Electronics System Thermal Design and Characterization · 13 Electronics System Thermal Design and...
Transcript of Electronics System Thermal Design and Characterization · 13 Electronics System Thermal Design and...
Roger Stout • 8-Jul-2007
Electronics System Thermal Design and Characterization
Roger Stout, P.E.Senior Research ScientistCorporate Research & DevelopmentAdvanced Packaging Technology
Corporate R&D • 8-Jul-20072 Electronics System Thermal Design and Characterization (RPS)
Course outline
• Introduction• Experimental Techniques• Linear Superposition• Thermal Runaway• References
Corporate R&D • 8-Jul-20073 Electronics System Thermal Design and Characterization (RPS)
Introduction
• Why This Course?• Terminology and Basic Principles• Facts and Fallacies
Corporate R&D • 8-Jul-20074 Electronics System Thermal Design and Characterization (RPS)
Can this device handle 2W?
Corporate R&D • 8-Jul-20075 Electronics System Thermal Design and Characterization (RPS)
I’m putting 5A into this part. What’s its junction temperature going to be?
Corporate R&D • 8-Jul-20076 Electronics System Thermal Design and Characterization (RPS)
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?
Corporate R&D • 8-Jul-20077 Electronics System Thermal Design and Characterization (RPS)
I’m putting together a data sheet for this new device. What’s theta-JA for this package?
Corporate R&D • 8-Jul-20078 Electronics System Thermal Design and Characterization (RPS)
I’m putting together a data sheet for this new device. What’s theta-JA for this package?
Corporate R&D • 8-Jul-20079 Electronics System Thermal Design and Characterization (RPS)
What’s the maximum power rating on this part going to be?
Corporate R&D • 8-Jul-200710 Electronics System Thermal Design and Characterization (RPS)
What’s the maximum power rating on this part going to be?
Corporate R&D • 8-Jul-200711 Electronics System Thermal Design and Characterization (RPS)
Why is our SOT-23 thermal number so much worse than our competition?
• Us– SOT-23 package– 60x60 die– solder D/A– copper leadframe– min-pad board– still air
• Them– SOT-23 package– 20x20 die– epoxy D/A– alloy 42 leadframe– 1” x 2oz spreader– big fan
Corporate R&D • 8-Jul-200712 Electronics System Thermal Design and Characterization (RPS)
Why θJA doesn’t belong in the “Maximum Ratings”* table
*let alone the “Absolute Maximum Ratings”
Corporate R&D • 8-Jul-200713 Electronics System Thermal Design and Characterization (RPS)
It’s like trying to sell your car (some bureaucrat says you must list its gas mileage in the ad)
1 20% grade uphill, 75mph, back seat and trunk full of bricks
mpg4Gas Mileage (Note 1)
UnitsValueSymbolDescription
MAXIMUM RATINGS
For sale:Geo Metro, 1999 model, excellent condition!
Corporate R&D • 8-Jul-200714 Electronics System Thermal Design and Characterization (RPS)
Gee, we’d better not be so “worst case,” should we?
1 20% grade uphill, 75mph
mpg10Gas Mileage (Note 1)
mpg/brick0.002Mileage derating factor
UnitsValueSymbolDescription
MAXIMUM RATINGS
For sale:Geo Metro, 1999 model, excellent condition!
Corporate R&D • 8-Jul-200715 Electronics System Thermal Design and Characterization (RPS)
Wait, they said “maximum”. Maybe we’re thinking about this all wrong …
1 20% grade downhill, empty vehicle (no bricks, not even a driver!), coasting
mpg/%2IDF (incline derating factor)
mpg/brick0.002BDF (brick derating factor)
mpg110Gas Mileage (Note 1)
mpg/mph0.07SDF (speed derating factor)
UnitsValueSymbolDescription
MAXIMUM RATINGS
For sale:Geo Metro, 1999 model, excellent condition!
Corporate R&D • 8-Jul-200716 Electronics System Thermal Design and Characterization (RPS)
Frankly, Tj-max is the only “thermal” specification that I
think belongs in the Maximum Ratings table.
Corporate R&D • 8-Jul-200717 Electronics System Thermal Design and Characterization (RPS)
Terminology and basic principles
Corporate R&D • 8-Jul-200718 Electronics System Thermal Design and Characterization (RPS)
“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.
Corporate R&D • 8-Jul-200719 Electronics System Thermal Design and Characterization (RPS)
Thermal/electrical analogy
temperature <=> voltage
power <=> current
∆temp/power <=> resistance
energy/degree <=> capacitance
Corporate R&D • 8-Jul-200720 Electronics System Thermal Design and Characterization (RPS)
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
Corporate R&D • 8-Jul-200721 Electronics System Thermal Design and Characterization (RPS)
A generic thermal system
Heat input
Corporate R&D • 8-Jul-200722 Electronics System Thermal Design and Characterization (RPS)
“Theta” (Greek letter θ)
Heat input
Tx
Ty
We know actual heat flowing along path of interest
true “thermal resistance”
path
yxxy q
TT −=θ
Corporate R&D • 8-Jul-200723 Electronics System Thermal Design and Characterization (RPS)
“Psi” (Greek letter Ψ)
Heat input
Tx
Ty??
We don’t know actual heat flowing along path of interest
All we know is total heat input
total
yxxy q
TT −=Ψ
Corporate R&D • 8-Jul-200724 Electronics System Thermal Design and Characterization (RPS)
When Ψ becomes θ
Heat input
ambient
ambient
ambient
ambient
Tj
Either or both “points”of interest are
isotherms
All heat flowing between them is
known
jx TT =
ambientTy =
devicepath PowerPower =
(a point)
(an isotherm)
xyJA PowerTT
Ψ=−
=total
ambientjθ
Corporate R&D • 8-Jul-200725 Electronics System Thermal Design and Characterization (RPS)
An example of a device with two different “Max Power” ratings
• Suppose a datasheet says:– Tjmax = 150°C– θJA = 100°C/W– Pd = 1.25W (Tamb=25°C)
• But it also says:– ΨJL = 25°C/W– Pd = 3.0W (TL=75°C)
Where’s the “inconsistency”?
1501252525.1*10025=+=
+
15075753*2575=+=
+
Corporate R&D • 8-Jul-200726 Electronics System Thermal Design and Characterization (RPS)
Where’s the inconsistency?
What’s TL?
25°C/W (ΨJL)
100°C/W(θJA)
TJ =150°C
TA =25°C
Not 75°C !!
(try about 119°C)
…¾ of the way from ambient to Tj
Corporate R&D • 8-Jul-200727 Electronics System Thermal Design and Characterization (RPS)
Facts and fallacies
Corporate R&D • 8-Jul-200728 Electronics System Thermal Design and Characterization (RPS)
Facts and fallacies• Basic idea:
– temperature difference is proportional to heat input
Corporate R&D • 8-Jul-200729 Electronics System Thermal Design and Characterization (RPS)
twice the heat, twice the temperature rise
Tf
To
Tf
To
PowerT ∝∆
( )tRPT *=∆
P=power heating P2power heating =
( )tRPT *2=∆
time time
junc
tion
tem
pera
ture
junc
tion
tem
pera
ture
Corporate R&D • 8-Jul-200730 Electronics System Thermal Design and Characterization (RPS)
Facts and fallacies• Basic idea:
– temperature difference is proportional to heat input• There are three modes of heat transfer
– conduction– convection– radiation (electromagnetic/infrared)
Corporate R&D • 8-Jul-200731 Electronics System Thermal Design and Characterization (RPS)
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
Corporate R&D • 8-Jul-200732 Electronics System Thermal Design and Characterization (RPS)
Facts and fallacies, cont’
• Basic idea:– “thermal resistance” is an intrinsic property of a package
Corporate R&D • 8-Jul-200733 Electronics System Thermal Design and Characterization (RPS)
back in the good old days ...
metal can --fair approximation of “isothermal” surface
axial leaded device --only two leads, heat
path fairly well defined
Corporate R&D • 8-Jul-200734 Electronics System Thermal Design and Characterization (RPS)
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
Corporate R&D • 8-Jul-200735 Electronics System Thermal Design and Characterization (RPS)
Which lead? Where on case?
