# Improve Your Power Designs Via A Better Understanding Of Thermal Resistance Data

Power MOSFET datasheets typically present thermal resistance data in two ways. First, one or more thermal resistance values are included in the maximum ratings table. Typically, the table lists a value for θjc (thermal resistance junction to case) if it’s appropriate for the package type as well as at least one value for θja (junction to ambient thermal resistance).

These values usually, but not always, are accompanied by notes detailing the thermal resistance measurement conditions such as the area, thickness, and material of the mounting pad on a printed-circuit board (PCB). While these thermal resistance values on a typical power MOSFET datasheet are valid for the conditions listed, it is unlikely they apply to a real-world system.

The typical real-world application hardware is characterised by packaged power MOSFETs surface-mounted to a PCB, where mounting pad areas on the PCB sometimes use thermal vias to additional conductive layers in the board. The typical system upon which datasheet thermal resistance values are based is a simple single-layer PCB operated in still air. This simple system does not comprise the air flow, additional heatsinking, or heat flow from neighboring powered devices typical of real-world hardware designs.

The second type of thermal resistance data found on power MOSFET datasheets is a curve displaying transient thermal response. This data can be more useful in determining a device junction temperature. But again, care must be practiced, as thermal transient data will often be based on a thermal system significantly different from a real-world system.

Consider first the steady-state thermal resistance values listed on a typical power MOSFET datasheet, θjc and θja. The well-known defining equations are:

θjc = (Tj – Tc)/Pd

and:

θja = (Tj – Ta)/Pd

where units are ºC/W, and:

Tj = device junction temperature
Tc = device case temperature
Ta = ambient temperature
Pd = instantaneous power dissipated by the device

Consider θjc. This parameter is associated with larger molded power MOSFET packages characterised by exposed drain pads, or mounting lead-frames, which can be soldered directly to the PCB. The exposed pad, and specifically the geometric centre of the pad, is usually considered the case, as described above. Common package types include the DPAK (TO-252), D2PAK (TO-263), SO8FL, and TO-220.

For the θjc value listed on the datasheet to be valid, 100% of the heat generated in the device must flow through the case, or in a typical real-world installation, from the die surface down through the die onto the lead frame and out into the board through the lead-frame connection to the board.

At first pass, this may seem to be valid. But in reality, significant heat will flow out through the mold compound to the package surface and edges, and some heat will flow out through package wire-bonds or clips to the PCB.

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The only package installation that can closely approximate 100% heat flow through the case is by mounting the device to an “infinite” heatsink or cold plate. Usually this installation is realised only in a laboratory, not in the real world.

Most, if not all, θjc values listed in power MOSFET datasheets assume an infinite heatsink. The values listed are then valid, but they’re of little use for a typical PCB application. Even where the devices are mounted to a heatsink, its capability is much more constrained than the cold plate used in thermal characterization.

At first glance it appears the problem of θjc is resolved if we instead use the listed θja value, as eventually all heat must flow out to the ambient. Thus the θja value from the datasheet is valid, but only for the conditions listed.

This is the rub, as how the part is mounted, where it is mounted in relation to other heat sources, and whether or not there is air flow across the device directly and significantly affects the θja value. It is unlikely a real-world application will match conditions listed for a datasheet θja value.

So what can we do to determine a device junction temperature? We can readily measure device power dissipation and temperature at some reference point. But we cannot readily use thermal resistance values listed on a typical datasheet, unless we know the system we are using matches that used to determine the datasheet thermal resistance values.

Transient thermal response data can help here, especially considering that in real-world applications, high instantaneous device power (and therefore the largest change in junction temperature) is of short duration. In most applications, typical high power duration ranges from a few microseconds to a few tens of milliseconds.

Key Observation
This is important when we consider Figure 1. This curve shows transient thermal response for a DPAK power MOSFET device, with die active area approximately equal to 6.3 mm2. The x-axis represents the duration of a single square wave power pulse. The y-axis represents thermal resistance.

The multiple curves on the graph represent different system conditions ranging from a cold plate measurement (i.e., junction to case thermal resistance) to multiple 2-oz copper mounting pad areas on a small FR4 circuit board in still air (junction to ambient thermal resistance).

The key observation is that for short power pulse durations, say less than 30 to 40 ms, all curves are essentially the same. This means for a single power pulse of duration less than the point where multiple curves begin to diverge, we can use the thermal resistance data to calculate peak junction temperature without concern about the system environment. The main device parameter affecting thermal resistance for short power-pulse durations is die active area.

So for power-pulse durations less than a few tens of milliseconds, the transient thermal response data is sufficient to determine peak junction temperature without regard to how well the real-world thermal system matches that on which the transient thermal response data is based.

However, this technique applies only to single-pulse or very low-duty ratio applications. So what do we do for multiple-pulse or repeating-pulse applications? In these cases, we can use the transient thermal response data to determine the rise in junction temperature for each short-duration power pulse, as described above.

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But if the time when the MOSET is off is not long enough for the junction temperature to return to initial conditions, the average junction temperature (Fig. 2) will continue to rise to a steady state value. This curve shows a series of power pulses at 50% duty ratio and the corresponding estimate for junction temperature. The delta junction temperature is nearly the same for each power pulse but the average (and peak) junction temperature slowly rises to a steady state value.

To understand at what rate the average junction temperature will rise, we must understand the entire thermal system. Unfortunately, this brings us back to our original problem—typical datasheet thermal resistance data often does not match that of a real-world system. If the real-world system can be modeled accurately, or accurate thermal resistance measurements can be made on the system, then junction temperature can be calculated for any series of power pulses.

Finding The Real World
Some power MOSFET suppliers, in addition to providing thermal resistance data on the datasheet, may also provide a resistor and capacitor network device thermal model. Such a network can be used with circuit simulation tools to calculate junction temperature for different power applications.

However, such models suffer the same issue previously discussed regarding thermal resistance data. The thermal models are developed assuming a specific system thermal environment, which likely does not match that of a real-world system.

Consider Figure 3. In this case, the transient thermal response is plotted for an SO8FL device for two cases: actual measured results and model predicted results. The y-axis is plotted as junction temperature rise. The test MOSFET was controlled to constant power (50 W) for various pulse widths and the starting and peak junction temperature indirectly measured via the source drain voltage drop of the body diode.

The measured data and model data diverge after pulse widths greater than 40 ms. This divergence is not necessarily an indictment that thermal models are not useful, but rather an illustration of the difficulty to model real world effects.

References

1. Roger Stout, ON Semiconductor Application Note AND8220, “How to Use Thermal Data Found in Data Sheets,” April 2006

2. David Billings, ON Semiconductor DPAK and SO8FL Thermal Models, 2009-2010