The active array temperature can be computed analytically from the temperature sense diode measurement, the thermal resistance from array to diode, the electrical power, and the illumination heat load. The relationship between array temperature and the temperature sense diode is provided by the following equations:

where

• T_ARRAY = computed array temperature (°C)
• T_DIODE = measured temperature sense diode temperature (°C)
• R_{ARRAY–TO–DIODE} = package thermal resistance from array to diode (°C/W)
• Q_ARRAY = total power, electrical plus absorbed, on the DMD array (W)
  Refer to Section 7.6.1 for details
• Q_ELECTRICAL = nominal electrical power dissipation by the DMD (W)
• Q_ILLUMINATION = absorbed illumination heat load (W)
• Q_INCIDENT = incident power on the DMD (W)

The temperature sense diode to array thermal resistance (R_{ARRAY–TO–DIODE}) assumes a non-uniform illumination distribution on the DMD as shown in Figure 7-5. For illumination profiles more uniform than the one highlighted in Figure 7-5, the value provided here is valid.  However, for more non-uniform profiles (e.g. Gaussian distribution), the thermal resistance will be higher. Please contact TI to determine an accurate value for this case.

The following sample calculations assume 10% of the total incident light falls outside of the active array and POM, and the mirrors are in the OFF state.

1. DMD Absorption Constant = 0.895 – 0.004783 × 90 = 0.46
2. Q_ELECTRICAL = 0.4 W
3. R_{ARRAY–TO–DIODE} = 0.8°C/W
4. Q_INCIDENT = 10 W
5. T_DIODE = 50°C
6. Q_ARRAY = 0.4 W + (0.46 × 10 W) = 5 W
7. T_ARRAY = 50°C + (5 W × 0.8°C/W) = 54.0°C