Figure 6-4 DMD Thermal Test Points

The active array temperature can be computed analytically from the thermal measurement point on the outside of the package, the package thermal resistance, the electrical power, and the illumination heat load. The relationship between array temperature and the reference ceramic temperature (TP1) in Figure 6-4 is provided by the following equations:

where

• T_ARRAY = computed array temperature (°C)
• T_CERAMIC = measured ceramic temperature at the TP1 location in Figure 6-4 (°C)
• R_{ARRAY–TO–CERAMIC} = DMD package thermal resistance from array to thermal test point TP1 (°C/W),
  
• Q_ARRAY = total power (electrical plus absorbed) on the DMD array (W)
• 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 DMD absorption constant is a function of illumination distribution on the active array and the array border, angle of incidence (AOI), f number of the system, and operating state of the mirrors. The absorption constant is higher in the OFF state than in the ON state. Equations to calculate the absorption constant are provided for both ON and OFF mirror states. They assume an AOI of 34 degrees, an f/1.7 system, and they account for the distribution of light on the active array, POM, and array border.

Electrical power dissipation of the DMD is variable and depends on the voltages, data rates, and operating frequencies.

The DMD package thermal resistance from array to ceramic (R_{ARRAY–TO–CERAMIC}) assumes a non-uniform illumination distribution on the DMD as shown in Non-Uniform Illumination Profile figure. For illumination profiles more uniform than the one highlighted in Non-Uniform Illumination Profile figure, the value provided here is valid.  However, for more non-uniform profiles (for example, Gaussian distribution) the thermal resistance will be higher. Please contact TI to determine an accurate value for this case.

Figure 6-5 Non-Uniform Illumination Profile

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. T_CERAMIC = 50°C (measured)
2. Q_INCIDENT = 10W (measured)
3. DMD Absorption Constant = 0.895 – 0.004783 × 90 = 0.46
4. Q_ELECTRICAL = 0.4W
5. R_{ARRAY–TO–CERAMIC} = 1.5°C/W
6. Q_ARRAY = 0.4W + (0.46 x 10 W) = 5W
7. T_ARRAY = 50°C × (5W x 1.5°C/W) = 57.5°C

When designing the DMD heatsink solution, the package thermal resistance from array to reference ceramic temperature (thermocouple location TP1 can be used to determine the temperature rise through the package as given by the following equations: