Electronics System Thermal Design and Characterization

Electronics System Thermal Design
and Characterization
Roger Stout, P.E.
Senior Research Scientist
Corporate Research & Development
Advanced Packaging Technology
Roger Stout • 8-Jul-2007
<[email protected]>
Course outline
•
•
•
•
•
2
Introduction
Experimental Techniques
Linear Superposition
Thermal Runaway
References
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Introduction
• Why This Course?
• Terminology and Basic Principles
• Facts and Fallacies
3
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Can this device handle 2W?
4
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
I’m putting 5A into this part. What’s its
junction temperature going to be?
5
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
I’m putting a 60W, 800ns pulse into this rectifier.
How much copper area do I need to make this
part work in my system?
6
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
I’m putting together a data sheet for this new
device. What’s theta-JA for this package?
7
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
I’m putting together a data sheet for this new
device. What’s theta-JA for this package?
8
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
What’s the maximum power rating on this part
going to be?
9
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
What’s the maximum power rating on this part
going to be?
10
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Why is our SOT-23 thermal number so much worse
than our competition?
• Us
–
–
–
–
–
–
11
• Them
SOT-23 package
60x60 die
solder D/A
copper leadframe
min-pad board
still air
Electronics System Thermal Design and Characterization (RPS)
–
–
–
–
–
–
SOT-23 package
20x20 die
epoxy D/A
alloy 42 leadframe
1” x 2oz spreader
big fan
Corporate R&D • 8-Jul-2007
Why θJA doesn’t belong in the
“Maximum Ratings”* table
*let alone the “Absolute Maximum Ratings”
12
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
It’s like trying to sell your car (some bureaucrat
says you must list its gas mileage in the ad)
For sale:
Geo Metro, 1999 model, excellent condition!
MAXIMUM RATINGS
Description
Symbol
Gas Mileage (Note 1)
1
13
Value
Units
4
mpg
20% grade uphill, 75mph, back seat and trunk full of bricks
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Gee, we’d better not be so “worst case,” should we?
For sale:
Geo Metro, 1999 model, excellent condition!
MAXIMUM RATINGS
Description
Gas Mileage (Note 1)
Mileage derating factor
1
14
Symbol
Value
Units
10
mpg
0.002
mpg/brick
20% grade uphill, 75mph
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Wait, they said “maximum”. Maybe we’re
thinking about this all wrong …
For sale:
Geo Metro, 1999 model, excellent condition!
MAXIMUM RATINGS
Description
Value
Units
110
mpg
BDF (brick derating factor)
0.002
mpg/brick
IDF (incline derating factor)
2
mpg/%
SDF (speed derating factor)
0.07
mpg/mph
Gas Mileage (Note 1)
1
15
Symbol
20% grade downhill, empty vehicle (no bricks, not even a driver!), coasting
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Frankly, Tj-max is the only
“thermal” specification that I
think belongs in the Maximum
Ratings table.
16
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Terminology and
basic principles
17
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
“Junction” temperature?
Historically, for discrete devices, the “junction” was literally the
essential “pn” junction of the device. This is still true for basic
rectifiers, bipolar transistors, and many other devices.
More generally, however, by “junction” these days we mean
the hottest place in the device, which will be somewhere on
the silicon (2nd Law of Thermodynamics).
This gets to be somewhat tricky to identify as we move to
complex devices where different parts of the silicon do
different jobs at different times.
18
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Thermal/electrical analogy
temperature <=> voltage
power <=> current
∆temp/power <=> resistance
energy/degree <=> capacitance
19
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Theta (θ) vs. psi (Ψ)
• JEDEC <http://www.jedec.org/> terminology
– ZθJX , RθJA older terms ref JESD23-3, 23-4
– θJA ref JESD 51, 51-1
– θJMA ref JESD 51-6
– ΨJT, ΨTA ref JESD 51-2
– ΨJB, ΨBA ref JESD 51-6, 51-8
– RθJB ref JESD 51-8
– Great overview, all terms: JESD 51-12
20
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
A generic thermal system
H
21
t
a
e
t
u
in p
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
“Theta” (Greek letter θ)
We know actual heat flowing along path of interest
θ xy =
at
e
H
t
u
in p
Tx − Ty
qpath
Ty
Tx
true “thermal resistance”
22
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
“Psi” (Greek letter Ψ)
We don’t know actual heat flowing along path of interest
Ψxy =
H
t
a
e
t
u
in p
??
Tx − Ty
q total
Ty
Tx
All we know is total heat input
23
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
When Ψ becomes θ
am
bi e
am
ut
p
in
t
a
e
H
Tj
24
Powertotal
= Ψxy
Electronics System Thermal Design and Characterization (RPS)
Tx = T j (a point)
T y = ambient
(an isotherm)
t
n
e
i
amb
nt
θ JA =
T j − Tambient
t
en
bi
am
t
n
e
bi
Either or both “points”
of interest are
isotherms
All heat flowing
between them is
known
Power path = Powerdevice
Corporate R&D • 8-Jul-2007
An example of a device with two
different “Max Power” ratings
• Suppose a datasheet says:
– Tjmax = 150°C
• But it also says:
– θJA = 100°C/W
– ΨJL = 25°C/W
– Pd = 1.25W (Tamb=25°C)
– Pd = 3.0W (TL=75°C)
25 + 100 *1.25
= 25 + 125 = 150
75 + 25* 3
= 75 + 75 = 150
Where’s the “inconsistency”?
25
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Where’s the inconsistency?
TJ =150°C
25°C/W
(ΨJL)
100°C/W
(θJA)
What’s TL?
Not 75°C !!
(try about 119°C)
TA =25°C
26
Electronics System Thermal Design and Characterization (RPS)
…¾ of the way from
ambient to Tj
Corporate R&D • 8-Jul-2007
Facts and fallacies
27
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Facts and fallacies
• Basic idea:
– temperature difference is proportional to heat input
28
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
∆T ∝ Power
heating power = P
Tf
Tf
∆T = P * R(t )
To
29
time
Electronics System Thermal Design and Characterization (RPS)
junction temperature
junction temperature
twice the heat, twice the temperature rise
To
heating power = 2 P
∆T = 2 P * R(t )
time
Corporate R&D • 8-Jul-2007
Facts and fallacies
• Basic idea:
– temperature difference is proportional to heat input
• There are three modes of heat transfer
– conduction
– convection
– radiation (electromagnetic/infrared)
30
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Facts and fallacies
• Basic idea:
– temperature difference is proportional to heat input
• Flaws in idea:
– conduction effects (material properties)
• depend on temperature
– convection effects (esp. “still air”)
• depend on temperature
– radiation effects
• depend on temperature
31
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Facts and fallacies, cont’
• Basic idea:
– “thermal resistance” is an intrinsic property of a package
32
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
back in the good old days ...
metal can -fair approximation of
“isothermal” surface
33
Electronics System Thermal Design and Characterization (RPS)
axial leaded device -only two leads, heat
path fairly well defined
Corporate R&D • 8-Jul-2007
Facts and fallacies, cont’
• Basic idea:
– “thermal resistance” is an intrinsic property of a package
• Flaws in idea:
– there is no isothermal “surface”, so you can’t define a
“case” temperature
• Plastic body (especially) has big gradients
– different leads are at different temperatures
34
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Which lead? Where on case?
35
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Facts and fallacies, cont’
• Basic idea:
– “thermal resistance” is an intrinsic property of a package
• Flaws in idea:
– there is no isothermal “surface”, so you can’t define a
“case” temperature
• Plastic body (especially) has big gradients
– different leads are at different temperatures
– multiple, parallel thermal paths out of package
36
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Same ref, different values
ΨJ −tab = 1.2°C/W
Pd = 50W
37
ΨJ −tab = 0.8°C/W
Pd = 1.5W
Tc = 25°C
Tc = 25°C
1 GPM of H 2O
still air
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Archetypal package
convection
10%
wire/clip
case
silicon
die attach
flag/leadframe
10%
20%
38
60%
circuit board
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Then we change things …
add an external heatsink …
flip the die over …
optional
heatsink
40%
60%
optional
heatsink
optional
“case”
m old
com pound/
case
wire/clip
die
attach
silicon
pads/
balls
die attach
flag/leadfram e
20%
39
application board
40%
Electronics System Thermal Design and Characterization (RPS)
silicon
optional
underfill
20%
application board
20%
Corporate R&D • 8-Jul-2007
A bare “flip chip”
10%
silicon
pads/
balls
underfill
application board
40
Electronics System Thermal Design and Characterization (RPS)
90%
Corporate R&D • 8-Jul-2007
Even when it’s constant, it’s not!