Corporate R&D • 8-Jul-200736 Electronics System Thermal Design and Characterization (RPS)
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
Corporate R&D • 8-Jul-200737 Electronics System Thermal Design and Characterization (RPS)
OH of GPM 1C25W50
C/W2.1
2
°==
°=Ψ −
c
d
tabJ
TP
air stillC25W5.1
C/W8.0
°==
°=Ψ −
c
d
tabJ
TP
Same ref, different values
Corporate R&D • 8-Jul-200738 Electronics System Thermal Design and Characterization (RPS)
Archetypal package
silicon
die attach
wire/clip
flag/leadframe
case
circuit board
convection
60%10%
20%
10%
Corporate R&D • 8-Jul-200739 Electronics System Thermal Design and Characterization (RPS)
Then we change things …
optional heatsink
mold compound/
case
flag/leadframe
application board
silicon
die attach
wire/clip
optional heatsink
optional “case”
application board
silicon die
attach
optional underfill
pads/balls
add an external heatsink … flip the die over …
40%
20%
60%
20% 20%40%
Corporate R&D • 8-Jul-200740 Electronics System Thermal Design and Characterization (RPS)
A bare “flip chip”
application board
silicon
underfill
pads/balls
90%
10%
Corporate R&D • 8-Jul-200741 Electronics System Thermal Design and Characterization (RPS)
21
43
3
RRRR1
R
++
+=
0
10
20
30
40
50
60
1 10 100 1000board
rstnc. [C/W]
psi-JC - var brd onlypsi-JC - var airflow
43
21
1
RRRR1
R
++
+=
4321 RR1
RR1
1
++
+
=
Even when it’s constant, it’s not!
0100200300400500600700800900
1000
1 10 100 1000board
rstnc. [C/W]
thetaJA - var brd onlythetaJA - var airflow
0
5
10
15
20
25
1 10 100 1000board
rstnc. [C/W]
psi-JL - var brd onlypsi-JL - var airflow
theta-JA
psi-JT
psi-JL
R1 (path down to board)
constant at 20
R2 (board resistance) vary
from 1 to 1000
R3 (path through case top)constant at 80
R4 (case to air path resistance) constant at 500, or 20x R2
TCTL
Tj
Tamb
total
LJJL Q
TT −=Ψ total
CJJT Q
TT −=Ψ
total
ambJJA Q
TT −=θ
packageenvironment
Corporate R&D • 8-Jul-200742 Electronics System Thermal Design and Characterization (RPS)
Typical thermal test board types
min-pad boardminimum metal area to attach device (plus traces to get signals and power in and out)
1-inch-pad boarddevice at center of 1”x1” metal area (typically 1-oz Cu); divided into sections based on lead count
Corporate R&D • 8-Jul-200743 Electronics System Thermal Design and Characterization (RPS)
ExperimentalTechniques
Corporate R&D • 8-Jul-200744 Electronics System Thermal Design and Characterization (RPS)
Experimental Techniques
• Temperature Sensitive Parameters (TSPs)
• Different Device Types and How to Test Them
• Heating vs Cooling Curve Techniques
• Test Conditions
Corporate R&D • 8-Jul-200745 Electronics System Thermal Design and Characterization (RPS)
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
Corporate R&D • 8-Jul-200746 Electronics System Thermal Design and Characterization (RPS)
Typical TSP Behavior
Vf
T
125°C
25°C
0.7 V0.5 V
1 ma
increasing current
Vf
sense current
calibrate forward voltage at controlled, small (say 1mA) sense current
Corporate R&D • 8-Jul-200747 Electronics System Thermal Design and Characterization (RPS)
DUT
true const. current supply
(1 mA typical)
DUT
10KΩ
If Vf-0.7V, then I-1mA
10.7V
How to measure Tj
OR
approximate const. current supply
Corporate R&D • 8-Jul-200748 Electronics System Thermal Design and Characterization (RPS)
DUT
10KΩheatingpowersupply
10.7V10.7V
DUT
10KΩheatingpowersupply
10.7V
How to heat
OR
sample current is off while heating current on
sample current is always on
Corporate R&D • 8-Jul-200749 Electronics System Thermal Design and Characterization (RPS)
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
Corporate R&D • 8-Jul-200750 Electronics System Thermal Design and Characterization (RPS)
0.90 W0.70 W0.64 W
The Importance of 4-wire measurements
Powersupply
+(1.00 V)
-(0 V)
1 A
0.18 V 0.82 V
0.95 V0.05 V 0.85 V0.15 V
Output = 1 W
Corporate R&D • 8-Jul-200751 Electronics System Thermal Design and Characterization (RPS)
Which raises an interesting question:
0.3 W
Powersupply
+(1.00 V)
-(0 V)
3 A
0.45 V 0.55 V
0.98 V0.02 V
Output = 3 W
Is this a fair characterization of a low-Rds-on device?
1.3 W 1.3 W
Corporate R&D • 8-Jul-200752 Electronics System Thermal Design and Characterization (RPS)
Bipolar transistor• TSP is Vce at designated
“constant” current• Heating is through Vce• Choose a base current
which permits adequate heating
bias supply
TSP=Vcebias resistor
TSP supply
switch
heating supply
10KΩ
Corporate R&D • 8-Jul-200753 Electronics System Thermal Design and Characterization (RPS)
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
Corporate R&D • 8-Jul-200754 Electronics System Thermal Design and Characterization (RPS)
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=Vsd
TSP supply
switch
heating supply
10KΩ
+
-
Corporate R&D • 8-Jul-200755 Electronics System Thermal Design and Characterization (RPS)
+
MOSFET / TMOS method 2
• If you have fast switches and stable supplies
• Forward bias everything and use two different gate voltages
TSP=Vds
TSP supply
close switch to heat
heating supply
10KΩ
-
+
-
V-gate for
heating-
V-gate for
measure
+
close switch to heat
close switch to measure
Corporate R&D • 8-Jul-200756 Electronics System Thermal Design and Characterization (RPS)
RF MOS
• They exist to amplify high frequencies (i.e. noise)!
TSP supply
close switch to heat
heating supply
10KΩ
-
+V-gate
for heating
-
+
close switch to heat
close switch to measure
• Feedback resistors may keep them in DC
+
-
TSP = body diode
TSP supply
Corporate R&D • 8-Jul-200757 Electronics System Thermal Design and Characterization (RPS)
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 TSP=Vds
gate voltage
TSP supply
switch
heating supply
10KΩ
Corporate R&D • 8-Jul-200758 Electronics System Thermal Design and Characterization (RPS)
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
TSP supply
switch10KΩ
heating supply
TSP=Vac
cathode
anodegate
Corporate R&D • 8-Jul-200759 Electronics System Thermal Design and Characterization (RPS)
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!)
Corporate R&D • 8-Jul-200760 Electronics System Thermal Design and Characterization (RPS)
Heating curve methodvs.
cooling curve method
Corporate R&D • 8-Jul-200761 Electronics System Thermal Design and Characterization (RPS)
DUT
10KΩheatingpowersupply
10.7V
Quick review:Basic Tj measurement
DUT
10KΩheatingpowersupply
10.7V
first we heat then we measure
Corporate R&D • 8-Jul-200762 Electronics System Thermal Design and Characterization (RPS)
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
Corporate R&D • 8-Jul-200763 Electronics System Thermal Design and Characterization (RPS)
Vf
Vf
T
125°C
25°C
.7V.5V
calibrate forward voltage @ 1mA sense currrent
pow
er-o
ff co
olin
g
high-current heating
measurements
convert cooling volts to
temperature
Basic“Heating Curve”Transient Method vo
ltage
curre
nt
1 ma
stea
dy s
tate
reac
hed
Tem
pera
ture
Time
pow
er-o
ff co
olin
g
high-current heating
pow
er-o
ff co
olin
g
high-current heating
pow
er-o
ff co
olin
g
high-current heating
measured temperatures
Corporate R&D • 8-Jul-200764 Electronics System Thermal Design and Characterization (RPS)
pow
er-o
ff co
olin
g
high-current heating
volta
ge
curre
nt
1 ma
Tem
pera
ture
Time
pow
er-o
ff co
olin
g
high-current heating
pow
er-o
ff co
olin
g
high-current heating
pow
er-o
ff co
olin
g
high-current heating
measured temperatures
Heating curve method #2
Time
Corporate R&D • 8-Jul-200765 Electronics System Thermal Design and Characterization (RPS)
Basic“Cooling Curve”
Transient MethodVf
Vf
T
125°C
25°C
.7V.5V
calibrate forward voltage @ 1mA sense currrentpower-off
coolinghigh-
current heating
volta
ge curre
nt
1 ma
measurements
heating period
transient cooling period (data taken)
stea
dy s
tate
reac
hed
Tem
pera
ture
Time
convert cooling volts to
temperature
Tem
pera
ture
Time (from start of cooling)
subtract cooling curve from peak temperature to obtain“heating” curve equivalent
Corporate R&D • 8-Jul-200766 Electronics System Thermal Design and Characterization (RPS)
Whoa!… that last step, there ...
