# Texas Instruments | Using Thermal Calculation Tools for Analog Components (Rev. A) | Application notes | Texas Instruments Using Thermal Calculation Tools for Analog Components (Rev. A) Application notes

```Application Report
SLUA566A – September 2010 – Revised September 2019
Using Thermal Calculation Tools for Analog Components
Siva Gurrum and Matt Romig
ABSTRACT
This document provides general guidance on the use of tools and calculations for thermal estimates of
component operating temperatures for analog devices. Of particular focus are components with direct
thermal paths to the PCB, which is common for components which need a low thermal resistance to
manage the dissipated power. This document provides practical considerations for estimation of operating
temperatures while still in the design stages of the system. All device operating temperatures must be
confirmed with measurements to ensure the maximum operating specs are met.
1
Component Thermal Classification
For the purposes of this discussion, electronic components are classified into three categories with regard
to their power dissipation and required thermal resistance. These are not rigid categories, and are a
function of several parameters such as:
• Package size
• Construction
• Materials
• Die size
• Power dissipation profile
These categories can serve as a general guideline when considering the level of thermal analysis needed
for a component during system design.
a. The first category is referred to as “low power” components. These are generally components such as
passives, logic devices, or other components that do not dissipate high levels of power during
operation. Low power components generally do not require any thermal analysis, and can be designed
into almost any system without concern of exceeding the maximum operating characteristics. There is
no rigid definition of this category but, generally, if the temperature rise in an appropriate JEDEC
thermal test environment, as calculated by the test coupon Theta-JA (θJA) multiplied by the power (θJA x
Power), is less than 10°C, it can be considered low power. Depending on the component construction
and application environment, the tolerance for low power could be as low as 100 mW or less, or could
reach as high as 500 mW or even 1 W (for example, in systems with forced airflow). Ultimately, if there
is any uncertainty, a component should be considered in the next category.
b. The second category is referred to as “medium power” components. These are generally components
which are dissipating enough power that their maximum operating temperatures may be exceeded, if
care is not taken with good system and PCB design. These components have generally been designed
to operate safely, provided that they are able to dissipate heat through a specific thermal path. For
example, many medium power components are designed with a direct thermal path, such as an
components require some thermal consideration during system design, and verification with
measurements on the assembled system is essential. Because their heat dissipation paths are often
carefully considered by the component supplier, medium power parts can often be analyzed during the
system design phase using calculators or simplified modeling approaches, and then confirmed with
measurements during the prototype phase. For these reasons, this document focuses particularly on
methods to design for medium power devices, and particularly those using exposed pads to connect to
the PCB thermal path. There is no rigid definition of this category but, generally, components that have
a temperature rise of at least 10°C above the ambient temperature can be considered as medium
power, or possibly even in the next category. This temperature rise can be estimated by multiplying the
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appropriate JEDEC θJA by the power (θJA x Power), but this calculation should only be considered as
preliminary. and as an initial threshold for more thorough analysis. Some examples of components
which are considered “medium power” are those which have a high temperature rise above the
ambient or PCB temperature, components that operate in an environment with high ambient
temperatures, or components that is in close proximity with other parts that contribute to the
temperature rise of the PCB and overall system.
c. The third category is referred to as “high power” components. These are generally components that
require careful and proactive system thermal design and validation to ensure maximum operating
specifications are not exceeded. High power components often require specific thermal management
solutions such as heat sinks, chassis conduction paths, or forced airflow. System designers are
encouraged to perform detailed system analysis using modeling tools or test components for high
power components to ensure the optimal heat dissipation path is available in the system. There is no
rigid definition of this category but, generally, components that have a high temperature rise above
ambient, and thus require a carefully designed thermal path (above and beyond traditional PCB layout
best practices), can be considered as high power.
In summary, there are no rigid definitions or universally accepted guidelines for component thermal
management, due to variations in the component construction, PCB construction and layout, and system
environment. For the general category of “medium power” components that are designed to dissipate heat
through a specific thermal path, it is often possible to use calculators or simplified approaches during the
system design phase.
2
Exposed pad packages are commonly used for medium power components. This is because they provide
a low thermal resistance through the exposed pad to the PCB, and when the PCB is designed
appropriately, it is often sufficient to operate the components within the maximum operating conditions.