Tj
R1 (path down
to board)
constant at 20
package
environment
R3 (path through
case top)
constant at 80
TC
TL
θ JA =
=
1000
theta-JA
psi-JL - var brd only
psi-JL - var airflow
psi-JC - var brd only
psi-JC - var airflow
60
50
20
40
15
T − TL
10
= J
=
Q total
R1
R1+R 2
5 1+
R 3 +R 4
0
1
41
1
1
+
R1+R 2 R 3 +R 4
psi-JT
25
ΨJL
1
10 rstnc. [C/W] 100
Tamb
psi-JL
TJ − Tamb
Q total
board
1
R4 (case to air path
resistance) constant
at 500, or 20x R2
R2 (board
resistance) vary
from 1 to 1000
thetaJA - var brd only
thetaJA - var airflow
1000
900
800
700
600
500
400
300
200
100
0
ΨJT =
30
20
board
Electronics System Thermal Design and Characterization (RPS)
0
1000
R3
R 3 +R 4
1
+
board
100
rstnc. [C/W]R
1+R 2
=
10
10 rstnc. [C/W] 100
TJ − TC
Q total
1
10
1000
Corporate R&D • 8-Jul-2007
Typical thermal test board types
min-pad board
minimum metal area to attach
device (plus traces to get
signals and power in and out)
42
Electronics System Thermal Design and Characterization (RPS)
1-inch-pad board
device at center of 1”x1” metal
area (typically 1-oz Cu);
divided into sections based on
lead count
Corporate R&D • 8-Jul-2007
Experimental
Techniques
43
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Experimental Techniques
• Temperature Sensitive Parameters (TSPs)
• Different Device Types and How to Test Them
• Heating vs Cooling Curve Techniques
• Test Conditions
44
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Temperature Sensitive Parameters
• JEDEC 51-1 good synopsis
• Basic diode physics (pg 5 of JESD 51-1)
– At constant current, forward voltage goes down
(linearly) with increasing temperature
• In principle, any device which has repeatable (not
necessarily linear) voltage vs. temperature
characteristics can be used
• Commercial thermal test equipment typically requires
linear TSP behavior
45
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Typical TSP Behavior
calibrate forward voltage at controlled,
small (say 1mA) sense current
inc
rea
s
125°C
sense
current
1m
a
T
Vf
cur
ren
t
25°C
0.5 V
46
ing
Electronics System Thermal Design and Characterization (RPS)
Vf
0.7 V
Corporate R&D • 8-Jul-2007
How to measure Tj
true const. current supply
approximate const. current supply
(1 mA typical)
10KΩ
DUT
OR
10.7V
DUT
If V f-0.7V, then
I-1mA
47
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
How to heat
sample current is off
while heating current on
10KΩ
sample current
is always on
10KΩ
heating
power
supply
10.7V
10.7V
DUT
48
heating
power
supply
Electronics System Thermal Design and Characterization (RPS)
OR
DUT
Corporate R&D • 8-Jul-2007
Superposition and TSP “self heating”
• Common warning:
– Keep the TSP power low! “self heating is bad!”
• But is this really a problem?
– If the “sample” power is always there, the “self heating” is
the same during calibration as during test, so they cancel
out
• You might unwittingly overheat the junction
• You might not be able to keep the “measurement”
current on during the heating
– But if this is a serious issue, reduce the effective “test”
power by the amount of “measurement” power
49
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
The Importance of 4-wire measurements
1A
+(1.00 V)
Power
Output = 1 W
supply
-(0 V)
0.18 V
0.82 V
0.64 W
0.70 W
0.05 V
50
0.15 V
Electronics System Thermal Design and Characterization (RPS)
0.90 W
0.85 V
0.95 V
Corporate R&D • 8-Jul-2007
Which raises an interesting question:
+(1.00 V)
3A
Power
Output = 3 W
supply
-(0 V)
0.55 V
0.45 V
1.3 W
0.02 V
0.3 W
1.3 W
0.98 V
Is this a fair characterization of a low-Rds-on device?
51
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Bipolar transistor
• TSP is Vce at designated
“constant” current
• Heating is through Vce
• Choose a base current
which permits adequate
heating
TSP supply
10KΩ
switch
bias resistor
TSP=Vce
bias supply
52
Electronics System Thermal Design and Characterization (RPS)
heating supply
Corporate R&D • 8-Jul-2007
Schottky diode
• TSP is forward voltage at “low” current
• Voltages are typically very small (especially
as temperature goes up)
• Highly non-linear, though maybe better as
TSP current increases; because voltage is
low, higher TSP current may be acceptable
• Heating current will be large
53
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
MOSFET / TMOS
• Typically, use reverse bias
“back body diode” for both
TSP and for heating
• May need to tie gate to
source (or drain) for
reliable TSP characteristic
TSP supply
10KΩ
switch
TSP=Vsd
heating
supply
+
54
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
MOSFET / TMOS method 2
• If you have fast switches and
stable supplies
• Forward bias everything and use
two different gate voltages
close
switch
to heat
+
V-gate
for
heating
-
55
Electronics System Thermal Design and Characterization (RPS)
close
switch to
measure
+
V-gate
for
measure
-
TSP supply
10KΩ
close
switch
to heat
TSP=Vds
+
heating
supply
-
Corporate R&D • 8-Jul-2007
RF MOS
• They exist to amplify high frequencies (i.e. noise)!
• Feedback resistors may keep
them in DC
TSP supply
10KΩ
-
close
switch
to heat
close
switch
to heat
close
switch to
measure
+
V-gate
for
heating
-
56
Electronics System Thermal Design and Characterization (RPS)
TSP =
body
diode
TSP
supply
+
+
heating
supply
-
Corporate R&D • 8-Jul-2007
IGBT
• Drain-source channel used
for both TSP and heating
• Find a gate voltage which
“turns on” the drain-source
channel enough for heating
purposes
• Use same gate voltage, but
typically low TSP current for
temperature measurement
57
Electronics System Thermal Design and Characterization (RPS)
TSP supply
10KΩ
switch
TSP=Vds
gate
voltage
heating supply
Corporate R&D • 8-Jul-2007
Thyristor
• Anode--to-cathode voltage path
used both for TSP and for heating
• typical TSP current probably
lower than “holding” current, so
gate must be turned on for TSP
readings; try tying it to the anode
(even so, we used 20mA to test
SCR2146)
• Hopefully, with anode tied to gate,
enough power can be dissipated
to heat device without exceeding
gate voltage limit
58
Electronics System Thermal Design and Characterization (RPS)
TSP supply
10KΩ
gate
switch
anode
TSP
=Vac
cathode
heating
supply
Corporate R&D • 8-Jul-2007
Logic and analog
• Find any TSP you can
– ESD diodes on inputs or outputs
– Body diodes somewhere
• Heat wherever you can
– High voltage limits on Vcc, Vee, whatever
– Body diodes or output drivers
– Live loads on outputs
• (be very careful how you measure power!)
59
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Heating curve method
vs.
cooling curve method
60
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Quick review:
Basic Tj measurement
first we heat
10KΩ
10KΩ
heating
power
supply
10.7V
heating
power
supply
10.7V
DUT
61
then we measure
Electronics System Thermal Design and Characterization (RPS)
DUT
Corporate R&D • 8-Jul-2007
Question
• What happens when you switch from
“heat” to “measure”?
Answer: stuff changes
• More specifically, while the electrical
signal is stabilizing, the junction starts
to cool down
62
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
current
measurements
voltage
Basic
“Heating Curve”
Transient Method
convert cooling
volts to
temperature
T
25°C
.5V
63
Vf
.7V
Electronics System Thermal Design and Characterization (RPS)
power-off cooling
highcurrent
heating
steady state reached
125°C
highcurrent
heating
Temperature
calibrate forward voltage
@ 1mA sense currrent
highcurrent
heating
power-off cooling
highcurrent
heating
power-off cooling
Vf
power-off cooling
1 ma
measured
temperatures
Time
Corporate R&D • 8-Jul-2007
current
voltage
Heating curve method #2
highcurrent
heating
measured temperatures
64
Electronics System Thermal Design and Characterization (RPS)
power-off cooling
highcurrent
heating
power-off cooling
highcurrent
heating
power-off cooling
Temperature
highcurrent
heating
power-off cooling
1 ma
Time
Time
Corporate R&D • 8-Jul-2007
Basic
“Cooling Curve”
Transient Method
voltage
current
measurements
Vf
1 ma
125°C
heating
period
65
Temperature
power-off
cooling
steady state reached
Temperature
highcurrent
heating
calibrate forward voltage
@ 1mA sense currrent
convert cooling
volts to
temperature
T
25°C
.5V
Time
transient cooling
period (data taken)
Vf
.7V
Time (from
start of cooling)
subtract cooling curve from
peak temperature to obtain
“heating” curve equivalent
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Whoa!
… that last step, there ...
• Heating vs. cooling
– Physics is symmetric, as long as the material and
system properties are independent of temperature
66
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Heating vs. cooling symmetry
Start of constant
power input
(“step heating”)
junction
Start of (constant)
power off
flag
lead
(all the same
curves, flipped
vertically)
back of board
edge of board
67
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
(cooling)
• For a theoretically valid cooling curve,
you must begin at true thermal
equilibrium (not uniform temperature,
but steady state)
• So whatever your θJA, max power is
limited to:
power =
68
T j max − Tambient
Electronics System Thermal Design and Characterization (RPS)
θ JA
Corporate R&D • 8-Jul-2007
(cooling)
By the way …
• Since you must have the device at steady state in
order to make a full transient cooling-curve
measurement, steady-state θJA is a freebie.