• Heating vs. cooling– Physics is symmetric, as long as the material and
system properties are independent of temperature
Corporate R&D • 8-Jul-200767 Electronics System Thermal Design and Characterization (RPS)
Heating vs. cooling symmetry
(all the same curves, flipped
vertically)
flag
lead
back of board
edge of board
Start of (constant) power off
junction
Start of constant power input(“step heating”)
Corporate R&D • 8-Jul-200768 Electronics System Thermal Design and Characterization (RPS)
• 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:
JA
j TTpower
θambientmax −=
(cooling)
Corporate R&D • 8-Jul-200769 Electronics System Thermal Design and Characterization (RPS)
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)
(cooling)
Corporate R&D • 8-Jul-200770 Electronics System Thermal Design and Characterization (RPS)
Effect of power on heating curve
< steady-state max power
Tj-max
Tamb
steady-state max power
2x steady-state power6x steady-
state power
10x steady-state power
3x steady-state power
time
junc
tion
tem
pera
ture
Corporate R&D • 8-Jul-200771 Electronics System Thermal Design and Characterization (RPS)
Some initial uncertainty
heating period transient cooling period (data taken)
stea
dy s
tate
reac
hed
Tem
pera
ture
Time
power-off cooling
high-current heating
but once we’re past the “uncertain” range, all the rest of the points are “good”
a few initial points may be uncertain
(cooling)
Corporate R&D • 8-Jul-200772 Electronics System Thermal Design and Characterization (RPS)
Heating vs. cooling tradeoffs
starting temperature
heatingpower
temperature of fastest data
errorcontrol
HEATING
ambient
limited by tester
closer to ambient
all points similar error
COOLING
?
limited to steady-state
closer toTj-max
error limited to first few points
Corporate R&D • 8-Jul-200773 Electronics System Thermal Design and Characterization (RPS)
•Still air, moving air•Various mounting configurations
– Min-pad board– 1” heat spreader board
•Coldplate testing– Single, dual, “ring”
Test Conditions
Corporate R&D • 8-Jul-200774 Electronics System Thermal Design and Characterization (RPS)
• 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
Still air vs. moving air
Corporate R&D • 8-Jul-200775 Electronics System Thermal Design and Characterization (RPS)
total system thermal resistance
0
10
20
30
40
50
60
70
80
90
100
0.1 1 10
air speed [m/s]
thet
a-JA
[C/W
]
board resistance
package resistance
Corporate R&D • 8-Jul-200776 Electronics System Thermal Design and Characterization (RPS)
• 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
Different boards
Corporate R&D • 8-Jul-200777 Electronics System Thermal Design and Characterization (RPS)
1" pad vs min-pad
0
50
100
150
200
250
300
350
0 100 200 300 400 500 600 700
min pad thetaJA (C/W)
1" p
ad th
etaJ
A (C
/W)
overall linear fit is:1" value = [0.51*(min-pad value) - 7]
SMBSMA & Pow ermite
Micro 8
TSOP-6(AL42)SOT-23
SOD-123
TSOP-6
SOD-123
SOT-23
SOD-323
SOT-23
SOD-123
Top Can
D2pak & TO220
Top Can
Dpak
SO-8SOT-223
TSOP-6SO-8
SMC
Source:Un-derated thermal data from old PPD database
Roger Stout 5/2
Corporate R&D • 8-Jul-200778 Electronics System Thermal Design and Characterization (RPS)
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
Corporate R&D • 8-Jul-200779 Electronics System Thermal Design and Characterization (RPS)
Standard coldplate testing
• Detailed design and placement of “case” TC can have significant effect on measured value
TC in 0.025” well, 0.25” from surface
DUT
.375”
.75”
Vleer pin assy
2.0”
TC on Vleer pin measures temperature at interface
Liquid Coolant Flow
Corporate R&D • 8-Jul-200780 Electronics System Thermal Design and Characterization (RPS)
“Dual” coldplate testing
• Alternative method for “two-parameter”characterization methods where two independent “isothermal” boundary conditions are desired
T1
T2
Corporate R&D • 8-Jul-200781 Electronics System Thermal Design and Characterization (RPS)
“Ring” coldplate
• For making somewhat higher-power board-mounted measurements; “ring” coldplate is clamped around outer edge of test board to constrain board temperature
Corporate R&D • 8-Jul-200782 Electronics System Thermal Design and Characterization (RPS)
2-parameter data reduction
heat in, Q
R1
R2
T1
Tj
T2
21 QQQ +=
( ) ( )22
11
11 TTR
TTR
Q jj −+−=
bxmxmy ++= 2211
( )111
11 TTxR
m j −==0≡b
( )222
21 TTxR
m j −==
where:
heat up, Q1
heat down, Q2
This has the form of a two-variable linear equation:
Corporate R&D • 8-Jul-200783 Electronics System Thermal Design and Characterization (RPS)
adJAJ TPT +⋅= θ
What’s wrong with theta-JA?
d
aJJA P
TT −=θ
d
tabJJtab P
TT −=Ψ
tabdJtabJ TPT +⋅Ψ=
2
Corporate R&D • 8-Jul-200784 Electronics System Thermal Design and Characterization (RPS)
Theta-JA vs copper area
Corporate R&D • 8-Jul-200785 Electronics System Thermal Design and Characterization (RPS)
Linear superposition
Corporate R&D • 8-Jul-200786 Electronics System Thermal Design and Characterization (RPS)
Ta
TjθJA
Corporate R&D • 8-Jul-200787 Electronics System Thermal Design and Characterization (RPS)
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
Corporate R&D • 8-Jul-200788 Electronics System Thermal Design and Characterization (RPS)
Our case-study will be this 6-component thermal system
Tj3 Tj2
Tj1Tj4
Tj5Tj6
Tref1
Tref5
Tref3
TB
Tamb
Corporate R&D • 8-Jul-200789 Electronics System Thermal Design and Characterization (RPS)
• 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.
Linear superposition– what is it?
nsource2source1sourcecomposite TTTT ∆++∆+∆=∆ L
Corporate R&D • 8-Jul-200790 Electronics System Thermal Design and Characterization (RPS)
DCBA q21q3q2T ⋅+⋅+⋅=∆ .
• The system must be “linear” – in brief, all individual responses must be proportional to all individual excitations.
Linear superposition– when does it apply?
DACABAAnet TTTT ←←← ∆+∆+∆=∆
Corporate R&D • 8-Jul-200791 Electronics System Thermal Design and Characterization (RPS)
Linear superposition doesn’t apply if the system isn’t linear.
( ) ( ) L+⋅+⋅=∆ 2211 qqTbqqTaT ,,
L+⋅+⋅=∆ 2n2
1n1 qbqaT
Corporate R&D • 8-Jul-200792 Electronics System Thermal Design and Characterization (RPS)
Linear superposition– when would you use it?
When you have multiple heat sources(that is, all the time!)
Corporate R&D • 8-Jul-200793 Electronics System Thermal Design and Characterization (RPS)
Linear superposition– how do you use it?