Exposed pad packages generally consist of an IC die sitting on a copper pad, where the copper pad is
exposed on the outside surface of the component package. Some examples of exposed pad packages
include:
• HQFP (thermal QFP and variations such as TQFP and LQFP)
• HTSSOP (thermal TSSOP and variations such as SSOP and VSSOP)
• Older power packages such as TO or DDPAK families
Figure 1 illustrates some examples of these packages.
QFN/SON
QFP
xSOP/SOIC
TO
Figure 1. Examples of Exposed Pad Packages
The means of heat dissipation out of exposed pad packages (often referred to as the “thermal path”) is
illustrated in Figure 2. The heat is generated on the top of the IC die. The heat then flows down through
the die, which is generally composed of silicon, which is a strong thermal conductor. Then the heat flows
through the die attach material, which is generally a thin layer of epoxy with moderate to poor thermal
conductivity. The heat then flows through the die pad, which is generally a copper alloy that has very high
thermal conductivity and helps to spread the heat out. This overall thermal path enables thermal
dissipation from the exposed die pad out into the PCB and system with relatively low thermal resistance.
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Thermal Path (red arrows)
IC Die
Die Attach
(Epoxy)
(Exposed)
Figure 2. Exposed Pad Package Thermal Path
3
PCB Design
PCB design is essential for the thermal management of medium and high power components. In many
cases, PCB design is more consequential than the component or package characteristics themselves! For
high power components, or components in particularly harsh systems, detailed, system-level thermal
modeling or prototype measurements are often required. Medium power components are cooled primarily
through the PCB thermal vias and copper planes. In this case, PCB design is the primary consideration for
thermal management. As PCB thermal factors are reasonable to estimate, they can often be adequately
addressed with good design practices, tools such as calculators or simplified modeling, and measurement
confirmation on the final system.
Several key factors impact PCB design for medium power components in exposed pad packages See
SLMA002 for more detail. Additionally, design rules are included in the data sheet for all devices with an
exposed pad. A short summary of the main factors are listed here and illustrated in Figure 3.
a. Landing pad: the landing pad on the top of the PCB must be the same size or larger than the exposed
pad of the component. The component must be soldered to the pad with reasonable coverage to
ensure good heat conduction from the component to the PCB (See SLMA002 for more details on
soldering). The outermost portions of the landing pad must be free from solder mask, as these are the
most important for spreading into the PCB.
b. Spreading plane: there must be at least one Cu spreading plane in the PCB. This plane serves to
conduct the heat from the small area of the component to a larger area in the PCB, where the heat is
then dissipated through convection and radiation into the surrounding environment. As such, the plane
must have sufficient thickness and area to provide adequate heat sinking for the component.
Electrically, the plane is normally held at ground for exposed pad packages. As illustrated in Figure 2,
the spreading plane may be located on the top layer and directly connected to the landing pad. This is
often the case for packages such as TSSOP or SON. The spreading plane (or planes) may also be
located on a buried layer (or layers) and connected to the vias. Buried spreading planes are commonly
used with packages such as QFN or QFP.
(connected to vias)
Thermal Path (red arrows)
Thermal vias
Figure 3. PCB Thermal Path
c. Vias: When a buried spreading plane is employed, the landing pad must be connected by an array of
vias to the buried plane to ensure good heat conduction from the exposed. See SLMA002 for details
on via designs. A landing pad with insufficient vias to buried power and ground planes will not conduct
sufficient heat from the package into the PCB spreading planes, and high temperatures may result.
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The spreading plane is of particular importance to the thermal performance of exposed pad packages, and
must be one of the primary considerations in PCB design. For adequate thermal management, it must
have a specific area. The larger the spreading plane, the cooler the devices will run, so it must be as large
as possible beyond the minimum area. Thermal analysis must be performed to ensure the plane meets
the minimum area required to keep the junction temperature below the absolute maximum temperature.
Figure 4 shows an example of a graph that illustrates the impact of spreading plane area on junction
temperature for an example device and PCB stack-ups. More precise definitions of Enhanced and
Minimum Thermal PCBs are described in later sections. The area of the spreading plane (assumed to be
continuous, and having no breaks) is shown on the x-axis, and the resulting temperature is shown on the
y-axis. It can be noted that below a certain size, the temperature rises dramatically, as there is little copper
area available to cool the component. Similarly, for a copper area larger than a certain size, the impact on
the temperature diminishes significantly as the heat is sufficiently spread out.
