Application Note 038
Discussion of Thermal Analysis and Junction Temperature Rise in Multi-Chip
Modules
By Nicolas Reginelli, Paul Musil and Bryan Horton Anaren Inc. -MSK Products;
Revised 10/28/2015
Introduction
Power dissipation and temperature rise is an important issue that needs to be considered
when designing high reliability microelectronics. The heat created by power dissipation can
cause specifications to drift out of tolerance and decrease the life of the part if not properly
managed. The majority of the heat is typically removed through the base plate or the bottom
of the device into a heat sink or PC board. Component junction temperatures are calculated
as a temperature rise from the case temperature. Each component is analyzed to verify that it
does not exceed the maximum junction temperature under the worst case operating
conditions. The operating conditions of a specific application will affect the thermal
characteristics of the part and will require thermal analysis. The operating conditions that
will impact thermal design include but are not limited to; operating case temperature, input
voltage range, output voltage, load current range, signal pin input voltage range, etc.
Thermal Model
The thermal model is used to predict the temperature at critical points in the assembly of a
microelectronic package. It consists of the thermal resistance, analogous to electrical
resistance, from the junction to case (RθJC), from the case to the heat sink (RθCS), and from
the heat sink to the ambient (RθSA). The junction temperature, TJ is defined as the
temperature of the active semiconductors on the die surface.
Governing Equation:
TJ = PD x (RθJC + RθCS + RθSA) + TA
Where:
TJ
PD
RθJC
RθCS
RθSA
TC
TA
TS
AN038
= Junction Temperature
= Total Power Dissipation
= Junction to Case Thermal Resistance
= Case to Heat Sink Thermal Resistance
= Heat Sink to Ambient Thermal Resistance
= Case Temperature
= Ambient Temperature
= Sink Temperature
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Examples
To gain a better understanding of thermal analysis as it applies to microelectronics; we will
use the MSK5985RH linear voltage regulator and the MSK0041RH medium power op-amp
as examples. Typically, thermal analysis is performed under worst case operating
conditions. In both examples, thermal grease is used as the case to heat sink interface. Most
thermal greases have an RθCS equal to 0.15°C/W.
Example #1
For the first example, the MSK5985RH is required to regulate a 3.0V input voltage down to
a 1.0V output voltage operating at a 1.5A output current.
1.) Find the power dissipated in the regulator:
PD = (Vin – Vo) * Iout
= (3.0V – 1.0V) * 1.5A
PD = 3.0W
2.) For a conservative design, set TJ = +125°C
3.) Assume ambient temperature; TA = +85°C
4.) Set RθCS = 0.15°C/W
5.) From the Electrical Specification table, RθJC = 3.2°C/W
6.) Rearrange the governing equation to solve for RθSA:
RθSA = [(TJ – TA) / PD] – [RθJC + RθCS]
= [(125°C - 85°C) / 3.0W] – [3.2°C/W + 0.15°C/W]
RθSA = 9.98°C/W
The heat sink in this example must have a thermal resistance of no more than 9.98°C/W to
maintain a junction temperature of less than +125°C.
Example #2
For the second example, the MSK0041RH is required to drive a 10V peak sine wave across
a purely resistive load of 100Ω with 0V of DC offset. The MSK0041RH has an RθJC of
90°C/W per output element. Each output transistor dissipates ½ of the total power therefore
the effective RθJC is equal to 45°C/W when the power is equally shared as in this example.
The power supplies are ±15VDC.
1.) Find the average power dissipated:
PDTot = PDq + PDout
PDTot = [Iq * (VCC+ – VCC-)] + [(4 * Vpk * (VCC+) – π * Vpk2) / (2π * RL)]
= [3.5mA * 30V] + [(4 * 10V * 15V - π * 100V2) / (2π * 100Ω)]
= 0.105W + [285.8V2 / (2π*100Ω)]
PDTot = 0.560W
2.) For a conservative design, set TJ = +125°C
3.) Assume room temperature, set TA = +85°C
4.) Set RθCS = 0.15°C/W
5.) Set RθJC = 45°C/W
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6.) Rearrange the governing equation to solve for RθSA:
RθSA = [(TJ – TA) / PD] – [RθJC + RθCS]
= [(125°C - 85°C) / 0.560W] – [45°C/W + 0.15°C/W]
RθSA = 26.3°C/W
The heat sink in this example must have a thermal resistance of no more than 26.3°C/W to
maintain a junction temperature of less than +125°C.
The formula for maximum output power dissipation for an op-amp driving an AC output
will change depending on the load.
For purely resistive loads:
PDout (max) =
(𝑉𝑐𝑐+ − 𝑉𝑐𝑐− )2
For primarily reactive loads (θ<40°):
PDout (max) =
(𝑉𝑐𝑐+ − 𝑉𝑐𝑐− )2
For primarily reactive loads (θ>40°):
PDout (max) =
(𝑉𝑐𝑐+ − 𝑉𝑐𝑐− )2
Where:
Vcc+ = Positive supply voltage
Vcc- = Negative supply voltage
ZL = Load impedance
θ
= Phase angle of load impedance
2∗𝜋∗𝑅𝐿
𝜋 2 ∗𝑍𝐿 ∗cos 𝜃
2∗𝑍𝐿
4
∗ �𝜋 − cos 𝜃�
It should also be noted that excessively low frequency signals will result in a higher
temperature peaks. The average power remains the same, but as the frequency decreases the
device experiences peak power for a longer duration of time. The thermal capacitance has
more time to charge leading to greater temperature swings. Power dissipation can typically
be averaged at frequencies that are greater than a few kilohertz.
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