Thermal Resistance
Heat flows from a high temperature (T1) to a relatively lower one (T2) at a rate determined by the thermal resistance (Θ12) between the two points (see Figure 1).
Figure 1 Thermal Resistance
The thermal resistance is the temperature rise (in °C) for every watt dissipated for the system in question. Therefore, the expression in Equation 1 and Equation 2:
Equation 1: T1 – T2 = PD x Θ12
Equation 2: Θ12 = (T1 – T2)/PD
(Where: T1 = Temperature of Point 1, T2 = Temperature of Point 2, PD = Power dissipated in the device)
Relating this model to an IC, we can say that the device’s thermal resistance from junction to ambient (ΘJA) is equal to the junction temperature minus ambient, divided by power dissipation, or as expressed in Equation 3.
Equation 3: ΘJA = (TJ – TA)/PD
The device junction temperature can be expressed as a function of power dissipation and thermal resistance by Equation 4.
Equation 4: TJ = (ΘJA x PD) + TA
Heat is transferred from the die (heat source) to the air, through several material interfaces. The thermal resistance between these interfaces comprise the ΘJA of the system. These interfaces are typically the die-to-package (ΘJC), package-to-heat sink (ΘCS), and heat sink-to-air (ΘSA) (see Figure 2).
Figure 2 Heat transfer
The thermal resistance can now be written as shown in Equation 5.
Equation 5: ΘJA = ΘJC + ΘCS + ΘSA
Equation 6 shows the equation for thermal resistance from junction to case if No Heat Sink is used. We will use this case for the following example.
Equation 6: ΘJA = °C/W
Example 1:
In Part 1 of this series we discussed the power dissipation in the MCP1700, a low power quality LDO from Microchip Technology, who is a leader in Analog! :) The MCP1700 is available in 3 package options but we will continue to use SOT23-3 for this example.
The MCP1700 (250mA in a SOT23-3 package) is being used to regulate a 5V supply down to 3V. The ΘJA for a SOT23-3 package is 308°C/W. (Maximum junction temperature = 150°C)
From Part I of this post we learned PDmax = 0.35W and TAmax = 70°C
We can calculate the junction temperature under these conditions by using Equation 4.
TJ = (ΘJA x PD) + TA
TJ = (308°C/Wx0.35W) + 70°C
TJ = 177°C
This junction temperature is above the maximum limit. The highest power dissipation allowable in this case is:
PDmax = (TJA - TJAmax)/ΘJA
PDmax = (150°C - 70°C)/308°C/W
PDmax = .26W
This example shows how critical thermal considerations are in designing your system. Due to the high ΘJA, the designer should consider keeping the system operating temperature lower through cooling techniques or select a more thermally capable package. The MCP1700 is also available in a TO92 and SOT89 packages, which have much better thermal characteristics.
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