Figure 4. Example Graph Showing Junction Temperature as a Function of Spreading Plane Area for the
TAS5701PAP Device at 0.5 W With 65°C Ambient Temperature
4
System Design Using Spreading Plane Estimates
A good, system-level thermal design and analysis must account for the primary factors in the system that
influence the flow of heat from the component out to the surrounding environment. It is often not practical
to analyze these factors in the full level of detail (through modeling or prototyping) due to restrictions of:
• Time
• Cost
• Availability of tools or expertise
• Resolution of fine geometric or thermal details
During system design, thermal estimates are often made to predict final thermal performance. These
estimates can include
• Explicitly using simplified tools or methods
• Implicitly using rules or thumb
• Basing decisions on historical success
• Planning for large margins of error
• Other methods of varying complexity
For low or medium power components using exposed pad packaging, where the board temperature
cannot be measured during the design stages, there are several reasonable methods of simplification that
can be used. Several of these are described here:
a. PCB layout is an important thermal design factor. The presence of the landing pad and vias, and the
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design and size of the spreading plane, are important for heat spreading to eventually transfer to the
surrounding environment. The variability in a real system is often due to PCB stackup (Number of
layers, thickness of Cu foil and plating, and plane design). Systems that plan to use medium power
components must have at least one spreading plane. This plane must be reasonably continuous
(minimal breaks in the direction of heat flow) in the area that is considered for spreading. The minimum
thickness of a spreading plane in a typical PCB is 0.5 Oz. Often, PCBs are enhanced by using planes
that are 1 Oz, or in rare occasions, even thicker. The presence of thicker or additional thermal
spreading planes can give further improvement, but the effect can be diminishing. For medium power
components with a reasonably continuous spreading plane, rather than analyzing the detailed plane
layout, it is a reasonable simplification to use a single continuous spreading plane of 0.5 to 1 Oz.
b. Other components on the PCB can have a significant thermal effect on the component of interest
depending on their design, thermal dissipation, and proximity. Every system and every component is
different, so it is nearly impossible to analyze in full detail the full list of components on the PCB, and
simplifications must be made. The first simplification that is commonly taken is to ignore components
such as passives, which have very low dissipation, and to focus only on components that have more
than 50–500 mW of dissipation (depending on the system and accuracy needed). The next level of
simplification, which is effective for focusing on a specific component is to use symmetry (or adiabatic)
lines which do not allow heat flow across them, so that the interaction between components is
effectively negated. Medium power components often have a spreading plane that is effectively
dedicated for them, so it is reasonable to draw symmetry lines around the spreading plane. For
components which share a spreading plane, it is reasonable to divide the total spreading plane area by
the number of components (or a ratio of their power dissipation), to derive an effective Cu spreading
plane area to use for calculations.
c. The design of the enclosure in which the PCB sits is an important contributor to the effectiveness of
the convection of the heat from the PCB to the surrounding air. Medium power components often do
not have forced airflow, and are cooled by natural convection. The effectiveness of natural convection
cooling is often dictated by the freedom of air to circulate within the enclosure. One important factor is
the orientation with respect to the gravitational direction, as a vertically-oriented PCB can create a
strong “chimney effect” which aids in the effectiveness of the convection. Unfortunately, it is rarely
possible to ensure that a system stays oriented vertically during use, so a horizontal orientation is the
conservative simplification to use. Another important contributor is the open space above or below the
PCB where the air to circulates. The rule is that if the space above and below the board is less than 6
mm and there is no fan circulating the air, there is no convection. This case is not considered by the
simple board level junction temperature estimator.
In summary, analysis of many medium power components during the design stage can be simplified using
assumptions of a 0.5 to 1 Oz continuous spreading layer in the PCB, which uses symmetry lines for heat
flow to focus on a particular component, using typical convection calculation methods if the available
space above the PCB is greater than 6 mm.