(given that you account for the slight cooling which
took place before your first good measurement
occurred)
69
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Effect of power on heating curve
10x steadystate power
3x steadystate power
2x steady-state power
6x steadystate power
Tj-max
junction temperature
steady-state max power
Tamb
70
Electronics System Thermal Design and Characterization (RPS)
< steady-state max power
time
Corporate R&D • 8-Jul-2007
Some initial uncertainty
a few initial points
may be uncertain
high-current
heating
steady state reached
Temperature
(cooling)
heating period
but once we’re past
the “uncertain” range,
all the rest of the
points are “good”
power-off
cooling
transient cooling period
(data taken)
Time
71
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Heating vs. cooling tradeoffs
HEATING
COOLING
ambient
?
heating
power
limited by
tester
limited to
steady-state
temperature of
fastest data
closer to
ambient
closer to
Tj-max
all points
similar error
error limited to
first few points
starting
temperature
error
control
72
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Test Conditions
•Still air, moving air
•Various mounting configurations
– Min-pad board
– 1” heat spreader board
•Coldplate testing
– Single, dual, “ring”
73
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Still air vs. moving air
• Varying the air speed is mainly varying the
heat loss from the test board surface area,
not from the package itself
• You just keep re-measuring your board’s
characteristics
74
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
100
90
total system thermal resistance
80
theta-JA [C/W]
70
60
package resistance
50
40
30
board resistance
20
10
0
0.1
1
10
air speed [m/s]
75
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Different boards
• min-pad board
• 1” heat spreader board
• you’re mainly characterizing how copper
area affects every package and board,
not how a particular package depends
on copper area
76
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
1" pad vs min-pad
350
Roger Stout 5/2
Source:
Un-derated thermal data
from old PPD database
300
SOD-323
250
SOT-23
1" pad thetaJA (C/W)
TSOP-6
SOT-23
200
SOD-123
TSOP-6(AL42)
150
TSOP-6
100
SO-8
50
Top Can
SOT-23
Micro 8
SMB
Dpak
D2pak & TO220
SOD-123
SOD-123
SMA & Pow ermite
overall linear fit is:
1" value = [0.51*(min-pad value) - 7]
SMC
SOT-223
SO-8
Top Can
0
0
100
200
300
400
500
600
700
min pad thetaJA (C/W)
77
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Standard coldplate testing
• “infinite” heatsink (that really isn’t) for
measuring theta-JC on high-power devices
• If both power and coldplate temperature are
independently controlled, “two parameter”
compact models may be created
78
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Standard coldplate testing
• Detailed design and placement of “case” TC can have
significant effect on measured value
2.0”
DUT
TC in 0.025” well,
0.25” from surface
Vleer pin assy
.75”
TC on Vleer pin measures
temperature at interface
.375”
Liquid Coolant Flow
79
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
“Dual” coldplate testing
• Alternative method for “two-parameter”
characterization methods where two independent
“isothermal” boundary conditions are desired
T1
T2
80
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
“Ring” coldplate
• For making somewhat higher-power board-mounted
measurements; “ring” coldplate is clamped around
outer edge of test board to constrain board
temperature
81
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
2-parameter data reduction
Q = Q1 + Q2
heat up, Q1
T1
Q=
R1
(
)
(
1
1
T j − T1 +
T j − T2
R1
R2
)
This has the form of a two-variable linear equation:
heat in, Q
y = m1 x1 + m2 x2 + b
Tj
R2
where:
T2
heat down, Q2
82
Electronics System Thermal Design and Characterization (RPS)
1
R1
1
m2 =
R2
m1 =
(
x1 = T j − T1
(
)
x2 = T j − T2
)
b≡0
Corporate R&D • 8-Jul-2007
What’s wrong with theta-JA?
2
θ JA
TJ − Ta
=
Pd
TJ = θ JA ⋅ Pd + Ta
83
Electronics System Thermal Design and Characterization (RPS)
ΨJtab =
TJ − Ttab
Pd
TJ = ΨJtab ⋅ Pd + Ttab
Corporate R&D • 8-Jul-2007
Theta-JA vs copper area
84
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Linear superposition
85
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Tj
θJA
Ta
86
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Facts and fallacies redux
•
Basic idea:
– “thermal
•
resistance” is an intrinsic property of a package
Flaws in idea:
– there is no isothermal “surface”, so you can’t define a
“case” temperature
• Plastic body (especially) has big gradients
– different leads are at different temperatures
– multiple, parallel thermal paths out of package
– other heat sources change everything
87
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Our case-study will be this
6-component thermal system
Tamb
Tref5
Tj5
Tj6
Tj3
Tj2
Tref3
Tref1
Tj4
Tj1
TB
88
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Linear superposition
– what is it?
• The total response of a point within
the system, to excitations at all
points of the system, is the sum of
the individual responses to each
excitation taken independently.
∆Tcomposite = ∆Tsource 1 + ∆Tsource 2 + L + ∆Tsource n
89
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Linear superposition
– when does it apply?
• The system must be “linear” – in brief,
all individual responses must be
proportional to all individual excitations.
∆Tnet A = ∆TA ←B + ∆TA ←C + ∆TA ←D
∆TA
90
=
2 ⋅ qB
Electronics System Thermal Design and Characterization (RPS)
+
3 ⋅ qC
+
1.2 ⋅ qD
Corporate R&D • 8-Jul-2007
Linear superposition doesn’t
apply if the system isn’t linear.
∆T = a(T, q1 ) ⋅ q1 + b(T, q2 ) ⋅ q2 + L
∆T = a ⋅ q1n1 + b ⋅ q2n2 + L
91
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Linear superposition
– when would you use it?
When you have multiple heat sources
(that is, all the time!)
92
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Linear superposition
– how do you use it?
Tamb
Tref5
Tj5
Tj6
Tj3
Tj2
Tref3
Tref1
Tj4
Tj1
TB
93
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
120
120
100
100
temperature rise [C] sum of sources
temperature rise [C], each source
Temperature direct contributions and totals
80
60
40
20
0
80
60
40
20
0
J1
J2
J3
J4
J5
J6
R1
R3
R5
B
J1
J2
result location
J1 at 0.4 W
J4 at 0.4 W
94
J2 at 0.4 W
J5 at 0.5 W
J3
J4
J5
J6
R1 R3 R5
B
result location
J3 at 0.4 W
J6 at 0.2 W
Electronics System Thermal Design and Characterization (RPS)
J1 at 0.4 W
J4 at 0.4 W
J2 at 0.4 W
J5 at 0.5 W
J3 at 0.4 W
J6 at 0.2 W
Corporate R&D • 8-Jul-2007
Normalized responses at each
location due to each source
normalized response [C/W], each source
200
180
J1 at 1 W
J2 at 1 W
J3 at 1 W
J4 at 1 W
J5 at 1 W
J6 at 1 W
160
140
120
100
80
60
40
20
0
J1
95
J2
J3
J4
J5
J6
R1
response location
Electronics System Thermal Design and Characterization (RPS)
R3
R5
B
Corporate R&D • 8-Jul-2007
junction
temperature
vector
⎧ Tj1 ⎫
⎪T ⎪
⎪ j2 ⎪
⎨ ⎬=
M
⎪ J⎪
⎪Tjn ⎪
⎩ ⎭
T
theta matrix assembled
from simplified subsystems
⎡θ J1A
⎢Ψ
⎢ 12
⎢ M
⎢
⎣ Ψ1n
Ψ12
Ψ1n ⎤ ⎧ q1 ⎫
⎥
⎪
⎪
θ J2 A
Ψ2n ⎥ ⎪q2 ⎪
q
+T
Taa
⎨
⎬
JAO M ⎥ ⎪ M ⎪
⎥⎪ ⎪
Ψ2n L θ JnA ⎦ ⎩qn ⎭
L
θ
self-heating terms
96
power
input
vector
Electronics System Thermal Design and Characterization (RPS)
board
interactions
Corporate R&D • 8-Jul-2007
junction
temperature
vector
⎧ Tj1 ⎫
⎪T ⎪
⎪ j2 ⎪
⎨ ⎬=
⎪ M ⎪
⎪Tjn ⎪
⎩ ⎭
L
Ψ12
Ψ1n
⎡θ JB1 + θ BA1
⎤ ⎧ q1 ⎫
⎢ Ψ
⎥⎪ ⎪
+
Ψ
θ
θ
12
JB 2
BA 2
2n
⎢
⎥ ⎪⎨q2 ⎪⎬ + T
a
⎢
⎥⎪ M ⎪
M
O
M
⎢
⎥⎪ ⎪
L θ JBn + θ BAn ⎦ ⎩qn ⎭
Ψ1n
Ψ2n
⎣
device
resistance
97
theta matrix assembled
from simplified subsystems
power
input
vector
board
resistance
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
visualizing theta and psi
heat in here
measurements
here are θ s
θ J1B
θ J1A
measurements
here are Ψs
(idle heat
source “x”)
ΨxA
θ BA
ΨyA
(idle heat
source “y”)
thermal ground
98
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
theta matrix doesn’t have to be square
junction
temperature
vector
one column for
each heat source
⎧ ∆Tj1 ⎫
⎪ ∆T ⎪
j2 ⎪
⎪⎪
⎪
⎨ ∆TxA ⎬
⎪∆T ⎪
⎪ L1A ⎪
⎪⎩ ∆TBA ⎪⎭
⎛ θ JA1 Ψ21 Ψ31 ⎞
⎜
⎟
⎜ Ψ12 θ JA 2 Ψ32 ⎟
⎜Ψ
⎟
Ψ
Ψ
2x
3x ⎟
⎜ 1x
⎜ Ψ1L1 Ψ2L1 Ψ3L1 ⎟
⎜
⎟
⎝ Ψ1B Ψ2B Ψ3B ⎠
=
power input
vector
⎧ q1 ⎫
⎪ ⎪
⎨q2 ⎬
⎪q ⎪
⎩ 3⎭
one row
for each
heat
source
one row for each temperature
location of interest
99
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
The reciprocity theorem
• What is it?
