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June 2017 • The PCB Magazine 25 conductive material comes in various sheet re- sistivities. The sheet resistivities range from 10 ohms per square to 250 ohms per square [3] . Each sheet resistivity has an associated power densi- ty rating which is a rating of safe power per unit area. The chart below details typical power den- sity data for the nickel phosphorus (NiP) resis- tive conductive material. Figure 3 shows that lower sheet resistivi- ties can operate at higher power densities. It is recommended to select sheet resistivities with the highest power density. Figure 4 illustrates how the resistor/heater size and power effect the temperature rise. The takeaway from the chart is that smaller areas get hotter for any giv- en power. Notice also the linear relationship be- tween temperature and power. Figure 5 shows a test conducted to measure temperature rise versus time for a NiP resistor fabricated on polyimide flex material. Let's take an example. Suppose 1 W is need- ed to heat a piece of silicon 12.7 mm by 12.7 mm (0.5 inch x 0.5 inch) with a thickness of 1 mm to 150°C in less than 60 seconds. The appli- cation has a fixed voltage source of 3.3V. Using the equations for power and Ohm's law, it is de- Figure 3: Power density plot for NiP resistive conductive material. Figure 5: Temperature rise versus time for NiP resistor on polyimide flex substrate. Figure 4: Temperature versus power for different size resistors/heater using 10 ohms per square. THIN FILM NiP EMBEDDED RESISTORS IN HEATER APPLICATIONS