5
Calculations Using Board Temperature
The best and most accurate method to estimate the component temperature (often called operating
temperature or junction temperature) is to use the board temperature. If the board temperature and
component power dissipation can be estimated, then the component temperature can be estimated using
the Equation 1:
TJ = TB + Pdiss x ΨJB
(1)
Where:
• TJ = Junction temperature of the device
• TB = Board temperature (1 mm from device, as defined by JESD51-2)
• Pdiss = Power dissipated by the device
• ΨJB = Junction to board thermal parameter (as defined by JESD51-2 or customized for a lesser PCB
stackup)
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TI’s PCB Thermal Calculator
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In this case, the calculation can be made independently of the PCB layout and is much simpler, provided
that the board temperature used can be maintained in the subsequent system environment. It should also
be noted that a PCB with a minimal thermal stackup (such as a single 0.5 Oz plane for heat spreading)
has a higher spreading resistance under the package, which can raise the ΨJB value up to 25% higher
than the JEDEC value.
6
TI’s PCB Thermal Calculator
To support the growing needs for quick and simplified analysis during the system design stage of medium
power components that use exposed-pad packaging, TI has used simplifications like those described in
Section 4 to create a calculator. This calculator is available at www.ti.com/pcbthermalcalc. This calculator
may be used for many of TI’s components to generate a quick estimate of the expected junction
temperature based on the Cu spreading area on the PCB.
Note that this calculator is based on detailed modeling and measurements under specific conditions, so
care must be taken to ensure that the simplifications made are appropriate to the system of interest.
These simplifications are described in Section 4, and the details of the data used for TI’s calculator are
described in this section. The modeling approach used in TI’s PCB Thermal Calculator are based on
measured data considering two packages on three PCB designs with two stackups, including three of the
four interactions, for a total of nine sets of data. The two packages included were the 48PHP (HTQFP
package requiring a buried spreading plane on the PCB), and the 56DCA (HTSSOP package allowing top
spreading plane on the PCB). The three PCB designs include Cu spreading areas of 25 x 25 mm, 40 x 40
mm, and 74 x 74 mm, as illustrated in Figure 5 and Figure 6. The two stack-ups include one with a thin
spreading plane of 0.5 Oz (measured at 17 µm), and a thick spreading plane based on plating and
measured at 62 µm to 73 µm.
74 mm
40 mm
74 mm
40 mm
25 mm
25 mm
Design 1
Design 2
Design 3
Design of Thermal Spreading Plane (Buried Layer)
Figure 5. PCB Designs for Thermal Measurements of HTQFP Package with Buried Spreading Plane
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74 mm
40 mm
74 mm
40 mm
25 mm
25 mm
Design 1
Design 2
Design 3
Design of Thermal Spreading Plane (Top Layer)
Figure 6. PCB Designs for Thermal Measurements of HTSSOP Package with Top Layer Spreading Plane
The measured data was collected using a K-factor thermal test die in a still air enclosure, using the test
methods defined in JESD 51-1, 51-2 and 51-4. Detailed models were then run to correlate specifically to
the measured data. Examples of the detailed models are shown in Figure 7, and the correlation of the
modeled to measured data is shown in Table 1. All of the modeling conditions correlated within 10% of
measured data across the entire range of packages, spreading planes, and considering part to part and
measurement to measurement variation. It must be noted that the spreader plane thicknesses considered
in TI’s calculator do not exactly match the thicknesses measured in PCBs used for thermal
measurements. Even though the goal was to match the PCB constructions used in calculator and
measurements, lack of precise plating thickness control lead to different final spreader plane thickness for
the outer layers. Such deviations are not uncommon due to PCB manufacturing technology, which
involves plating to form vias, which also plates copper over the outer exposed copper foils. Nevertheless,
the thicknesses considered in calculator are within the 17 µm and 73 µm range found in PCBs used for
measurements (they are interpolating, not extrapolating). The modeling approach was kept same for all
the measured cases and was calibrated for these differences between measured geometry and calculator
conditions. The error was within 10% for all cases, which is well within typical error ranges for thermal
measurements and modeling.
