### Calculating Junction Temperature from Thermal

```DESIGN APPLICATION NOTE --- AN027
Calculating Junction Temperature from Thermal Resistance
DETERMINING THE JUNCTION TEMPERATURE APPLICATION
FROM DEVICENOTE
THERMAL
RESISTANCE
EA-101542
Rev A
FOR PACKAGED SEMICONDUCTOR DEVICES
To illustrate the thermal resistance of a packaged power semiconductor device, the analogy of an electrical resistor
network will be used. In the electrical resistor model the electrical resistance is defined by the potential difference
(voltage) across the resistor divided by the current through that resistor. In a thermal resistance the thermal
potential difference (temperature) divided by the thermal current (heat) through the thermal resistor defines the
thermal resistance, RTh.
Figure 1 will be used to illustrate the electrical resistor equivalent circuit for a semiconductor device. Starting from
the heat source (transistor junction), heat may transport through two paths. In the first path heat transfers from the
transistor junction, through the molding compound by conduction, and then to the air surrounding the device by
convection. In the second path, which is parallel with the first, heat flows from the junction of the device through
the lead, through the PCB, into the chassis by conduction and finally to the air surrounding by convection. The
second path is the primary focus of calculating the junction temperature since the majority of heat generated in the
device transports through this path. The following example illustrates how to calculate the junction temperature of
a device given its thermal resistance.
The first consideration involves how the device will be used in operation. If a significant amount of power is output
as RF energy, that energy is not being dissipated in the device and needs to be subtracted from the dissipated
power in the calculation of junction temperature. To account for this, the effective power (Peff) dissipated is
calculated by adding the DC and RF input powers (PDC & PRFin) and subtracting the RF output power (PRFout).
Peff = PDC + PRFin − PRFout
If the input and the output RF power are very small
compare to the DC power, Peff can be simplified to:
Peff = PDC
The remaining steps are illustrated in the following
example of determining the junction temperature of
a device, given its operating parameters and
thermal resistance.
Junction
High Thermal
Resistance Path.
Usually neglected
Dominant
Path
R Th, j - l
R Th, j - p
Package
Surface
or
Exposed
Backside
Ground
PCB
R Th, p - a
Air
R Th, l - p
Ground
R Th, p - c
Chassis
Firgure 1: Thermal Resistance Equivalent Circut
The information provided herein is believed to be reliable at press time.RFMD assumes no responsibility for inaccuracies or omissions.RFMD assumes no responsibility for
the use of this information, and all such information shall be entirely at the user’s own risk. Prices and specifications are subject to change without notice. No patent rights or licenses to any of the circuits described
herein are implied or granted to any third party.RFMD does not authorize or warrant anyRFMD product for use in life-support devices and/or systems.
Copyright 2002 RFMD All worldwide rights reserved.
522 Almanor Ave., Sunnyvale, CA 94085
Phone: (800) SMI-MMIC
1
http://www.RFMD.com
EAN-101542 Rev B
DESIGN APPLICATION NOTE --- AN027
Calculating Junction Temperature from Thermal Resistance
Example 1
Given the following information, calculate the junction temperature of a NGA-589 device.
Tchassis = 70oC where Tchassis is the temperature of the chassis that the PCB is attached to
P
= 1mW
P
RFin
V
= 50mW
RFout
= 5.0V
I
dev
= 80mA
dev
RTh, j - l = 100oC/W where RTh, j - l is the thermal resistance from the junction to the lead of the device
∆T Lead-PCB = 10oC where ∆T Lead-PCB is the temperature difference between the lead of the device and the PCB
∆T PCB-Chassis = 5oC where ∆T PCB-Chassis is the temperature difference between PCB and the Chassis
Solution:
Step 1: Calculate Effective Dissipated Power
Peff = PDC + PRFin − PRFout
(1)
Peff = [(5.0V ) * (0.080 A)] + (0.001W ) − (0.050W )
Peff = 0.351W
Step 2: Setup Junction Temperature Equation
TJunction = ∆TJunct −Chassis + TChassis
(2)
∆TJunct−Chassis = ∑∆Ti = ∑(RTh,i ) * (Peff )
(3)
i
i
where i is each thermal resistance from Fig. 1
Step 3: Calculate each ∆Ti from Fig. 1
∆TJunct − Lead = ( RTh , j −l ) * ( Peff )
from (3)
∆TJunct−Lead = (100o C / W ) * (0.351W )
PCB
Screw
NGA-589
Step 4: Solve Equation (3)
∆TJunct−Chassis = (35.1+ 10 + 5)o C
Chassis
Figure 2: Cross Section of a PCB Assembly
∆TJunct−Chassis = 50.1o C
Step 5: Solve Equation (2)
TJunction = ∆TJunct−Chassis + TChassis
TJunction = 50.1o C + 70 o C
TJunction = 120 .1o C
522 Almanor Ave., Sunnyvale, CA 94085
Phone: (800) SMI-MMIC
2
http://www.RFMD.com
EAN-101542 Rev B
```