The power budget calculator estimates the maximum (or idealized) heat dissipation on a passive device. The calculation is based on the assumption that all surfaces dissipate heat at a uniform temperature.

    The heat dissipation in a real device can be considerably lower. The idealized value can be adjusted by a factor (0 – 1).

    Example: Determine the power budget for the new iPhone 6+. The product dimensions are, length 77.8 mm, width 7.1 mm, and height 158.1 mm. Assuming an ambient temperature of 25 °C and maximum touch temperature of 40 °C (metal/glass surface). The calculator estimates  an ideal budget of 4.3 W. Considering the iPhone 6+ is a well designed product (thermally), a factor of 75% efficiency is applied to give a total power budget of 3.2 W.

    These estimations help thermal designers to quickly determine if a product can be passively cooled.

    The calculator determines the maximum heat removed by convection and radiation. The device is assumed to be floating in air.
    Heat dissipation by radiation:

        \[ q = \epsilon\ \sigma\ A(T_{Surface}^4-T_{Amb}^4) \]

    Heat dissipation by convection:

        \[ q=h\ A(T_{Surface}-T_{Amb}) \]


        \[ h=\frac{Nu\ k}{L} \]

    The Nusselt number is then calculated using empirical correlations.
    Top surface:

        \[ Nu=0.54\ Ra_L^{1/4}\quad 10^4<Ra_L<10^7\\ \]

        \[ Nu=0.15\ Ra_L^{1/3}\quad 10^7<Ra_L<10^{11}\\ \]

    Bottom surface:

        \[ Nu=0.27\ Ra_L^{1/4}\quad 10^5<Ra_L<10^{10} \]

    Sides, front and back:

        \[ Nu=0.68+\frac{0.67\ Ra_L^{1/4}}{[1+(0.492/Pr)^{9/16}]^{4/9}}\quad Ra_L<10^9 \]

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3 Responsesso far.

  1. Yin Xiong says:

    I have similar calculator built in Excel based on the same equations you presented. A couple of suggestions:
    1. different surface material has different emissivity. You can add more details here.
    2. Show how you calculate characteristic length. This relates to the orientation of the box;
    3. Show how you get the air properties based on which temperature.

  2. FTD Admin says:

    Hi Yin
    1 The calculator assumes all surfaces have the same emissivity. Not true for all cases.
    2 Right now the calculator assumes the devices is floating in free air on vertical orientation (the height should be aligned with the gravity vector). Again not true for all cases.
    3 Air properties are calculated from the given ambient temperature.
    More details can be easily added but the main idea of the calculator is to get a quick estimation of the power dissipation assuming a Cu-block case (all surfaces dissipating heat at a uniform temperature).
    Thanks for your valuable comment!

  3. This article is about the thermal design envelope of microprocessors. For the general concept, see power rating .

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