Tj3 Tj2
Tj1Tj4
Tj5Tj6
Tref1
Tref5
Tref3
TB
Tamb
Corporate R&D • 8-Jul-200794 Electronics System Thermal Design and Characterization (RPS)
Temperature direct contributions and totals
0
20
40
60
80
100
120
J1 J2 J3 J4 J5 J6 R1 R3 R5 B
result location
tem
pera
ture
rise
[C],
each
sou
rce
J1 at 0.4 W J2 at 0.4 W J3 at 0.4 WJ4 at 0.4 W J5 at 0.5 W J6 at 0.2 W
0
20
40
60
80
100
120
J1 J2 J3 J4 J5 J6 R1 R3 R5 B
result location
tem
pera
ture
rise
[C] s
um o
f sou
rces
J1 at 0.4 W J2 at 0.4 W J3 at 0.4 WJ4 at 0.4 W J5 at 0.5 W J6 at 0.2 W
Corporate R&D • 8-Jul-200795 Electronics System Thermal Design and Characterization (RPS)
Normalized responses at each location due to each source
0
20
40
60
80
100
120
140
160
180
200
J1 J2 J3 J4 J5 J6 R1 R3 R5 Bresponse location
norm
aliz
ed re
spon
se [C
/W],
each
sou
rce J1 at 1 W
J2 at 1 WJ3 at 1 WJ4 at 1 WJ5 at 1 WJ6 at 1 W
Corporate R&D • 8-Jul-200796 Electronics System Thermal Design and Characterization (RPS)
a
n
2
1
JnAn2n1
n2A2J12
n112A1J
jn
2j
1j
T
q
T
TT
+
⎪⎪⎭
⎪⎪⎬
⎫
⎪⎪⎩
⎪⎪⎨
⎧
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
ΨΨ
ΨΨΨΨ
=
⎪⎪⎭
⎪⎪⎬
⎫
⎪⎪⎩
⎪⎪⎨
⎧
M
L
MOM
L
M
θ
θθ
theta matrix assembled from simplified subsystems
junction temperature
vector
power input vector
board interactions
JT qJAθ aT
self-heating terms
Corporate R&D • 8-Jul-200797 Electronics System Thermal Design and Characterization (RPS)
a
n
2
1
BAnJBnn2n1
n22BA2JB12
n1121BA1JB
jn
2j
1j
T
q
T
TT
+
⎪⎪⎭
⎪⎪⎬
⎫
⎪⎪⎩
⎪⎪⎨
⎧
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
+ΨΨ
Ψ+ΨΨΨ+
=
⎪⎪⎭
⎪⎪⎬
⎫
⎪⎪⎩
⎪⎪⎨
⎧
M
L
MOM
L
M
θθ
θθθθ
theta matrix assembled from simplified subsystems
junction temperature
vector
power input vector
device resistance board
resistance
Corporate R&D • 8-Jul-200798 Electronics System Thermal Design and Characterization (RPS)
visualizing theta and psi
(idle heat source “x”)
thermal ground
measurements here are s
Ψ
xAΨyAΨ
AJ1θ
BJ1θ
BAθ
θmeasurements
here are s
(idle heat source “y”)
heat in here
Corporate R&D • 8-Jul-200799 Electronics System Thermal Design and Characterization (RPS)
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜
⎝
⎛
ΨΨΨΨΨΨΨΨΨΨΨΨΨ
=
⎪⎪⎪
⎭
⎪⎪⎪
⎬
⎫
⎪⎪⎪
⎩
⎪⎪⎪
⎨
⎧
∆∆∆∆∆
3
2
1
B3B2B1
1L31L21L1
x3x2x1
322JA12
31211JA
BA
A1L
xA
2j
1j
qqq
TTTTT
θθ
one column for each heat source
junction temperature
vectorpower input
vector
one row for each
heat source
one row for each temperature location of interest
theta matrix doesn’t have to be square
Corporate R&D • 8-Jul-2007100 Electronics System Thermal Design and Characterization (RPS)
• What is it?• When does it not apply?
The reciprocity theorem
Corporate R&D • 8-Jul-2007101 Electronics System Thermal Design and Characterization (RPS)
Electrical reciprocity
IV
-
+
Corporate R&D • 8-Jul-2007102 Electronics System Thermal Design and Characterization (RPS)
Electrical reciprocity
5 V+
-
? V+
-0.3 V
-
+
2 A0.3 V-
+
Corporate R&D • 8-Jul-2007103 Electronics System Thermal Design and Characterization (RPS)
Thermal reciprocity
heat input here
same response
here
response here
Corporate R&D • 8-Jul-2007104 Electronics System Thermal Design and Characterization (RPS)
Another thermal reciprocity example
heat input here
same response
here
response here
(s)
(s)
(r)
(r)
Corporate R&D • 8-Jul-2007105 Electronics System Thermal Design and Characterization (RPS)
(square part of) matrix is symmetric
12
15
15
10
180
14
11
15
11
10
21
95
21
22
14
125
18
21
25
22
63
19
61
59
11
18
73
61
55
60
62
14
63
55
15
21
61
65
60
55
6365
2420
6055
6573
1110
2522
5560
6055
7165
6575
B
R5
R3
R1
J6
J5
J4
J3
J2
J1
rows are the “y”response locations
columns are the “x” heat sources
Corporate R&D • 8-Jul-2007106 Electronics System Thermal Design and Characterization (RPS)
When does reciprocity NOT Apply?
AD
Cairflow
Heat in at “A” will raise temperature of “C” more than heat in at “C” will raise temperature of “A”
• Upwind and downwind in forced-convection dominated applications
“B” and “D” may still be roughly reciprocal
B
Corporate R&D • 8-Jul-2007107 Electronics System Thermal Design and Characterization (RPS)
A linear superposition example
(unequivocal proof that a published theta-JA is virtually meaningless)
Corporate R&D • 8-Jul-2007108 Electronics System Thermal Design and Characterization (RPS)
Superposition example
Tj3 Tj2
Tj1Tj4
Tj5Tj6
Tref1
Tref5
Tref3
TB
Tamb
Corporate R&D • 8-Jul-2007109 Electronics System Thermal Design and Characterization (RPS)
Device 1 heated, 1.1 W
Tj3=85.5 Tj2=96.5
Tj1=107.5Tj4=91.0
Tj5=49.2Tj6=36.0
Tref1=105.3
Tref5=47.0
Tref3=85.5
TB=96.5
Tamb=25
Corporate R&D • 8-Jul-2007110 Electronics System Thermal Design and Characterization (RPS)
Reduce the data
65Ψ BA
20Ψ r5A
55Ψ r3A
73Ψ r1A
10Ψ j6A
22Ψ j5A
60Ψ j4A
55Ψ j3A
65Ψ j2A
75θj1A
7511
255107qTT
1
amb1jA1j =
−=
−=
..θ
6511
25596qTT
1
amb2jA2j =
−=
−=Ψ
..
6511
25596qTT
1
ambBBA =
−=
−=Ψ
..
