Active array temperature can be computed analytically from measurement points on the outside of the package, the package thermal resistance, the electrical power, and the illumination heat load.

Relationship between array temperature and the reference ceramic temperature (thermocouple location TP1 in Figure 7-4) is provided by the following equations.

where

• T_ARRAY = computed DMD array temperature (°C)
• T_CERAMIC = measured ceramic temperature (TP1 location in Figure 7-4) (°C)
• R_{ARRAY-TO-CERAMIC} = DMD package thermal resistance from array to TP1 (°C/watt) (see Section 6.5)
• Q_ARRAY = total power, electrical plus absorbed, on the DMD array (watts)
• Q_ELECTRICAL = nominal electrical power dissipation by the DMD (watts)
• Q_ILLUMINATION = (C_L2W × S_L)
• C_L2W = conversion constant for screen lumens to power on the DMD (watts/lumen)
• S_L = measured screen lumens (lm)

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

Absorbed power from the illumination source is variable and depends on the operating state of the mirrors and the intensity of the light source.

Equations shown previous are valid for a 1-chip DMD system with total projection efficiency from DMD to the screen of 87%.

The constant C_L2W is based on the DMD array characteristics. It assumes a spectral efficiency of 300 lumens/watt for the projected light and illumination distribution of 83.7% on the active array, and 16.3% on the array border.

Sample calculation:

• S_L = 50 lm
• C_L2W = 0.00293 W/lm
• Q_ELECTRICAL = 0.105 W
• R_{ARRAY-TO-CERAMIC} = 5°C/W
• T_CERAMIC = 55°C
  Equation 3. Q_ARRAY = 0.105 W + (0.00293 × 50 lm) = 0.252 W
  Equation 4. T_ARRAY = 55°C + (0.252 W × 5°C/W) = 56.26°C

Figure 7-4 Thermocouple Location