Active array temperature cannot be measured directly; therefore, it must be computed analytically from measurement points on the outside of the package, package thermal resistance, electrical power, and illumination heat load. The relationship between array temperature and the reference ceramic temperature (test point number 1 in Figure 8-11) is provided by the following equations:
Equation 1. TArray = Measured Ceramic temperature at location (test point number 3) + (Temperature increase due to power incident to the array × array-to-ceramic resistance)
Equation 2. = TCeramic+ (QArray × RArray-To-Ceramic)
where
- TCeramic = Measured ceramic temperature (°C) at location (test point number 3)
- 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)
- QArray = QElectrical + (QIllumination × DMD absorption constant (0.42))
where
- QElectrical = Approximate nominal electrical internal power dissipation (W)
- QIllumination = [Illumination power density × illumination area on DMD] (W)
- DMD absorption constant = 0.42
The electrical power dissipation of the DMD is variable and depends on the voltages, data rates and operating frequencies. The nominal electrical power dissipation of the DMD is variable and depends on the operating state of mirrors and the intensity of the light source. The DMD absorption constant of 0.42 assumes nominal operation with an illumination distribution of 83.7% on the active array, 11.9% on the array border, and 4.4% on the window aperture. A system aperture may be required to limit power incident on the package aperture since this area absorbs much more efficiently than the array.
Equation 3. Sample Calculation:
- Illumination power density = 2 W/cm2
- Illumination area = (1.4008 cm × 1.0506 cm) / 83.7% = 1.76 cm2 (assumes 83.7% on the active array and 16.3% overfill)
- QIllumination= 2 W/cm2 × 1.76 cm2 = 3.52 W
- QElectrical= 2.0 W
- RArray-To-Ceramic = 0.9°C/W
- TCeramic= 20°C (measured on ceramic)
- QArray = 2.0 W + (3.52 W × 0.42) = 3.48 W
- TArray = 20°C + (3.48 W × 0.9°C/W) =23.1°C