquid nitrogen bath is rather off-label, and that using the published thermal resistance figures directly in that case is probably not valid. It’s a salient point, which begs at least for some napkin-grade calculations to better feel out just how far off the mark the notion might actually be.

The cooling effect of a liquid nitrogen bath is due largely to the energy needed to convert the stuff from a liquid to a gas; just as a pot of boiling water doesn’t get much above 100°C until the water’s been completely boiled off, so too a vat of liquid nitrogen doesn’t get much above -196°C until all the nitrogen is boiled off. In the theoretical attempt to extract rated performance from an IRL3713, it was estimated above that 333 watts of thermal power need to be extracted from the device. Based on known properties of liquid nitrogen, that’s enough power to convert about 1.7 grams of nitrogen from liquid to gas per second, which translates into an estimated gas volume flow rate of just under 0.8 cubic feet per minute (about 22 liters per minute) as shown in figure 14.

The 0.016 °C/W thermal resistance of the 345-1173-ND heat sink proposed for use in achieving the advertised drain current of the IRL3713 is characterized under forced convection conditions, with a 100 cubic foot per minute volume flow rate of air–more than two decimal places more flow than is expected to be generated. Ordinarily, a flow rate less than the manufacturer’s spec would result in a higher effective thermal resistance than published, in this case however, the gas being produced is extremely cold and will be about four times more dense than air at room temperature or thereabouts–and thus would be expected to be more effective at extracting heat from the surface of the heat sink through convection. Moreover, there’s the prospect of nitrogen in liquid form contacting the surface of the heat sink, which is 200 times denser still, and likely a comparable degree more effective at carrying heat away from a surface.

This leads into an interesting question and area of study; would it be primarily liquid or gaseous nitrogen in contact with the heat sink surface in this scenario, and (more to the point) what would the thermal resistance of this heatsink actually be in a vat of liquid nitrogen? It’s not a trivial thing to predict at all; boiling is actually a rather complex phenomenon, with heat transfer rates commonly being a non-monotonic (and forget about linear…) function of surface temperatures. Under such conditions, the apparent steady-state thermal resistance of a heat sink in a liquid nitrogen bath might be observed to vary depending on one’s order of operations, i.e. whether or not the heat sink was allowed to cool below some critical temperature prior to the application of thermal input power to the system.

Properties of nitrogen, courtesy of Airliquide:

  • Liquid density: 806 kg/m3
  • Boiling point @ 1 atm: -196°C
  • Heat of vaporization: 199 kJ/kg
  • Gas density at boiling point: 4.61 kg/m3

Figure 14. Estimation of evaporation rate for cooling a 333 watt load in a liquid nitrogen bath.

(1) If sight of a footnote reference causes you to immediately cease reading the main text and seek out the secrets that a footnote holds, congratulations–you’re well on your way to guarding against an attacking datasheet.

(2) Casual observation indicates that references to cocktail napkins in such context appear to have declined over time, in a manner roughly proportional to the deprecation of the three martini lunch. Availability of similar materials (most notably the reverse sides of envelopes) is also threatened by the invasion of electronic species. Experts disagree as to if and when alternatives will be found.

Appendix C: Suggested Reading

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