M
Corporate R&D • 8-Jul-2007111 Electronics System Thermal Design and Characterization (RPS)
Collect the θ/Ψ values in the matrix
65
20
55
73
10
22
60
55
65
75
B
R5
R3
R1
J6
J5
J4
J3
J2
J1
Corporate R&D • 8-Jul-2007112 Electronics System Thermal Design and Characterization (RPS)
Device 2 heated, 1.2 W
Tj3=97.0 Tj2=110.2
Tj1=103.0Tj4=91.0
Tj5=55.0Tj6=38.2
Tref1=103.0
Tref5=53.8
Tref3=97.0
TB=100.6
Tamb=25
63Ψ BA
24Ψ r5A
60Ψ r3A
65Ψ r1A
11Ψ j6A
25Ψ j5A
55Ψ j4A
60Ψ j3A
71θ j2A
65Ψj1A
Corporate R&D • 8-Jul-2007113 Electronics System Thermal Design and Characterization (RPS)
Collect the θ/Ψ values
6365
2420
6055
6573
1110
2522
5560
6055
7165
6575
B
R5
R3
R1
J6
J5
J4
J3
J2
J1
Corporate R&D • 8-Jul-2007114 Electronics System Thermal Design and Characterization (RPS)
Device 3 heated, 1.3 W
Tj3=109.5 Tj2=103.0
Tj1=96.5Tj4=104.3
Tj5=52.3Tj6=44.5
Tref1=96.5
Tref5=43.2
Tref3=106.9
TB=105.6
Tamb=25
62Ψ BA
14Ψ r5A
63Ψ r3A
55Ψ r1A
15Ψ j6A
21Ψ j5A
61Ψ j4A
65θ j3A
60Ψ j2A
55Ψj1A
Corporate R&D • 8-Jul-2007115 Electronics System Thermal Design and Characterization (RPS)
Collect the θ/Ψ values
62
14
63
55
15
21
61
65
60
55
6365
2420
6055
6573
1110
2522
5560
6055
7165
6575
B
R5
R3
R1
J6
J5
J4
J3
J2
J1
Corporate R&D • 8-Jul-2007116 Electronics System Thermal Design and Characterization (RPS)
Device 4 heated, 1.1 W
Tj3=92.1 Tj2=85.5
Tj1=91.0Tj4=105.3
Tj5=44.8Tj6=37.1
Tref1=89.9
Tref5=45.9
Tref3=92.1
TB=94.3
Tamb=25
63Ψ BA
19Ψ r5A
61Ψ r3A
59Ψ r1A
11Ψ j6A
18Ψ j5A
73θ j4A
61Ψ j3A
55Ψ j2A
60Ψj1A
Corporate R&D • 8-Jul-2007117 Electronics System Thermal Design and Characterization (RPS)
Collect the θ/Ψ values
63
19
61
59
11
18
73
61
55
60
62
14
63
55
15
21
61
65
60
55
6365
2420
6055
6573
1110
2522
5560
6055
7165
6575
B
R5
R3
R1
J6
J5
J4
J3
J2
J1
Corporate R&D • 8-Jul-2007118 Electronics System Thermal Design and Characterization (RPS)
Device 5 heated, 0.7 W
Tj3=39.7 Tj2=42.5
Tj1=40.4Tj4=37.6
Tj5=112.5Tj6=34.8
Tref1=40.4
Tref5=91.5
Tref3=39.7
TB=39.7
Tamb=25
21Ψ BA
95Ψ r5A
21Ψ r3A
22Ψ r1A
14Ψ j6A
125θ j5A
18Ψ j4A
21Ψ j3A
25Ψ j2A
22Ψj1A
Corporate R&D • 8-Jul-2007119 Electronics System Thermal Design and Characterization (RPS)
Collect the θ/Ψ values
21
95
21
22
14
125
18
21
25
22
63
19
61
59
11
18
73
61
55
60
62
14
63
55
15
21
61
65
60
55
6365
2420
6055
6573
1110
2522
5560
6055
7165
6575
B
R5
R3
R1
J6
J5
J4
J3
J2
J1
Corporate R&D • 8-Jul-2007120 Electronics System Thermal Design and Characterization (RPS)
Device 6 heated, 0.5 W
Tj3=32.5 Tj2=30.5
Tj1=30.0Tj4=30.5
Tj5=32.0Tj6=115.0
Tref1=30.0
Tref5=32.5
Tref3=32.5
TB=31.0
Tamb=25
12Ψ BA
15Ψ r5A
15Ψ r3A
10Ψ r1A
180θ j6A
14Ψ j5A
11Ψ j4A
15Ψ j3A
11Ψ j2A
10Ψj1A
Corporate R&D • 8-Jul-2007121 Electronics System Thermal Design and Characterization (RPS)
Collect the θ/Ψ values
12
15
15
10
180
14
11
15
11
10
21
95
21
22
14
125
18
21
25
22
63
19
61
59
11
18
73
61
55
60
62
14
63
55
15
21
61
65
60
55
6365
2420
6055
6573
1110
2522
5560
6055
7165
6575
B
R5
R3
R1
J6
J5
J4
J3
J2
J1
Corporate R&D • 8-Jul-2007122 Electronics System Thermal Design and Characterization (RPS)
Now apply actual power
Tj3=134.9 Tj2=140.1
Tj1=140.0Tj4=135.8
Tj5=124.7Tj6=139.1
Tref1=138.8
Tref5=106.3
Tref3=134.1
TB=139.1
Tamb=25
.2qj6
.5qj5
.4qj4
.4qj3
.4qj2
.4qj1
Actual power in application
Corporate R&D • 8-Jul-2007123 Electronics System Thermal Design and Characterization (RPS)
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:
7511
255107qTT
1
amb1jA1j =
−=
−=
..θ
28840
25140qTT
1
amb1jA1j =
−=
−=
.θ
Now let’s see: ≠
Corporate R&D • 8-Jul-2007124 Electronics System Thermal Design and Characterization (RPS)
And that’s not just a single aberration!
180
125
73
65
71
75
vs
vs
vs
vs
vs
vs
309θ j6A
199θ j5A
277θ j4A
274θ j3A
288θ j2A
288θ j1A
Self heating
10.0
3.0
8.0
10.0
vs
vs
vs
vs
-8.3Ψj4-B
-10.5Ψj3-B
2.5Ψj2-B
2.2Ψj1-B
Junction to Board
30.0
2.0
2.0
vs
vs
vs
36.8Ψj5-R5
2.0Ψj3-R3
3.0Ψj1-R1
Junction to Reference
3.8x
4.1x
4.2x
3.8x
1.6x
1.7x
1.5x
1.0x
1.2x
0.2x
0.3x-3.5x
-0.8x
Corporate R&D • 8-Jul-2007125 Electronics System Thermal Design and Characterization (RPS)
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.
Corporate R&D • 8-Jul-2007126 Electronics System Thermal Design and Characterization (RPS)
ann12121A1J1j TqqqT +Ψ+Ψ+= Kθ
a
n
2
1
JnAn2n1
n2A2J12
n112A1J
jn
2j
1j
T
q
T
TT
+
⎪⎪⎭
⎪⎪⎬
⎫
⎪⎪⎩
⎪⎪⎨
⎧
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
ΨΨ
ΨΨΨΨ
=
⎪⎪⎭
⎪⎪⎬
⎫
⎪⎪⎩
⎪⎪⎨
⎧
M
L
MOM
L
M
θ
θθ
So is it really this bad?Only sort-of. Let’s revisit the math for one device …
a
n
2nn11A1J1j TqqT +Ψ+= ∑θ
00“effective”ambient
Corporate R&D • 8-Jul-2007127 Electronics System Thermal Design and Characterization (RPS)
a1A1J1j TqT += θ
power, q
Tajunction temperature , TJ1
Ta’ junction temperature , TJ1
′+=
+Ψ+= ∑
a1A1J
a
n
2nn11A1J1j
Tq
TqqT
θ
θ
Ta
shift in effectiveambient
Device in a system
still the same slope
1
θJ1A
1
θJ1A
Isolated device
A graphical view
Corporate R&D • 8-Jul-2007128 Electronics System Thermal Design and Characterization (RPS)
when Q1 is zero, both of these will be zero
( ) a
n
2ii1i1a1j1j TQQT +⋅Ψ+⋅= ∑
=θ
How does effective ambient relate to board temperature?
temperature rise, board to J1
effective ambient
“system” slope for isolated device
temperature rise, ambient to board
a1a1B1B1j TQQ ′+⋅+⋅= θθ
aa1BB1j TTT ′+∆+∆=
( ) a1a1BB1j TQ ′+⋅+= θθ
if any of these are non-zero, will be higher thanaT′ aT
when Q1 is not zero, both of these will be non-zero
Corporate R&D • 8-Jul-2007129 Electronics System Thermal Design and Characterization (RPS)
How does effective ambient relate to local air temperature?
NOT.