• When does it not apply?
100
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Electrical reciprocity
+
V
I
101
Electronics System Thermal Design and Characterization (RPS)
-
Corporate R&D • 8-Jul-2007
Electrical reciprocity
+
5V
-
102
+
0.3
2 AV
+
?V
-
+
0.3 V
-
-
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Thermal reciprocity
heat input here
response
here
103
Electronics System Thermal Design and Characterization (RPS)
same
response
here
Corporate R&D • 8-Jul-2007
Another thermal reciprocity example
(r)
heat input here
same
response
here
response
here
(s)
104
(s)
Electronics System Thermal Design and Characterization (RPS)
(r)
Corporate R&D • 8-Jul-2007
(square part of) matrix is symmetric
columns are the “x” heat sources
rows are
the “y”
response
locations
105
J1
75
65
55
60
22
10
J2
65
71
60
55
25
11
J3
55
60
65
61
21
15
J4
60
55
61
73
18
11
J5
22
25
21
18
125
14
J6
10
11
15
11
14
180
R1
73
65
55
59
22
10
R3
55
60
63
61
21
15
R5
20
24
14
19
95
15
B
65
63
62
63
21
12
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
When does reciprocity NOT Apply?
• Upwind and downwind in forced-convection
dominated applications
B
C
airflow
A
D
Heat in at “A” will raise temperature
of “C” more than heat in at “C” will
raise temperature of “A”
106
Electronics System Thermal Design and Characterization (RPS)
“B” and “D” may
still be roughly
reciprocal
Corporate R&D • 8-Jul-2007
A linear superposition example
(unequivocal proof that a published
theta-JA is virtually meaningless)
107
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Superposition example
Tamb
Tref5
Tj5
Tj6
Tj3
Tj2
Tref3
Tref1
Tj4
Tj1
TB
108
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Device 1 heated, 1.1 W
Tamb=25
Tref5=47.0
Tj6=36.0
Tj5=49.2
Tj3=85.5
Tj2=96.5
Tref3=85.5
Tref1=105.3
Tj1=107.5
Tj4=91.0
TB=96.5
109
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Reduce the data
θ j1A =
Ψ j2 A =
Tj1 − Tamb
q1
Tj2 − Tamb
q1
=
=
107.5 − 25
= 75
1 .1
96.5 − 25
= 65
1.1
M
ΨBA
TB − Tamb 96.5 − 25
=
=
= 65
q1
1 .1
θj1A
75
Ψ j2A
65
Ψ j3A
55
Ψ j4A
60
Ψ j5A
22
Ψ j6A
10
Ψ r1A 73
Ψ r3A 55
Ψ r5A 20
Ψ BA
110
Electronics System Thermal Design and Characterization (RPS)
65
Corporate R&D • 8-Jul-2007
Collect the θ/Ψ values in the matrix
111
J1
75
J2
65
J3
55
J4
60
J5
22
J6
10
R1
73
R3
55
R5
20
B
65
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Device 2 heated, 1.2 W
Tamb=25
Tref5=53.8
Tj6=38.2
Tj5=55.0
Tj3=97.0
Tj2=110.2
Tref3=97.0
Tref1=103.0
Tj1=103.0
Tj4=91.0
TB=100.6
112
Electronics System Thermal Design and Characterization (RPS)
Ψj1A
65
θ j2A
71
Ψ j3A
60
Ψ j4A
55
Ψ j5A
25
Ψ j6A
11
Ψ r1A
65
Ψ r3A
60
Ψ r5A
24
Ψ BA
63
Corporate R&D • 8-Jul-2007
Collect the θ/Ψ values
113
J1
75
65
J2
65
71
J3
55
60
J4
60
55
J5
22
25
J6
10
11
R1
73
65
R3
55
60
R5
20
24
B
65
63
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Device 3 heated, 1.3 W
Tamb=25
Tref5=43.2
Tj6=44.5
Tj5=52.3
Tj3=109.5
Tj2=103.0
Tref3=106.9
Tref1=96.5
Tj1=96.5
Tj4=104.3
TB=105.6
114
Electronics System Thermal Design and Characterization (RPS)
Ψj1A
55
Ψ j2A
60
θ j3A
65
Ψ j4A
61
Ψ j5A
21
Ψ j6A
15
Ψ r1A
55
Ψ r3A
63
Ψ r5A
14
Ψ BA
62
Corporate R&D • 8-Jul-2007
Collect the θ/Ψ values
115
J1
75
65
55
J2
65
71
60
J3
55
60
65
J4
60
55
61
J5
22
25
21
J6
10
11
15
R1
73
65
55
R3
55
60
63
R5
20
24
14
B
65
63
62
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Device 4 heated, 1.1 W
Tamb=25
Tref5=45.9
Tj6=37.1
Tj5=44.8
Tj3=92.1
Tj2=85.5
Tref3=92.1
Tref1=89.9
Tj1=91.0
Tj4=105.3
TB=94.3
116
Electronics System Thermal Design and Characterization (RPS)
Ψj1A
60
Ψ j2A
55
Ψ j3A
61
θ j4A
73
Ψ j5A
18
Ψ j6A
11
Ψ r1A
59
Ψ r3A
61
Ψ r5A
19
Ψ BA
63
Corporate R&D • 8-Jul-2007
Collect the θ/Ψ values
117
J1
75
65
55
60
J2
65
71
60
55
J3
55
60
65
61
J4
60
55
61
73
J5
22
25
21
18
J6
10
11
15
11
R1
73
65
55
59
R3
55
60
63
61
R5
20
24
14
19
B
65
63
62
63
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Device 5 heated, 0.7 W
Tamb=25
Tref5=91.5
Tj6=34.8
Tj5=112.5
Tj3=39.7
Tj2=42.5
Tref3=39.7
Tref1=40.4
Tj1=40.4
Tj4=37.6
TB=39.7
118
Electronics System Thermal Design and Characterization (RPS)
Ψj1A
22
Ψ j2A
25
Ψ j3A
21
Ψ j4A
18
θ j5A
125
Ψ j6A
14
Ψ r1A
22
Ψ r3A
21
Ψ r5A
95
Ψ BA
21
Corporate R&D • 8-Jul-2007
Collect the θ/Ψ values
119
J1
75
65
55
60
22
J2
65
71
60
55
25
J3
55
60
65
61
21
J4
60
55
61
73
18
J5
22
25
21
18
125
J6
10
11
15
11
14
R1
73
65
55
59
22
R3
55
60
63
61
21
R5
20
24
14
19
95
B
65
63
62
63
21
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Device 6 heated, 0.5 W
Tamb=25
Tref5=32.5
Tj6=115.0
Tj5=32.0
Tj3=32.5
Tj2=30.5
Tref3=32.5
Tref1=30.0
Tj1=30.0
Tj4=30.5
TB=31.0
120
Electronics System Thermal Design and Characterization (RPS)
Ψj1A
10
Ψ j2A
11
Ψ j3A
15
Ψ j4A
11
Ψ j5A
14
θ j6A
180
Ψ r1A
10
Ψ r3A
15
Ψ r5A
15
Ψ BA
12
Corporate R&D • 8-Jul-2007
Collect the θ/Ψ values
121
J1
75
65
55
60
22
10
J2
65
71
60
55
25
11
J3
55
60
65
61
21
15
J4
60
55
61
73
18
11
J5
22
25
21
18
125
14
J6
10
11
15
11
14
180
R1
73
65
55
59
22
10
R3
55
60
63
61
21
15
R5
20
24
14
19
95
15
B
65
63
62
63
21
12
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Now apply actual power
Tamb=25
Actual power
in application
Tref5=106.3
Tj6=139.1
Tj5=124.7
qj1 .4
qj2 .4
Tj3=134.9
Tj2=140.1
Tref3=134.1
Tref1=138.8
Tj1=140.0
Tj4=135.8
qj3 .4
qj4 .4
qj5 .5
qj6 .2
TB=139.1
122
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Compute some effective θ/Ψ values
Take Tj1, for instance. Remember when it was
heated all alone, we calculated its self-heating
theta-JA like this:
θ j1A =
Tj1 − Tamb
q1
≠
Now let’s see:
θ j1A =
123
107.5 − 25
=
= 75
1 .1
Tj1 − Tamb
q1
Electronics System Thermal Design and Characterization (RPS)
140 − 25
=
= 288
0 .4
Corporate R&D • 8-Jul-2007
And that’s not just a single aberration!
Junction to Reference
Self heating
124
θ j1A
288
75
vs
3.8x
θ j2A
288
71
vs
4.1x
θ j3A
274
65
vs
4.2x
θ j4A
277
73
vs
3.8x
θ j5A
199
vs 125
1.6x
θ j6A
309
vs 180
1.7x
Electronics System Thermal Design and Characterization (RPS)
Ψj1-R1
3.0
1.5x
vs
2.0
Ψj3-R3
2.0
vs
1.0x
2.0
Ψj5-R5
36.8
vs
1.2x
30.0
Junction to Board
Ψj1-B
2.2
0.2x
vs
10.0
Ψj2-B
2.5
vs
0.3x
8.0
Ψj3-B
-10.5
-3.5x
vs
3.0
Ψj4-B
-8.3
-0.8x
vs
10.0
Corporate R&D • 8-Jul-2007
Is the moral clear?
