where
- TCeramic = Measured ceramic temperature (°C) at location (test point number 1)
- RArray-To-Ceramic = DMD package thermal resistance from array to outside ceramic (°C/W)
- QArray = Total DMD array power, which is both electrical plus absorbed on the DMD active array (W)
where
- QElectrical = Approximate nominal electrical internal power dissipation (W)
- QIllumination = [Illumination power density × illumination area on DMD] (W)
- DMD absorption constant = 0.42
- Illumination power density = 2 W/cm2
- Illumination area = (2.0736 cm × 1.1664 cm) / 83.7% = 2.89 cm2 (assumes 83.7% on the active array and 16.3% overfill)
- QIllumination= 2 W/cm2 × 2.89 cm2 = 5.78 W
- QElectrical = 4.4 W
- RArray-To-Ceramic = 0.5°C/W
- TCeramic = 20°C (measured on ceramic)
- QArray = 4.4 W + (5.78 W × 0.42) = 6.83 W
- TArray = 20°C + (6.83 W × 0.5°C/W) = 23.4°C
Micromirror array temperature cannot be measured directly; therefore, it must be computed analytically from:
- the measurement points (Figure 7-10)
- the package thermal resistance
- the electrical power
- the illumination heat load
The relationship between micromirror array temperature and the reference ceramic temperature (thermal test point TP1 in Figure 7-10) is provided by the following equations:
TARRAY = T CERAMIC + (QARRAY × RARRAY-TO-CERAMIC)
QARRAY = QELECTRICAL + QILLUMINATION
where
- TARRAY = computed array temperature (°C)
- TCERAMIC = measured ceramic temperature (°C) (TP1 location)
- RARRAY-TO-CERAMIC = thermal resistance of DMD package (specified in Section 6.5) from array to ceramic TP1 (°C/W)
- QARRAY = total power (electrical + absorbed) on the array (Watts)
- QELECTRICAL = nominal electrical power (Watts)
- QILLUMINATION = (CL2W × SL) (Watts)
- CL2W = conversion constant for screen lumens to power on DMD (Watts/lumen)
- SL = measured screen lumens
The electrical power dissipation of the DMD is variable and depends on the voltages, data rates, and operating frequencies. A nominal electrical power dissipation to use when calculating array temperature is 4.4 Watts. The absorbed power from the illumination source is variable and depends on the operating state of the micromirrors and the intensity of the light source. The conversion constant CL2W is based on the DMD input illumination characteristics. It assumes a spectral efficiency of 300 lumens/Watt for the projected light and an illumination distribution of 83.7% on the active array and 16.3% on the array border. The equations shown above are valid for a system with a total projection efficiency through the projection lens from the DMD to the screen of 87%.
Sample calculation for typical application:
- TCeramic = 55°C (measured)
- SL = 2000 lm (measured)
- QELECTRICAL = 4.4 Watts
- RARRAY-TO-CERAMIC = 0.5 °C/W
- CL2W = 0.00274 W/lm
- QARRAY = 4.4 + (0.00274 W/lm × 2000 lm) = 9.88 W
- TARRAY = 55°C + (9.88 W x 0.5 °C) = 59.9 °C