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Package
56 DCA Inline
Package
Temperature (deg C)
57.7
Temperature (deg C)
65.2
50.3
56.2
42.9
47.2
35.5
38.1
29.1
28.2
20.1
20.8
Figure 7. Examples of Detailed Models for Correlation to Measured Data
Table 1. Summary of Modeled and Measured Data
Package
Type
Plane
Thickness
17 µm
48PHP
62 µm
56DCA
73 µm
Plane
Size (mm)
θJA
θJB
Measured
Average
(C/W)
Model
Prediction
(C/W)
Deviation
(%)
Measured
Average
(C/W)
Model
Prediction
(C/W)
Deviation
(%)
25 x 25
51.5
52.8
2.6
17.1
18.5
8.1
40 x 40
46.9
48.2
2.6
17.3
18.3
5.8
74 x 74
43.9
44.7
1.9
17.3
18.4
6.5
25 x 25
40.5
44.0
8.8
13.1
14.3
9.7
40 x 40
34.7
36.4
4.9
12.7
12.8
0.9
74 x 74
31.7
29.9
-5.5
13.7
12.6
-8.4
25 x 25
39.5
41.9
6.2
9.9
10.8
8.9
40 x 40
34.4
34.6
0.6
10.1
10.3
2.2
74 x 74
30.3
29.0
-4.2
10.5
10.3
-2.2
This section provides a summary of modeling used to generate actual calculator data, the interpolation
approach, and validation cases.
a. The TI PCB Thermal Calculator estimates junction and board temperatures for devices using a thermal
resistance network from junction to ambient. For the user-selected device, thermal resistances in the
network are interpolated from pre-generated resistance data on different package sizes and exposed
pad sizes. The thermal resistance data is generated from CFD simulations using commercially
available thermal modeling software. Specific details on the simplified model are shown in Figure 8 and
Figure 9. For exposed-pad packages, the primary heat flow path is through the exposed pad itself. For
general applicability, the package model ignores the variations in leadframe geometries that are found
in customized designs for real devices. PCB traces on the top plane are treated as patches with
orthotropic thermal conductivity in the in-plane direction. In the case of quad packages, thermal vias
are modeled as an orthotropic block with effective properties. This simplifies parametric simulations
needed for thermal resistance data generation. System details and layout of the metal stack-up in
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PCBs is summarized through Figure 8, Figure 9, and Table 2. PCB constructions are based on
recommendations as indicated in SLMA002 for thermal design of spreader plane and vias.
h = 6 W/m2K
Package
LX
Air
Solder
304.8 mm
Trace patch 42 μm
thick, 50% Cu
coverage
LY
PCB Dielectric FR-4
1.6 mm thick
Board
Temperature
Location
Orthotropic Via
Block, 0.3 mm
diameter, 25 μm
plating at 1 mm
pitch
LX = LY
PCB Copper Area = LX*LY
LX
h = 6 W/m2K
Figure 8. System Model Details for Quad Packages
h = 6 W/m2K
Package
LX
Air
Solder
304.8 mm
Trace patch, 50% Cu
coverage
LY
PCB Dielectric FR-4
1.6 mm thick
Board
Temperature
Location
LX = LY
PCB Copper Area = LX*LY
LX
h = 6 W/m2K
Figure 9. System Model Details for Inline Packages
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TI’s PCB Thermal Calculator
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Table 2. PCB Construction for Quad and Inline Packages
PCB Feature
Inline Packages
Minimum Thermal PCB EnhancedThermal PCB MinimumThermal PCB EnhancedThermal PCB
17-µm thick 1st Buried
plane
35-µm thick 1st Buried
plane
42-µm thick top plane
(0.5 Oz + 25 µm plating)
60 µm thick top plane (1
Oz + 25 µm plating)
Trace Patch
42 µm top plane at 50%
Cu Coverage
42 µm top plane at 50%
Cu Coverage
42 µm top plane at 50%
Cu Coverage
60 µm top plane at 50%
Cu Coverage
Thermal Vias
None
None
Spacer
b. The calculator uses the resistance network shown in Figure 10 to generate curves for temperature rise.
Heat transfer from an exposed-pad package can be divided to flow through three paths: a) bottom of
the package through the PCB to ambient air, b) top of the package to ambient air, and c) four sides of
the package to the ambient air. Thermal resistances for these paths are extracted from more than a
thousand CFD simulations with package and PCB copper area variations. For the user-selected
device, each of θTOP, θSIDE, θCA thermal resistances are interpolated from the extracted thermal
resistance data. θCA is in turn calculated by summing the Case-to-Board and Board-to-Ambient thermal
resistance, where the latter depends on the PCB copper spreading area. Once these resistances are
calculated, the Junction-to-Ambient thermal resistance θJA and junction temperature TJ are calculated
using the following analysis for thermal resistances in parallel:
1
1
1
1
=
+
+
q JA q JC ,Bottom + qCA qTOP qSIDE
TJ = q JA ´ Pdiss + TA
(2)
Board temperature can be estimated using thermal characterization parameter θJB as follows:
TB = TJ - ΨJB x Pdiss
(3)
where: θJB is interpolated from extracted thermal characterization parameter data and device specific
Junction-to-Case thermal resistance θJC,Bottom.
Figure 10. Schematic of Thermal Resistance Network
The interpolation approach was additionally validated with detailed models on packages not used in
generating thermal resistance data. Validation was performed for two different package sizes for each
of the Quad and Inline categories. As a further challenge, internal package features such as die size
and pad size are varied to result in a wide range of θJC,Bottom values. The validation is summarized in
Figure 11 for Quad, and Figure 12 for Inline packages. The interpolation approach predicts thermal
resistance well for both Enhanced Thermal and Minimum Thermal PCBs.
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Figure 11. Validation of Interpolation Approach for Quad Packages
Figure 12. Validation of Interpolation Approach for Inline Packages
c. As an example of calculator usage, Figure 13 shows the output curves from the calculator for
TPS74201RGWR device in a 5 x 5 mm Quad package with θJC,Bottom of 2.4°C/W . In this example, the
user inputs a power dissipation value of 1 W with a 50°C ambient air temperature. Upon clicking the
Update button, two curves are plotted in the window for each type of PCB. The curves show the
junction temperature and board temperature as a function of PCB copper coverage area. Larger
copper area leads to lower temperatures.
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Summary
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Figure 13. TI PCB Thermal Calculator Example
d. There are a few key assumptions (made by the calculator) to note when analyzing the results obtained
from the tool. First, the ambient temperature is the ambient air temperature to which the copper cooling
area of the PCB is exposed. This ambient temperature is not necessarily the same temperature as the
external ambient temperature, nor is it the same as the ambient temperature that is measured at other
locations in the system. Next, the calculator assumes that the copper spreading area is entirely
dedicated to the selected device. If other hot devices are on the same copper plane, then the copper
spreading area used to determine the junction temperature must be scaled down based on the power
dissipation ratio of the devices. Also, the CFD simulations used to create the resistance networks
includes the effects of natural convection, which typically requires at least 6 mm of space above and
below the PCB for air currents to develop. For tighter enclosures, the loss in effectiveness of the
convection must be considered. Finally, for exposed-pad packages, the PCB is often the primary
contributor to thermal resistance. The PCB thermal resistance is often much more significant than the
device thermal resistance.
The TI PCB Thermal Calculator also includes the θJB values for the components (including values for
Enhanced and Minimum Thermal PCB stackup), and as an output it provides the board temperature
based on spreading area. It also allows the user to use board temperature as a reference and will
estimate the junction temperature for each of the PCB stackup configurations.
7
Summary
Components can generally be classified into low power, medium power, and high power categories,
although it is difficult to make a precise definition. Medium power components with an exposed pad can be
cooled to below the specified maximum junction temperature by appropriate design of PCB spreader
planes and thermal vias, and availability of air for natural convection cooling (free-air). Temperature rise
for these components is a strong function of PCB construction, such as spreader plane area, thickness,
and number of vias, in addition to component thermal characteristics. TI’s PCB Thermal Calculator can
help estimate the first-pass spreader plane area required to ensure that the temperature rise is below the
maximum allowable device operating temperature. Predictions are provided for two types of PCBs
(Minimum and Enhanced Thermal Capability). The PCB construction described in the previous sections
must be compared with PCB owned by the user, and appropriate decisions must be made. For example, if
the PCB owned by the user has a top spreader plane thickness that is larger than 60 µm for an inline
package, it is expected that the temperature rise is smaller than that predicted by the calculator for the
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Enhanced Thermal PCB. Care must be taken in defining the available copper spreader area when there
are multiple medium power components using the same spreader plane. It must be noted that the intent of
the calculator is to reduce cycle time for design and development, and is not a replacement for detailed
system-level CFD analysis using commercial software. Final design should always be verified through
careful measurements against the maximum operating conditions as specified in the device data sheet.
8
Referenced Documents
Texas Instruments, PowerPAD™ Thermally-Enhanced Package Application Report (SLMA002)
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Revision History
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Revision History
NOTE: Page numbers for previous revisions may differ from page numbers in the current version.
Changes from Original (September 2010) to A Revision ............................................................................................... Page
•
14
Changed Calculate button to Update button ......................................................................................... 11
Revision History
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