• You simply cannot use published theta-JA
values for devices in your real system, even if
those values are perfectly accurate and correct
as reported on the datasheet and you know the
exact specifications of the test conditions.
• Not unless your actual application is identical to
the manufacturer’s test board – and uses just
that one device all by itself.
125
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
So is it really this bad?
Only sort-of. Let’s revisit the math for one device …
⎧ Tj1 ⎫
⎪T ⎪
⎪ j2 ⎪
⎨ ⎬=
M
⎪ ⎪
⎪Tjn ⎪
⎩ ⎭
⎡θ J1A
⎢Ψ
⎢ 12
⎢ M
⎢
⎣ Ψ1n
Ψ12
θ J2 A
Ψ2n
Ψ1n ⎤ ⎧ q1 ⎫
⎥
⎪
⎪
Ψ2n ⎥ ⎪q2 ⎪
+ Ta
⎨
⎬
O
M ⎥⎪ M ⎪
⎥⎪ ⎪
L θ JnA ⎦ ⎩qn ⎭
L
Tj1 = θ J1A q1 + Ψ12 q2 + K Ψ1n qn + Ta
Tj1 = θ J1A q1
+
n0
∑ Ψ1nqn
2
126
Electronics System Thermal Design and Characterization (RPS)
0
+ Ta
“effective”
ambient
Corporate R&D • 8-Jul-2007
A graphical view
power, q
Isolated device
1
Tj1 = θ J1A q1 + Ta
θJ1A
junction temperature , TJ1
Ta
Device in a system
n
shift in effective
ambient
Tj1 = θ J1A q1 + ∑ Ψ1n qn + Ta
1
2
= θ J1A q1 +
127
Ta′
Electronics System Thermal Design and Characterization (RPS)
θJ1A
Ta
Ta’
still the
same slope
junction temperature , TJ1
Corporate R&D • 8-Jul-2007
How does effective ambient relate to board temperature?
if any of these are non-zero,
Ta′ will be higher than Ta
“system” slope for
isolated device
θ j1a ⋅ Q1
Tj1 =
(
+
n
∑ (Ψi1 ⋅ Qi ) + Ta
i= 2
)
= θ j1B + θ B1a ⋅ Q1
effective
′
T
a
ambient
= θ j1B ⋅ Q1 + θ B1a ⋅ Q1
+
Ta′
=
+
Ta′
∆Tj1B
temperature
rise, board to J1
128
+
+
∆TB1a
when Q1 is zero,
notboth
zero,ofboth
these
of these
will bewill
zero
be non-zero
temperature rise,
ambient to board
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
How does effective ambient relate
to local air temperature?
NOT.
129
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
What about that “system” theta we
saw earlier that was so different?
device #1
power/temperature
perturbations will
fall on this line
power
q1
NOT this one
the “system”
theta-JA
1
θJ1A
θJ1A
1
n
Ta
130
∑ Ψ1nqn
2
Ta’
the isolated-device
theta-JA
TJ1
Electronics System Thermal Design and Characterization (RPS)
junction temperature
Corporate R&D • 8-Jul-2007
System modeling
131
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Filling in the theta-matrix
• Handy formulas for quick estimates
• Utilizing symmetry
132
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Conduction resistance
basic heat transfer relationship for 1-D conduction
dT
q = k⋅A⋅
dx
≈
∆T
k⋅A⋅
L
if we define
∆T
R=
q
then
L
R=
k⋅A
133
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Convection resistance
basic heat transfer relationship for surface cooling
q = h ⋅ A ⋅ ∆T
if we define
∆T
R=
q
then
1
R=
hA
134
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Radiation resistance
basic heat transfer relationship for surface radiation
(
= σ ⋅ ε ⋅ F ⋅ A ⋅ (T
= σ ⋅ ε ⋅ F ⋅ A ⋅ (T
q = σ ⋅ ε ⋅ F ⋅ A ⋅ T 4 − Ta4
2
+ Ta2
2
+ Ta2
)
)(T + T )(T − T )
)(T + T )∆T
a
a
a
if we define
∆T
R=
q
then
R=
135
(
1
)
σεFA T 2 + Ta2 (T + Ta )
Electronics System Thermal Design and Characterization (RPS)
temperatures must
be expressed in
degrees “absolute”!
Corporate R&D • 8-Jul-2007
Thermal capacitance and time constant
capacitance is ability to store energy
specific heat is energy storage/mass
based on simple RC concept,
relate rate of storage to rate of flux
result is
C = ρc p V
so if
and if
R=
L
and C = ρc p (L ⋅ A )
k⋅A
then
R=
1
and C = ρc p (L ⋅ A )
h⋅A
then
τ =
136
τ = RC
ρc pL2
k
=
L2
α
Electronics System Thermal Design and Characterization (RPS)
τ =
ρc p L
h
Corporate R&D • 8-Jul-2007
Some useful formulas
• conduction resistance…………..………
• convection resistance…………...………
• thermal capacitance……………...……..
• characteristic time…………………..….
– (dominated by 1-D conduction)
• characteristic time……………………...
– (dominated by 1-D convection)
L
k⋅A
1
R=
h⋅A
C = ρc p V
R=
τ =
τ =
L2
α
ρc pL
• short-time 1-D transient response……... ∆ T =
137
Electronics System Thermal Design and Characterization (RPS)
h
2
Q
π Aη
t
Corporate R&D • 8-Jul-2007
Terms used in preceding formulas
•
•
•
•
•
•
•
•
•
•
•
•
138
L - thermal path length
A - thermal path cross-sectional area
k - thermal conductivity
ρ - density
k
cp - heat capacity
α=
ρc p
V – volume of material (L·A)
α - thermal diffusivity
η = ρcpk
η - thermal effusivity
h - convection heat-transfer “film coefficient”)
∆T - junction temperature rise
Q - heating power
t - time since heat was first applied
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
When do these effects enter?
hundreds of seconds
tens of seconds
mainly environmental
convection and radiation
effects
junction temperature
a second or so
mainly local
application
board conduction
effects
mainly package
typical heating curve
for device on FR-4
board in still-air
time
materials/conduction effects
139
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Utilize symmetry whenever possible
140
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
if
⇒R
then
and
≈ 2R
≈ 4R
141
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Cylindrical and spherical conduction (through
radial thickness) resistance formulas
Half-cylinder
[included angle]
Full cylinder
[solid angle]
⎛r ⎞
ln⎜⎜ o ⎟⎟
r
R= ⎝ i ⎠
2π ⋅ k ⋅ L
where
142
1 1
−
r ro
R= i
2π ⋅ k
⎛r ⎞
ln⎜⎜ o ⎟⎟
ri ⎠
⎝
R=
π ⋅k ⋅L
•
•
•
Electronics System Thermal Design and Characterization (RPS)
1 1
−
ri ro
R=
4π ⋅ k
Hemisphere
Full sphere
L – cylinder length
ri – inner radius
ro – outer radius
Corporate R&D • 8-Jul-2007
Predicting the temperature of
high power components
• The device and system are
equally important to get right
143
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Using the previous board example …
theta array
144
J1
75
65
55
60
22
10
J2
65
71
60
55
25
11
J3
55
60
65
61
21
15
J4
60
55
61
73
18
11
J5
22
25
21
18
125
14
J6
10
11
15
11
14
180
R1
73
65
55
59
22
10
R3
55
60
63
61
21
15
R5
20
24
14
19
95
15
B
65
63
62
63
21
12
Electronics System Thermal Design and Characterization (RPS)
power
vector
qj1
0.5
qj2
0.5
qj3
0.5
qj4
0.5
qj5
0.2
qj6
0.02
Corporate R&D • 8-Jul-2007
Observe the relative contributions
For junction 1 (a high power component) we have:
the device itself …
the other devices …
= (75 x 0.5) +
(65 x 0.5) + (55 x 0.5) + (60 x 0.5) + (22 x 0.2) + (10 x 0.02)
+ 25
=
37.5
+ 32.5 + 27.5 + 30 + 4.4 + 0.2
= 37.5 +
145
94.6
Electronics System Thermal Design and Characterization (RPS)
+
+
25
25
Corporate R&D • 8-Jul-2007
Graphically, it looks like this:
power
increasing
power
q1=0.5 W
note the “embedded”
theta-JA looks like
264 C/W
decreasing
power
1
264 C/W
∆=94.6 C
⎛
⎞
⎜ ∑ Ψ1n qn ⎟
⎜
⎟
⎝ 2
⎠
n
25 C
146
Electronics System Thermal Design and Characterization (RPS)
1
75 C/W
∆=37.5 C
(θ J1A q1 )
157 C
TJ1
junction temperature
Corporate R&D • 8-Jul-2007
Predicting the temperature of
low power components
• The system is probably more
important than the device
147
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Using the previous board example …
theta array
148
power
vector
J1
75
65
55
60
22
10
J2
65
71
60
55
25
11
J3
55
60
65
61
21
15
J4
60
55
61
73
18
11
qj1
0.5
J5
22
25
21
18
125
14
qj2
0.5
J6
10
11
15
11
14
180
qj3
0.5
R1
73
65
55
59
22
10
qj4
0.5
R3
55
60
63
61
21
15
qj5
0.2
qj6
0.02
R5
20
24
14
19
95
15
B
65
63
62
63
21
12
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Relative contributions to ∆TJ6
the other devices …
= (10 x 0.5) + (11 x 0.5) + (15 x 0.5) + (11 x 0.5) + (14 x 0.2)
+
(180 x 0.02)
+ 25
the device itself …
=
5.0 + 5.5 + 7.5 + 5.5 + 2.8 + 3.6
= 26.3 +
149
Electronics System Thermal Design and Characterization (RPS)
3.6
+ 25
+ 25
Corporate R&D • 8-Jul-2007
Graphically, low-power device #6 looks like this:
power
and just in case you were
wondering, the “embedded”
theta-JA looks like 1495 C/W !
