[Design Application]
Calculate Dissipation For MOSFETs In High-Power Supplies
An iterative process that assumes a MOSFET junction temperature and works back to the maximum ambient temperature makes calculations easier.
Perhaps the toughest challenge that designers of portable power supplies face is powering modern high-performance CPUs. Recently, their supply currents have doubled about every two years. In fact, today's portable core supplies can require up to 40 A or more, at between 0.9 and 1.75 V. But while current requirements have increased steadily, the space available for power supplies has not—a fact that has stretched thermal designs to the limit and beyond.
Such high-current supplies are typically broken into two or more phases, with each phase handling between 15 and 25 A. This approach eases the component-selection task. For example, a 40-A supply essentially becomes two 20-A supplies. But because this approach doesn't create additional board space, it hardly eases the thermal design challenge.
The most difficult components to specify for high-current power supplies are their MOSFETs. This is especially true for notebook computers, an environment where heatsinks, fans, heatpipes, and other means of disposing heat are typically reserved for the CPU itself. Thus, the power supply often contends with cramped space, still air, and heat from nearby components. Moreover, nothing is available to aid power dissipation except some minimal amount of pc-board copper situated underneath the supply.
MOSFET selection begins by choosing devices that can handle the re-quired current, given an adequate thermal dissipation path. It ends when the thermal dissipation needed is quantified and the dissipation path ensured. This article provides step-by-step instructions for calculating the power dissipation of these MOSFETs and determining the temperature at which they operate. It then illustrates these concepts by stepping through the design of one 20-A phase of a multiphase, synchronous-rectified, step-down CPU core supply.
Calculating Power Dissipation: To determine whether or not a MOSFET is suitable for a particular application, you need to calculate its power dissipation. Resistive losses and switching losses mainly make up the dissipation:
PDDEVICE TOTAL = PDRESISTIVE + PDSWITCHING
Because a MOSFET's power dissipation depends greatly on its on-resistance (RDS(ON)), calculating RDS(ON) seems a good place to start. But a MOSFET's on-resistance depends on the junction temperature (TJ). In turn, TJ depends on the power dissipated in the MOSFET and the thermal resistance of the MOSFET (ΘJA). So it's hard to know where to begin. Because several terms within the power-dissipation calculation depend on each other, an iterative process is needed to determine this number (Fig. 1).
This process starts by first assuming a junction temperature for each MOSFET. The same procedure is implemented for both MOSFETs, individually. Both the MOSFET's power dissipation and allowable ambient temperature are calculated.
The process ends when the allowable ambient temperature is at or slightly above the maximum temperature expected within the enclosure that houses the power supply and the circuitry it powers. Making this calculated ambient temperature as high as possible may seem tempting, but it's not usually a good idea. Doing so would require a more expensive MOSFET, more copper underneath the MOSFET, or moving more air by a larger, faster fan—all of which would be unwarranted.
In a sense, this approach entails working backward. After all, the ambient temperature determines the MOSFET's junction temperature—not the other way around. But the calculations required when starting with an assumed junction temperature are easier to accomplish than when starting by assuming an ambient temperature and working from there.
For both the switching MOSFET and the synchronous rectifier, select a maximum permitted die junction temperature (TJ(HOT)) to use as a starting point for this iterative process. Most MOSFET data sheets only specify a maximum RDS(ON) at 25°C. But recently, some have offered maximums at 125°C as well. MOSFET RDS(ON) increases with temperature exhibiting typical temperature coefficients that range from 0.35%/°C to 0.5%/°C (Fig. 2). If in doubt, use the more pessimistic temperature coefficient and the MOSFET's 25°C specification (or its 125°C specification, if available) to calculate an approximate maximum RDS(ON) at your chosen TJ(HOT):
where RDS(ON)SPEC is the MOSFET on-resistance used for the calculation, while TSPEC is the temperature at which RDS(ON)SPEC is specified. Use the calculated RDS(ON)HOT to determine the power dissipation of both the synchronous rectifier and switching MOSFETs, as described below. The paragraphs that discuss calculating the power dissipation of each MOSFET at its assumed die temperature are followed by a description of the additional steps needed to complete this iterative process.
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