∆=3.6 C
q6=0.02 W
∆=26.3 C
25 C
150
Electronics System Thermal Design and Characterization (RPS)
54 C
TJ6
1
180 C/W
junction
temperature
Corporate R&D • 8-Jul-2007
Controlling the matrix
How to harness this math in Excel®
151
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
3x3 theta matrix, 3x1 power vector Excel® math
Matrix MULTiply
obtained by using
multi-cell placement
Ctrl-Shift-Enter rather
{=array formula notation} than ordinary Enter
of array formula
theta
matrix
152
power
vector
array reference
to theta matrix
Electronics System Thermal Design and Characterization (RPS)
array reference
to power vector
Corporate R&D • 8-Jul-2007
7x3 theta matrix, 3x1 power vector Excel® math
don’t forget to use
theta matrix is no longer square –
Ctrl-Shift-Enter
# of columns still must equal
# of rows of power vector to invoke array formula notation
153
Electronics System Thermal Design and Characterization (RPS)
array formula now
occupies 7 cells
Corporate R&D • 8-Jul-2007
7x3 theta matrix, 3x2 power vector Excel® math
power “vector” is now a 3x2 array –
each column is a different power
scenario, yet both are still processed
using a single array (MMULT) formula
154
Electronics System Thermal Design and Characterization (RPS)
the single MMULT array formula now occupies
7 rows and 2 columns (one column for each
independent power scenario result)
Corporate R&D • 8-Jul-2007
Package-shrink “gotcha”
Often, much or even most of theta-JA
depends on what isn’t the package?
For instance, what if your cooling depends
significantly on convection from the board
surface (whether free or forced air)?
q = h ⋅ A ⋅ ∆T
⇔
q
A=
h ⋅ ∆T
So never mind the package resistance, the board
can only transfer a certain amount of heat to the air:
155
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Heat transfer 101
SOT23 @ 0.25W, ∆T = 100°C, 4 packages per 1000 mm^2
Decrease
size but not
power
dissipation
Decrease size
and reduce
power dissipation
SOT723 @ 0.25 W, ∆T = 100°C, 4 packages per 1000 mm^2
SOT723 @ 0.125 W, ∆T = 100°C, 8 packages per 1000 mm^2
(RDSON or other
electrical
performance)
156
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Thermal runaway
• Theory
– What is it?
– When can it happen?
– A mathematical model of power-law runaway
• An actual device example
• The surrounding system
– A paradox and its resolution
– how other components in a complete system
affect runaway in a susceptible device
• Review
157
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
typical thermal response
power
goes up
Thermal
runaway
temperature
rises
nonlinear electrical response
158
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Thermal runaway
• System thermal resistance isn’t low enough to
shed small perturbations of power
• Nonlinear power vs. junction temperature
device characteristic
159
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Balance of power
inputIN
power
power
increases
temperature
temperature
increases
is fixed
160
thermal
thermal
system
system
Electronics System Thermal Design and Characterization (RPS)
power
equals
dissipation
power OUT
rises
Corporate R&D • 8-Jul-2007
Device nonlinearity
causes trouble
By design,
temperature
power
is balanced
increases
and
temperature is fixed.
power
dissipation
rises
161
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
A linear thermal cooling system
TJ = Q ⋅ θ Jx + Tx
Q=
TJ − Tx
θ Jx
dQ
1
=
dT θ Jx
162
Electronics System Thermal Design and Characterization (RPS)
junction temperature as function of
power, theta, and ground
… solving for power
sensitivity (slope) of power with
respect to temperature
Corporate R&D • 8-Jul-2007
Operating point of thermal system with
temperature-independent power
power
system line
as temperature rises, more
heat may be dissipated
tendency to cool
Q
device line
power does not change
with temperature
tendency to heat
a decrease in temperature
means system dissipates
less power than device
produces, so temperature
rises
θJx
Tx
163
at small increase in
temperature, system
dissipates more power
than device produces, so
temperature falls
1
Electronics System Thermal Design and Characterization (RPS)
TJ
junction temperature
Corporate R&D • 8-Jul-2007
Operating point of thermal system where
power decreases with temperature
power
Q
system line
as temperature rises, more
heat may be dissipated
tendency
to cool
device line
tendency
to heat
power goes down
with increasing
temperature
1
θJx
Tx
164
TJ
Electronics System Thermal Design and Characterization (RPS)
junction temperature
Corporate R&D • 8-Jul-2007
Operating point of thermal system where power
increases with temperature, slopes favorable
power
system line
tendency
to cool
device line
Q
tendency
to heat
at small positive increase
in temperature, system can
still dissipate more power
than device produces
1
θJx
Tx
165
TJ
Electronics System Thermal Design and Characterization (RPS)
junction temperature
Corporate R&D • 8-Jul-2007
Operating point of thermal system where power
increases with temperature, slopes unfavorable
power
device line tendency to heat
power goes way up with
system line
increasing temperature
as temperature rises, more
heat may be dissipated
Q
tendency
to cool
Tx
166
TJ
Electronics System Thermal Design and Characterization (RPS)
for a small positive increase in
temperature, increased device
power exceeds increased
system dissipation capacity, so
device “runs away”
junction temperature
Corporate R&D • 8-Jul-2007
Operating points of thermal system when
device line has negative second derivative
power
Q2
system line
the stable (that is,
real) operating point
device line
an unachievable
operating point
tendency
to heat
Q1
power goes up with
increasing temperature
but rate of increase
falls with increase
(negative second
derivative)
tendency
to cool
Tx
167
tendency
to cool
TJ1
Electronics System Thermal Design and Characterization (RPS)
TJ2
junction temperature
Corporate R&D • 8-Jul-2007
System with no operating point, negative
second derivative, cannot be powered up
system line
power
tendency to cool
everywhere
Tx
168
Electronics System Thermal Design and Characterization (RPS)
device line
junction temperature
Corporate R&D • 8-Jul-2007
Device with negative second derivative,
system has unrealizable operating point,
system line
power
an unachievable
operating point
tendency
to cool
device line
tendency
to cool
Tx
169
Electronics System Thermal Design and Characterization (RPS)
junction temperature
Corporate R&D • 8-Jul-2007
Operating points of thermal system when
device line has positive second derivative
tendency
to heat
system line
power
an unachievable
operating point
the stable
(that is, real)
operating
point
Q
tendency
to heat
170
device line
tendency
power goes up with
to cool
increasing temperature,
but rate of increase rises
with increase (positive
second derivative)
Tx TJ
Electronics System Thermal Design and Characterization (RPS)
junction temperature
Corporate R&D • 8-Jul-2007
System with NO operating point,
overheats as soon as powered up
power
device line
system line
tendency to heat
everywhere
Tx
171
Electronics System Thermal Design and Characterization (RPS)
junction temperature
Corporate R&D • 8-Jul-2007
System with exactly one “runaway” operating point,
device has positive second derivative
power
device line
system line
neutral
tendency at only
this point
tendency
to heat
Q
the exact “runaway”
condition; slope of device
line equals slope of system
line at point of intersection
tendency
to heat
Tx
172
TJ
Electronics System Thermal Design and Characterization (RPS)
junction temperature
Corporate R&D • 8-Jul-2007
Let’s see how it works
stable
operating
point
10°C/W
system
25°C/W
system
40°C/W
system
173
2.0
1.6
Device Power Dissipation [W]
device
operating
curve
unstable operating point
1.2
NO
operating
point!
0.8
0.4
0.0
20
40
60
Junction Temperature [C]
Electronics System Thermal Design and Characterization (RPS)
80
100
Corporate R&D • 8-Jul-2007
Generic power law device and
generic linear cooling system
power
device
line
unstable
operating
point
system
line C
θJx1
1
θJx2
1
runaway point for
original theta
runaway point for
original thermal ground
Q
Tx
174
system line B
1
θJx1
stable
operating
point
system line A
TJ Ty
TR2
TR1
Electronics System Thermal Design and Characterization (RPS)
junction temperature
Corporate R&D • 8-Jul-2007
Don’t get confused by the terms!
device power
Q = V ⋅I
a mathematical
“power law”
y = ax
an “exponential”
power law (base is e)
y = ex
175
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Definition of power law device
rule of thumb for leakage;
2x increase for every 10°C
I = Io
I = Io
T
2 10
(ln 2 ) T
10
e
= Io e
T
⎛ 10 ⎞
⎜
⎟
⎝ ln 2 ⎠
I = Io e λ
176
T
T
Q = VRIo e λ = Qo e λ
1st and 2nd derivatives
T
defining:
for constant voltage, power does
the same
T
T −T
λ= 1 2
I
ln⎛⎜ 1 ⎞⎟
⎝ I2 ⎠
Electronics System Thermal Design and Characterization (RPS)
dQ Q o λ
=
e
λ
dT
2
d Q
dT 2
=
Qo
λ2
T
eλ
both always positive
Corporate R&D • 8-Jul-2007
The mathematical essence
Leads to:
System line
Q=
T − Tx
θ Jx
Power law
device line
T
Q = Qo e λ
Non-dimensionalizing
z=
T − Tx
λ
⎛ 1 −Tx
q=⎜
e λ
⎜ Qo
⎝
(system)
q = kz
temperature
⎞
⎟Q
⎟
⎠
where:
k=
power
Electronics System Thermal Design and Characterization (RPS)
θ Jx Q o
e
λ
(power law device)
q = ez
Eliminating q:
177
λ
− Tx
kz = e z
Corporate R&D • 8-Jul-2007
Perfect runaway transformed
ez
at point of tangency,
slope equals height
k=ez
k=ez
k=ez
k=ez
z0
1
zTz
0
1 z
0
zT
z=
1
z0
zT
1
zT
T − Tx
λ
zT − z0 = 1
178
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Transforming the nominal system
ez
“operating”
points
nominal
system line A
k>e
(2 intersections)
k<e
(no intersections)
k=e
at point of
tangency, slope
equals height
1
179
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Everything transformed
device
line
non-dimensional
power
unstable,
non-operating
point
system line B
1
stable
operating
point
system line C
k1
runaway point for
original theta
k2 = e
k1
k2
1z
x1
1
zR2
system line A
runaway point for
original thermal ground
non-dimensional temperature
zR1
z x1 = ln(k 1 ) − 1 z R 2 = 1 zR1 = ln (k 1 )
180
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
“Perfect runaway” results
in original terms
runaway temperature based on
original slope
TR1
⎛ λ
= λ ln⎜⎜
⎝ θ Jx1Q o
⎞
⎟
⎟
⎠
max ambient that goes
with it
Tx1
181
⎛ λ
= λ ln⎜⎜
⎝ θ Jx1Q o
⎞
⎟−λ
⎟
⎠
Electronics System Thermal Design and Characterization (RPS)
runaway temperature based on
original ambient
TR 2 = Tx + λ
system resistance that
goes with it
θ Jx 2 =
λ
Qo
⎞
⎛T
− ⎜ x +1⎟
e ⎝λ ⎠
Corporate R&D • 8-Jul-2007
The “operating” points
ez
kz
“operating”
points
unstable
kz u = e zu
stable
kz s = e z s
1
zs
182
Electronics System Thermal Design and Characterization (RPS)
zu
Corporate R&D • 8-Jul-2007
Newton’s method for the intersections
z i +1
− F (z i )
= zi −
F ′(z i )
kz = e z
ln kz = z
F(z ) = z − ln kz
1
F′(z ) = 1 −
z
z i +1
⎛k ⎞
ln ⎜ z i ⎟
e ⎠
⎝
=
1
1−
zi
For k/e ranging between 1.01 and 1000, convergence is
to a dozen significant digits in fewer than 10 iterations.
1
1 this initial guess
zo = =
k e ⋅ k converges to lower,
e stable point
183
Electronics System Thermal Design and Characterization (RPS)
this initial guess
⎛k ⎞
z
=
k
=
1
+
ln
ln
⎜ ⎟
converges to upper, o
⎝e⎠
unstable point
Corporate R&D • 8-Jul-2007
Excel® implementation of Newton’s method
184
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
And the intersection points come from …
find the non-dimensional intersections first, then
Tstable = Tx + λ ⋅ z stable
Tunstable = Tx + λ ⋅ z unstable
185
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Real datasheet example
the device power curve parameters
raw device data†
Vr [V]
12
40
Tmax [°C]
125
125
Tref [°C]
75
75
Itmax [A]
8.50E-3
2.80E-2
Itref [A]
5.20E-4
1.70E-3
λ
Tmax − Tref
λ=
I
⎞
ln⎛⎜ max
⎟
I
ref
⎝
⎠
I = I0 e λ
I0 = It max e
−
Tmax
λ
= Itref e
−
@40V
17.9
17.8
9.4E-5
1.02E-3
[°C]
Q o [W]
T
@12V
Tref
λ
rule of thumb
10
gave us:
=
ln (2)
= 14.4
Q0 = VRIo
† MBRS140T3
186
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Runaway analysis in nominal system
computed results
raw device data†
Vr [V]
12
40
λ
Tmax [°C]
125
125
Q o [W]
Tref [°C]
75
75
Itmax [A]
8.50E-3
2.80E-2
Itref [A]
5.20E-4
1.70E-3
k
λ
=
e
e θ Jx Q o
− Tx
λ
−1
Tx = 75
[°C]
k (compare to unity)
e
Tx max [°C]
given
theta
TR1[°C]
given
ambient
θ Jx2 max [°C/W]
TR 2[°C]
@12V
@40V
17.9
17.8
9.4E-5
1.02E-3
10.6
0.97
1.609
117.2
74.4
83.5
135.1
92.2
101.3
1055
96.6
92.9
92.8
θ Jx1 = 100
These translate into:
a stable operating point at 80.6°C (and 0.09 W),
an unstable point at 116.3°C (0.69 W)
@40V
θ Jx1 = 60
z = 0.312
z = 2.315
† MBRS140T3
187
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
How about the real thermal system?
• Is ambient really ambient?
• Is theta-JA what you think it is?
188
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
A paradox
0.5 W
0.5 W
Case A
Case B
100°C junction
100°C junction
identical
50°C/W
75°C
lead
50°C/W
75°C
100°C/W
25°C
thermal ground
thermal runaway,
based on θJx=150°C/W,
calculated to be at 125°C
189
Electronics System Thermal Design and Characterization (RPS)
lead
0.2°C/W
74.9°C
thermal ground
thermal runaway,
based on θJx=50.2°C/W,
calculated to be at 150°C
Corporate R&D • 8-Jul-2007
Paradox lost
raise the power by 0.1 W and see what happens
0.5 + 0.1 W
0.5 + 0.1 W
Case A
100 + 15°C
junction
Case B
100 + 5.02°C
50°C/W
50°C/W
75 + 10°C
lead
75 + 0.02°C
190
Electronics System Thermal Design and Characterization (RPS)
lead
0.2°C/W
100°C/W
(fixed) 25°C
junction
(fixed) 74.9°C
Corporate R&D • 8-Jul-2007
Illustrating the paradox
Case B
device
line
Case A
common nominal
operating point
0.5 W
25 C
191
74.9C 100 C
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Consider the following 6-component example of
a complete system, using linear superposition to
describe the thermal behavior
Tamb
Tref5
Tj5
Tj6
This is the
one we’re
interested in
Tj3
Tj2
Tref3
Tref1
Tj4
Tj1
TB
192
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Linear superposition math
matrix
product
Tj = θ ⋅ Q + Ta
temperature
(vector)
theta
(matrix)
193
Electronics System Thermal Design and Characterization (RPS)
power
(vector)
ambient
(scalar)
Corporate R&D • 8-Jul-2007
Putting illustrative numbers on the problem:
theta array
194
power
vector
J1
75
65
55
60
22
10
J2
65
71
60
55
25
11
J3
55
60
65
61
21
15
J4
60
55
61
73
18
11
Qj1
J5
22
25
21
18
125
14
Q j2 0.5
J6
10
11
15
11
14
180
Q j3 0.5
R1
73
65
55
59
22
10
Q j4 0.5
R3
55
60
63
61
21
15
Q j5 0.2
Q j6 0.02
R5
20
24
14
19
95
15
B
65
63
62
63
21
12
Electronics System Thermal Design and Characterization (RPS)
0.5
Corporate R&D • 8-Jul-2007
Observe the relative contributions
the other devices …
= (10 x 0.5) + (11 x 0.5) + (15 x 0.5) + (11 x 0.5) + (14 x 0.2)
+
(180 x 0.02)
+ 25
the device itself …
=
5.0 + 5.5 + 7.5 + 5.5 + 2.8 + 3.6
= 26.3 +
3.6
+
+
25
25
(ambient)
195
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Symbolically, for just Tj6, we’d write this:
“system” slope
effective ambient
+
5
Tj6 = ∑ (ψ i6 ⋅ Qi ) + θ j6a ⋅ Q 6 + Ta
i=1
temperature
of device #6
power of
other
devices
“interaction” terms from
theta matrix (offdiagonal elements)
196
Electronics System Thermal Design and Characterization (RPS)
power of
device #6
ambient
(scalar)
device #6 “self heating”
term from theta matrix
Corporate R&D • 8-Jul-2007
Graphically, it looks like this
2.0
25°C/W
system
1.6
Device Power Dissipation [W]
device
operating
curve
real
runaway
margin
what you
thought
was your
margin
1.2
0.8
0.4
∑ (ψ ij ⋅ Qi )
0.0
i≠ j
20
197
system with
“background
heating” of
other
devices
40
60
Junction Temperature [C]
Electronics System Thermal Design and Characterization (RPS)
80
100
Corporate R&D • 8-Jul-2007
How does effective ambient relate to board temperature?
if any of these are non-zero,
Ta′ will be higher than Ta
“system” slope for
isolated device
θ j6 a ⋅ Q 6
Tj6 =
(
+
5
∑ (Ψi6 ⋅ Qi ) + Ta
i=1
)
= θ j6B + θ B6a ⋅ Q 6
effective
′
T
a
ambient
= θ j6B ⋅ Q 6 + θ B6a ⋅ Q 6
+
Ta′
=
+
Ta′
∆Tj6B
temperature
rise, board to J6
198
+
+
∆TB6a
when Q6 is zero,
notboth
zero,ofboth
these
of these
will bewill
zero
be non-zero
temperature rise,
ambient to board
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
11:55
References
On the lighter side, not “technical” as such, but very
informative, accurate, and humorous:
1. Tony Kordyban, Hot Air Rises and Heat Sinks (Everything
You Know About Cooling Electronics is Wrong), ASME Press,
1998 (ISBN 0-7918-0074-1)
2. Tony Kordyban, More Hot Air, ASME Press, 2005 (ISBN 07918-0223-X)
199
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Thermal Test Standards
3.
EIA/JEDEC Standard JESD51-2, Integrated Circuits Thermal Test Method
Environmental Conditions - Natural Convection (Still Air), Electronic Industries
Alliance, December 1995
4.
EIA/JEDEC Standard JESD51-6, Integrated Circuit Thermal Test Method
Environmental Conditions - Forced Convection (Moving Air), Electronic
Industries Alliance, March 1999
5.
EIA/JEDEC Standard JESD51-8, Integrated Circuit Thermal Test Method
Environmental Conditions - Junction-to-Board, Electronic Industries Alliance,
October 1999
6.
EIA/JEDEC Standard JESD51-12, Guidelines for Reporting and Using
Electronic Package Thermal Information - Electronic Industries Alliance,
May 2005
7.
JEDEC Standards No. 24-3, 24-4, 51-1, Electronic Industries Alliance, 1990
8.
MIL-STD-883E, Method 1012.1, U.S. Department of Defense, 31 December
1996
200
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Math and electrical references
9.
M. Abramowitz, I. Stegun (eds), Handbook of Mathematical Functions, Dover
Publications, Inc., 9th Printing, Dec. 1972
10. S.D. Senturia, B.D. Wedlock, Electronic Circuits and Applications, John Wiley
& Sons, 1975
11. M.F. Gardner & J.L. Barnes, Transients in Linear Systems (Studied by the
Laplace Transformation), Vol. I, John Wiley and Sons, 1942
12. R.S. Muller, T.I. Kamins, Device Electronics for Integrated Circuits, 2nd Ed.,
John Wiley & Sons, 1986
13. Ben Nobel, Applied Linear Algebra, Prentice Hall, 1969
14. H.H. Skilling, Electric Networks, John Wiley and Sons, 1974
15. L. Weinberg, Network Analysis and Synthesis, McGraw Hill Book Company,
Inc., 1962
16. H. Wayland, Complex Variables Applied in Science and Engineering, Van
Nostrand Reinhold Company
201
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Thermal textbooks & references
17. H.S. Carslaw & J.C. Jaeger, Conduction of Heat In Solids, Oxford Press, 1959
18. E.R.G. Eckert & R.M. Drake Jr., Heat and Mass Transfer, McGraw Hill, 1959
19. J.P. Holman, Heat Transfer, 3rd Ed., McGraw Hill, 1972
20. J. VanSant, Conduction Heat Transfer Solutions, Lawrence Livermore National
Laboratory, Livermore, CA, 1980
Related papers by Stout, et al
21. “Two-Dimensional Axisymmetric ANSYS® Simulation for Two-Parameter
Thermal Models of Semiconductor Packages,” 7th International ANSYS
Conference & Exhibition, May 1996, R.P. Stout & R.L. Coronado
22. “End User's Method for Estimating Junction Temperatures Due to
Interactions of Other Dominant Heat Sources in Close Proximity to the
Device in Question,” ITHERM, May 1996, D.T. Billings & R.P. Stout
202
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
Related papers by Stout, et al, cont’
23. “Evaluation of Isothermal and Isoflux Natural Convection Coefficient Correlations for
Utilization in Electronic Package Level Thermal Analysis,” 13th Annual IEEE
Semiconductor Thermal Measurement and Management Symposium, January 1997,
B.A. Zahn and R.P. Stout
24. "Electrical Package Thermal Response Prediction to Power Surge", ITHERM, May 2000,
Y.L. Xu, R.P. Stout, D.T. Billings
25. “Accuracy and Time Resolution in Thermal Transient Finite Element Analysis,” ANSYS
2002 Conference & Exhibition, April 2002, R.P. Stout & D.T. Billings
26. “Minimizing Scatter in Experimental Data Sets,” ITHERM 2002 (Eighth Intersociety
Conference on Thermal and Thermomechanical Phenomena in Electronic Systems),
June 2002, R.P. Stout
27. “Combining Experiment and FEA into One, in Device Characterization,” ITHERM 2002
(Eighth Intersociety Conference on Thermal and Thermomechanical Phenomena in
Electronic Systems), June 2002, R.P. Stout, D.T. Billings
28. “A Two-Port Analytical Board Model,” ITHERM 2002 (Eighth Intersociety Conference on
Thermal and Thermomechanical Phenomena in Electronic Systems), June 2002, R.P.
Stout
29. “On the Treatment of Circuit Boards as Thermal Two-Ports,” InterPack2003, July 2003,
R.P. Stout
203
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
web links
30.
<http://en.wikipedia.org/wiki/Thermal_runaway>
31.
“Basic Thermal Management of Power Semiconductors,” AN1083/D, ON Semiconductor Application
Note, October 2003 <http://www.onsemi.com/pub/Collateral/AN1083-D.PDF>
32.
“Basic Semiconductor Thermal Management,” AN1570/D, ON Semiconductor Application Note,
January 2004 <http://www.onsemi.com/pub/Collateral/AN1570-D.PDF>
33.
“Transient Thermal Resistance - General Data and its Use,” AN569/D, ON Semiconductor Application
Note, May 2003 <http://www.onsemi.com/pub/Collateral/AN569-D.PDF>
34.
“Single-Channel 1206A ChipFET™ Power MOSFET Recommended Pad Pattern and Thermal
Performance,” AND8044/D, ON Semiconductor Application Note, December 2005
<http://www.onsemi.com/pub/Collateral/AND8044-D.PDF>
35.
“Thermal Analysis and Reliability of WIRE BONDED ECL,” AND8072/D, ON Semiconductor
Application Note, April 2006 <http://www.onsemi.com/pub/Collateral/AND8072-D.PDF>
36.
“TSOP vs. SC70 Leadless Package Thermal Performance,” AND8080/D, ON Semiconductor
Application Note, January 2004 <http://www.onsemi.com/pub/Collateral/AND8080-D.PDF>
37.
“Thermal Stability of MOSFETs,” AND8199/D, ON Semiconductor Application Note, August 2005
<http://www.onsemi.com/pub/Collateral/AND8199-D.PDF>
38.
R.P. Stout, “General Thermal Transient RC Networks ,” AND8214/D, ON Semiconductor Application
Note, April 2006 <http://www.onsemi.com/pub/Collateral/AND8214-D.PDF>
204
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
web links, cont’
39.
R.P. Stout, “Semiconductor Package Thermal Characterization,” AND8215/D, ON Semiconductor
Application Note, April 2006 <http://www.onsemi.com/pub/Collateral/AND8215-D.PDF>
40.
R.P. Stout, “Minimizing Scatter in Experimental Data Sets,” AND8216/D, ON Semiconductor
Application Note, April 2006 <http://www.onsemi.com/pub/Collateral/AND8216-D.PDF>
41.
R.P. Stout, “What's Wrong with %Error in Junction Temperature,” AND8217/D, ON Semiconductor
Application Note, April 2006 <http://www.onsemi.com/pub/Collateral/AND8217-D.PDF>
42.
R.P. Stout, “How to Extend a Thermal - RC - Network Model,” AND8218/D, ON Semiconductor
Application Note, April 2006 <http://www.onsemi.com/pub/Collateral/AND8218-D.PDF>
43.
R.P. Stout, “How to Generate Square Wave, Constant Duty Cycle, Thermal Transient Response
Curves,” AND8219/D, ON Semiconductor Application Note, April 2006
<http://www.onsemi.com/pub/Collateral/AND8219-D.PDF>
44.
R.P. Stout, “How To Use Thermal Data Found in Data Sheets,” AND8220/D, ON Semiconductor
Application Note, April 2006 <http://www.onsemi.com/pub/Collateral/AND8220-D.PDF>
45.
R.P. Stout, “Thermal RC Ladder Networks,” AND8221/D, ON Semiconductor Application Note, April
2006 <http://www.onsemi.com/pub/Collateral/AND8221-D.PDF>
46.
R.P. Stout, “Predicting the Effect of Circuit Boards on Semiconductor Package Thermal
Performance,” AND8222/D, ON Semiconductor Application Note, April 2006
<http://www.onsemi.com/pub/Collateral/AND8222-D.PDF>
47.
R. P. Stout, Predicting Thermal Runaway,” AND8223/D, ON Semiconductor Application Note, April
2006 <http://www.onsemi.com/pub/Collateral/AND8223-D.PDF>
205
Electronics System Thermal Design and Characterization (RPS)
Corporate R&D • 8-Jul-2007
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