Corporate R&D • 8-Jul-2007130 Electronics System Thermal Design and Characterization (RPS)
What about that “system” theta we saw earlier that was so different?
junction temperature
power
Ta’
1
θJ1A
Ta
the “system”theta-JA
the isolated-device theta-JA∑Ψ
n
2nn1 q
1
θJ1A
device #1 power/temperature perturbations will fall on this line
NOT this oneq1
TJ1
Corporate R&D • 8-Jul-2007131 Electronics System Thermal Design and Characterization (RPS)
System modeling
Corporate R&D • 8-Jul-2007132 Electronics System Thermal Design and Characterization (RPS)
• Handy formulas for quick estimates• Utilizing symmetry
Filling in the theta-matrix
Corporate R&D • 8-Jul-2007133 Electronics System Thermal Design and Characterization (RPS)
Conduction resistance
LTAk
dxdTAkq ∆
⋅⋅≈⋅⋅=
basic heat transfer relationship for 1-D conduction
if we define
thenqTR ∆
=
AkLR⋅
=
Corporate R&D • 8-Jul-2007134 Electronics System Thermal Design and Characterization (RPS)
Convection resistance
TAhq ∆⋅⋅=
basic heat transfer relationship for surface cooling
if we define
thenqTR ∆
=
hA1R =
Corporate R&D • 8-Jul-2007135 Electronics System Thermal Design and Characterization (RPS)
( )( )( )( )( )( ) TTTTTAF
TTTTTTAF
TTAFq
a2a
2aa
2a
2
4a
4
∆++⋅⋅⋅⋅=
−++⋅⋅⋅⋅=
−⋅⋅⋅⋅=
εσ
εσ
εσ
Radiation resistance
temperatures must be expressed in
degrees “absolute”!
basic heat transfer relationship for surface radiation
if we define
thenqTR ∆
=
( )( )a2a
2 TTTTFA1R
++=σε
Corporate R&D • 8-Jul-2007136 Electronics System Thermal Design and Characterization (RPS)
Thermal capacitance and time constant
RC=τVcC pρ=
Ah
1R⋅
= Ak
LR⋅
=
capacitance is ability to store energyspecific heat is energy storage/mass
based on simple RC concept, relate rate of storage to rate of fluxresult is
so if and if
and
thenthen
and( )ALcC p ⋅= ρ
αρ
τ22
p Lk
Lc==
( )ALcC p ⋅= ρ
hLcpρ
τ =
Corporate R&D • 8-Jul-2007137 Electronics System Thermal Design and Characterization (RPS)
Some useful formulas
• conduction resistance…………..………
• convection resistance…………...………
• thermal capacitance……………...……..
• characteristic time…………………..….– (dominated by 1-D conduction)
• characteristic time……………………...– (dominated by 1-D convection)
• short-time 1-D transient response……... tAQ2T
hLc
L
VcCAh
1R
AkLR
p
2
p
ηπ
ρτ
ατ
ρ
=∆
=
=
=⋅
=
⋅=
Corporate R&D • 8-Jul-2007138 Electronics System Thermal Design and Characterization (RPS)
Terms used in preceding formulas• L - thermal path length• A - thermal path cross-sectional area• k - thermal conductivity• ρ - density• cp - heat capacity• V – volume of material (L·A)• α - thermal diffusivity• η - thermal effusivity• h - convection heat-transfer “film coefficient”)• ∆T - junction temperature rise• Q - heating power• t - time since heat was first applied
kcpρη =
pckρ
α =
Corporate R&D • 8-Jul-2007139 Electronics System Thermal Design and Characterization (RPS)
mainly package
materials/conduction effects
mainly local application
board conduction effects
mainly environmental convection and radiation
effects
When do these effects enter?
time
junc
tion
tem
pera
ture
typical heating curve for device on FR-4
board in still-air
hundreds of seconds
a second or so
tens of seconds
Corporate R&D • 8-Jul-2007140 Electronics System Thermal Design and Characterization (RPS)
Utilize symmetry whenever possible
Corporate R&D • 8-Jul-2007141 Electronics System Thermal Design and Characterization (RPS)
if
then and
R⇒
R2≈
R4≈
Corporate R&D • 8-Jul-2007142 Electronics System Thermal Design and Characterization (RPS)
Cylindrical and spherical conduction (through radial thickness) resistance formulas
Lk2rr
R
Lkrr
R
i
o
i
o
⋅⋅
⎟⎟⎠
⎞⎜⎜⎝
⎛
=
⋅⋅
⎟⎟⎠
⎞⎜⎜⎝
⎛
=
π
π
ln
ln
• L – cylinder length• ri – inner radius• ro – outer radius
where
Half-cylinder
Full cylinderk4r1
r1
R
k2r1
r1
R
oi
oi
⋅
−=
⋅
−=
π
π Hemisphere
Full sphere
[included angle][solid angle]
Corporate R&D • 8-Jul-2007143 Electronics System Thermal Design and Characterization (RPS)
• The device and system are equally important to get right
Predicting the temperature of high power components
Corporate R&D • 8-Jul-2007144 Electronics System Thermal Design and Characterization (RPS)
Using the previous board example …
12
15
15
10
180
14
11
15
11
10
21
95
21
22
14
125
18
21
25
22
63
19
61
59
11
18
73
61
55
60
62
14
63
55
15
21
61
65
60
55
6365
2420
6055
6573
1110
2522
5560
6055
7165
6575
B
R5
R3
R1
J6
J5
J4
J3
J2
J1
0.02qj6
0.2qj5
0.5qj4
0.5qj3
0.5qj2
0.5qj1
power vector
theta array
Corporate R&D • 8-Jul-2007145 Electronics System Thermal Design and Characterization (RPS)
Observe the relative contributions
= (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
For junction 1 (a high power component) we have:
= 37.5 + 32.5 + 27.5 + 30 + 4.4 + 0.2 + 25
= 37.5 + 94.6 + 25
the device itself …the other devices …
Corporate R&D • 8-Jul-2007146 Electronics System Thermal Design and Characterization (RPS)
Graphically, it looks like this:
junction temperature
power
1
75 C/W
25 C
q1=0.5 W
TJ1
∆=94.6 C ∆=37.5 C
⎟⎟⎠
⎞⎜⎜⎝
⎛Ψ∑
n
2nn1 q
note the “embedded”theta-JA looks like 264 C/W
264 C/W
increasing power
decreasing power
( )1A1J qθ
1
157 C
Corporate R&D • 8-Jul-2007147 Electronics System Thermal Design and Characterization (RPS)
• The system is probably more important than the device
Predicting the temperature of low power components
Corporate R&D • 8-Jul-2007148 Electronics System Thermal Design and Characterization (RPS)
Using the previous board example …
12
15
15
10
180
14
11
15
11
10
21
95
21
22
14
125
18
21
25
22
63
19
61
59
11
18
73
61
55
60
62
14
63
55
15
21
61
65
60
55
6365
2420
6055
6573
1110
2522
5560
6055
7165
6575
B
R5
R3
R1
J6
J5
J4
J3
J2
J1
0.02qj6
0.2qj5
0.5qj4
0.5qj3
0.5qj2
0.5qj1
power vector
theta array
Corporate R&D • 8-Jul-2007149 Electronics System Thermal Design and Characterization (RPS)
Relative contributions to ∆TJ6
= (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
= 5.0 + 5.5 + 7.5 + 5.5 + 2.8 + 3.6 + 25
= 26.3 + 3.6 + 25
the device itself …
the other devices …
Corporate R&D • 8-Jul-2007150 Electronics System Thermal Design and Characterization (RPS)
Graphically, low-power device #6 looks like this:
junction temperature
power
1
180 C/W
25 C
q6=0.02 W
TJ6
∆=26.3 C
∆=3.6 C
and just in case you were wondering, the “embedded”theta-JA looks like 1495 C/W !
54 C
Corporate R&D • 8-Jul-2007151 Electronics System Thermal Design and Characterization (RPS)
How to harness this math in Excel®
Controlling the matrix
Corporate R&D • 8-Jul-2007152 Electronics System Thermal Design and Characterization (RPS)
3x3 theta matrix, 3x1 power vector Excel® math
theta matrix
power vector
Matrix MULTiply
=array formula notation
array reference to theta matrix
array reference to power vector
obtained by using Ctrl-Shift-Enter rather than ordinary Enter
multi-cell placement of array formula
Corporate R&D • 8-Jul-2007153 Electronics System Thermal Design and Characterization (RPS)
7x3 theta matrix, 3x1 power vector Excel® math
array formula now occupies 7 cells
theta matrix is no longer square –# of columns still must equal
# of rows of power vector
don’t forget to useCtrl-Shift-Enter
to invoke array formula notation
Corporate R&D • 8-Jul-2007154 Electronics System Thermal Design and Characterization (RPS)
7x3 theta matrix, 3x2 power vector Excel® maththe single MMULT array formula now occupies
7 rows and 2 columns (one column for each independent power scenario result)
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
Corporate R&D • 8-Jul-2007155 Electronics System Thermal Design and Characterization (RPS)
For instance, what if your cooling depends significantly on convection from the board
surface (whether free or forced air)?
Package-shrink “gotcha”
TAhq ∆⋅⋅=Th
qA∆⋅
=
Often, much or even most of theta-JA depends on what isn’t the package?
So never mind the package resistance, the boardcan only transfer a certain amount of heat to the air:
⇔
Corporate R&D • 8-Jul-2007156 Electronics System Thermal Design and Characterization (RPS)
SOT23 @ 0.25W, ∆T = 100°C, 4 packages per 1000 mm^2
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
Decrease size but not
power dissipation
Decrease size and reduce
power dissipation
(RDSON or other electrical
performance)
Heat transfer 101
Corporate R&D • 8-Jul-2007157 Electronics System Thermal Design and Characterization (RPS)
• 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
Thermal runaway
Corporate R&D • 8-Jul-2007158 Electronics System Thermal Design and Characterization (RPS)
power goes up temperature
rises
typical thermal response
nonlinear electrical response
Thermal runaway
Corporate R&D • 8-Jul-2007159 Electronics System Thermal Design and Characterization (RPS)
Thermal runaway
• System thermal resistance isn’t low enough to shed small perturbations of power
• Nonlinear power vs. junction temperature device characteristic
Corporate R&D • 8-Jul-2007160 Electronics System Thermal Design and Characterization (RPS)
equals power OUT
thermal system
temperature increasestemperature
is fixed
power IN
power dissipation
rises
input power
increases
Balance of power
thermal system
Corporate R&D • 8-Jul-2007161 Electronics System Thermal Design and Characterization (RPS)
temperature increases
power dissipation
rises
Device nonlinearity causes trouble
By design,power is balanced
andtemperature is fixed.
Corporate R&D • 8-Jul-2007162 Electronics System Thermal Design and Characterization (RPS)
A linear thermal cooling system
xJxJ TQT +⋅= θ
Jx
xJ TTQθ−
=
Jx
1dTdQ
θ=
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-2007163 Electronics System Thermal Design and Characterization (RPS)
Operating point of thermal system with temperature-independent power
junction temperature
power does not change with temperature
device line
as temperature rises, more heat may be dissipated
power
Q
Tx
1
θJx
TJ
system line
at small increase in temperature, system dissipates more power than device produces, so temperature falls
tendency to cool
tendency to heat
a decrease in temperature means system dissipates less power than device produces, so temperature rises
Corporate R&D • 8-Jul-2007164 Electronics System Thermal Design and Characterization (RPS)
power
junction temperature
Q
Tx
1
TJ
power goes down with increasing temperature
device line
system lineas temperature rises, more heat may be dissipated
tendency to cool
tendency to heat
Operating point of thermal system where power decreases with temperature
θJx
Corporate R&D • 8-Jul-2007165 Electronics System Thermal Design and Characterization (RPS)
Operating point of thermal system where power increases with temperature, slopes favorable
power
junction temperature
Q
Tx
1
TJ
device line
system line
at small positive increase in temperature, system can still dissipate more power than device produces
tendency to cool
tendency to heat
θJx
Corporate R&D • 8-Jul-2007166 Electronics System Thermal Design and Characterization (RPS)
power
junction temperature
Q
Tx TJ
power goes way up with increasing temperature
device line
system line
as temperature rises, more heat may be dissipated
for a small positive increase in temperature, increased device power exceeds increased system dissipation capacity, so device “runs away”
tendency to cool
tendency to heat
Operating point of thermal system where power increases with temperature, slopes unfavorable
Corporate R&D • 8-Jul-2007167 Electronics System Thermal Design and Characterization (RPS)
Operating points of thermal system when device line has negative second derivative
power
junction temperature
Q2
Tx
TJ2
power goes up with increasing temperature
device line
system line
the stable (that is, real) operating point
an unachievable operating point
tendency to cool
tendency to heat
tendency to cool
Q1
TJ1
but rate of increase falls with increase (negative second derivative)
Corporate R&D • 8-Jul-2007168 Electronics System Thermal Design and Characterization (RPS)
System with no operating point, negative second derivative, cannot be powered up
power
junction temperatureTx
device line
system line
tendency to cool everywhere
Corporate R&D • 8-Jul-2007169 Electronics System Thermal Design and Characterization (RPS)
Device with negative second derivative, system has unrealizable operating point,
power
junction temperatureTx
device line
system line tendency to cool
tendency to cool
an unachievable operating point
Corporate R&D • 8-Jul-2007170 Electronics System Thermal Design and Characterization (RPS)
Operating points of thermal system when device line has positive second derivative
power
junction temperature
Q
Tx TJ
power goes up with increasing temperature, but rate of increase rises with increase (positive second derivative)
device line
system line
the stable (that is, real) operating point
an unachievable operating point
tendency to cool
tendency to heat
tendency to heat
Corporate R&D • 8-Jul-2007171 Electronics System Thermal Design and Characterization (RPS)
System with NO operating point, overheats as soon as powered up
power
junction temperatureTx
device linesystem line
tendency to heat everywhere
Corporate R&D • 8-Jul-2007172 Electronics System Thermal Design and Characterization (RPS)
System with exactly one “runaway” operating point, device has positive second derivative
power
junction temperature
Q
Tx TJ
device linesystem line
the exact “runaway”condition; slope of device line equals slope of system line at point of intersection
tendency to heat
tendency to heat
neutral tendency at only this point
Corporate R&D • 8-Jul-2007173 Electronics System Thermal Design and Characterization (RPS)
Let’s see how it works
device operating
curve
25°C/W system
stable operating
point
unstable operating point
10°C/W system
NO operating
point!
40°C/W system
0.0
0.4
0.8
1.2
1.6
2.0
20 40 60 80 100Junction Temperature [C]
Dev
ice
Pow
er D
issi
patio
n [W
]
Corporate R&D • 8-Jul-2007174 Electronics System Thermal Design and Characterization (RPS)
Generic power law device and generic linear cooling system
power
junction temperatureTx
device lineunstable
operating point
system line B
Ty
stable operating point
runaway point for original theta
runaway point for original thermal ground
system line C
1
θJx1 θJx1
1
1θJx2
system line A
TR2 TR1
Q
TJ
Corporate R&D • 8-Jul-2007175 Electronics System Thermal Design and Characterization (RPS)
Don’t get confused by the terms!
xay =
xey =
IVQ ⋅=
a mathematical “power law”device power
an “exponential”power law (base is e)
Corporate R&D • 8-Jul-2007176 Electronics System Thermal Design and Characterization (RPS)
Definition of power law device
10T
o 2II =
( ) ⎟⎠⎞
⎜⎝⎛
== 210T
o10T2
o eIeII lnln
λT
oeII =
⎟⎠⎞⎜
⎝⎛−
=
21
21
II
TT
lnλ
λλT
o
T
oR eQeIVQ ==
λλ
To eQ
dTdQ
= λ
λ
T
2o
2
2eQ
dTQd
=
rule of thumb for leakage;2x increase for every 10°C for constant voltage, power does
the same
1st and 2nd derivatives
both always positive
defining:
Corporate R&D • 8-Jul-2007177 Electronics System Thermal Design and Characterization (RPS)
The mathematical essence
Jx
xTTQθ−
=
λT
oeQQ =
λθλ xT
oJxe
Qk
−
=
zekz =
System line
Power law device line
λxTTz −
=
QeQ1q
xT
o ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛=
−λ
Non-dimensionalizing
temperature
power
where:
zeq =(power law device)
kzq =
Leads to:
(system)
Eliminating q:
Corporate R&D • 8-Jul-2007178 Electronics System Thermal Design and Characterization (RPS)
Perfect runaway transformed
ez
at point of tangency, slope equals height
zT1z0
k=ez
1zz 0T =−
λxTTz −
=zT1z0
k=ez
zT1z0
k=ez
zT1z0
k=ez
Corporate R&D • 8-Jul-2007179 Electronics System Thermal Design and Characterization (RPS)
Transforming the nominal system
ez
at point of tangency, slope equals height
1
k=e
“operating”points
k > e(2 intersections)
k < e(no intersections)
nominal system line A
Corporate R&D • 8-Jul-2007180 Electronics System Thermal Design and Characterization (RPS)
Everything transformednon-dimensional power
device line
unstable, non-operating point
stable operating point
system line A
zR2
runaway point for original theta
runaway point for original thermal ground
system line B
system line C
non-dimensional temperaturezR1
k1
1 zx1
k2
1
( )11R kz ln=( ) 1kz 11x −= ln 1z 2R =
ek2 =
k1
1
Corporate R&D • 8-Jul-2007181 Electronics System Thermal Design and Characterization (RPS)
“Perfect runaway” resultsin original terms
⎟⎟⎠
⎞⎜⎜⎝
⎛=
o1Jx1R Q
Tθ
λλ ln
λθ
λλ −⎟⎟⎠
⎞⎜⎜⎝
⎛=
o1Jx1x Q
T ln⎟⎠⎞
⎜⎝⎛ +−
=1T
o2Jx
x
eQ
λλθ
λ+= x2R TT
runaway temperature based on original slope
max ambient that goes with it
runaway temperature based on original ambient
system resistance that goes with it
Corporate R&D • 8-Jul-2007182 Electronics System Thermal Design and Characterization (RPS)
The “operating” points
ez
“operating”points
1
kz
szs ekz =
uzu ekz =
sz uz
stable
unstable
Corporate R&D • 8-Jul-2007183 Electronics System Thermal Design and Characterization (RPS)
Newton’s method for the intersections
i
i
1i
z11
zek
z−
⎟⎠⎞
⎜⎝⎛
=+
ln( )( )i
ii1i zF
zFzz′
−−=+
zkz =ln
( ) kzzzF ln−=
For k/e ranging between 1.01 and 1000, convergence is to a dozen significant digits in fewer than 10 iterations.
zekz =
eke
1k1zo
⋅== this initial guess
converges to lower, stable point
⎟⎠⎞
⎜⎝⎛+==
ek1kzo lnln
this initial guess converges to upper,
unstable point
( )z11zF −=′
Corporate R&D • 8-Jul-2007184 Electronics System Thermal Design and Characterization (RPS)
Excel® implementation of Newton’s method
Corporate R&D • 8-Jul-2007185 Electronics System Thermal Design and Characterization (RPS)
And the intersection points come from …
stablexstable zTT ⋅+= λ
find the non-dimensional intersections first, then
unstablexunstable zTT ⋅+= λ
Corporate R&D • 8-Jul-2007186 Electronics System Thermal Design and Characterization (RPS)
1.02E-39.4E-5[W]
17.817.9[°C]
Real datasheet example
1.70E-35.20E-4Itref [A]
2.80E-28.50E-3Itmax [A]
7575Tref [°C]
125125Tmax [°C]
4012Vr [V]
λoQ
the device power curve parameters@12V @40V
⎟⎠⎞⎜
⎝⎛
−=
ref
ref
II
TT
max
max
lnλ
oR0 IVQ =λλrefT
tref
T
t0 eIeII−−
==max
max
λT
0eII =( ) 4142
10 .ln
==rule of thumb gave us:
† MBRS140T3
raw device data†
Corporate R&D • 8-Jul-2007187 Electronics System Thermal Design and Characterization (RPS)
101.3
83.5
1.609
1.02E-39.4E-5[W]
17.817.9[°C]
92.892.9[°C]
96.61055max [°C/W]givenambient
92.2135.1[°C]
74.4117.2max [°C]giventheta
0.9710.6(compare to unity)
Runaway analysis in nominal system
1.70E-35.20E-4Itref [A]
2.80E-28.50E-3Itmax [A]
7575Tref [°C]
125125Tmax [°C]
4012Vr [V] λoQ
ek
xT
1RT
2Jxθ
2RT
3120z .=
raw device data†
computed results@12V @40V @40V
3152z .=
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)
1001Jx =θ 601Jx =θ
75Tx =1T
oJx
x
eQe
k −−
= λθλ
† MBRS140T3
Corporate R&D • 8-Jul-2007188 Electronics System Thermal Design and Characterization (RPS)
How about the real thermal system?
• Is ambient really ambient?
• Is theta-JA what you think it is?
Corporate R&D • 8-Jul-2007189 Electronics System Thermal Design and Characterization (RPS)
A paradox
junction
thermal ground
50°C/W
lead
100°C/W
100°C
75°C
25°C
0.5 W
thermal runaway,based on θJx=150°C/W,
calculated to be at 125°C
junction
thermal ground
50°C/W
lead
0.2°C/W
100°C
75°C
74.9°C
0.5 W
thermal runaway,based on θJx=50.2°C/W,calculated to be at 150°C
identical
Case A Case B
Corporate R&D • 8-Jul-2007190 Electronics System Thermal Design and Characterization (RPS)
Paradox lost
junction
50°C/W
lead
100°C/W
100 + 15°C
75 + 10°C
(fixed) 25°C
0.5 + 0.1 W
junction
50°C/W
lead
0.2°C/W
100 + 5.02°C
75 + 0.02°C
(fixed) 74.9°C
Case A Case B
raise the power by 0.1 W and see what happens0.5 + 0.1 W
Corporate R&D • 8-Jul-2007191 Electronics System Thermal Design and Characterization (RPS)
Illustrating the paradox
100 C25 C 74.9C
common nominal operating point
0.5 W
Case A
Case Bdevice line
Corporate R&D • 8-Jul-2007192 Electronics System Thermal Design and Characterization (RPS)
Consider the following 6-component example of a complete system, using linear superposition to
describe the thermal behavior
Tj3 Tj2
Tj1Tj4
Tj5Tj6
Tref1
Tref5
Tref3
TB
Tamb
This is the one we’re
interested in
Corporate R&D • 8-Jul-2007193 Electronics System Thermal Design and Characterization (RPS)
Linear superposition math
aT+⋅= QθTj
temperature (vector) power
(vector)theta
(matrix)
ambient (scalar)
matrix product
Corporate R&D • 8-Jul-2007194 Electronics System Thermal Design and Characterization (RPS)
Putting illustrative numbers on the problem:
12
15
15
10
180
14
11
15
11
10
21
95
21
22
14
125
18
21
25
22
63
19
61
59
11
18
73
61
55
60
62
14
63
55
15
21
61
65
60
55
6365
2420
6055
6573
1110
2522
5560
6055
7165
6575
B
R5
R3
R1
J6
J5
J4
J3
J2
J1
0.02Q j6
0.2Q j5
0.5Q j4
0.5Q j3
0.5Q j2
0.5Qj1
power vector
theta array
Corporate R&D • 8-Jul-2007195 Electronics System Thermal Design and Characterization (RPS)
Observe the relative contributions
= (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
= 5.0 + 5.5 + 7.5 + 5.5 + 2.8 + 3.6 + 25
= 26.3 + 3.6 + 25
the device itself …
the other devices …
(ambient)
Corporate R&D • 8-Jul-2007196 Electronics System Thermal Design and Characterization (RPS)
Symbolically, for just Tj6, we’d write this:
( ) a6a6j
5
1ii6i6j TQQT +⋅+⋅= ∑
=
θψ
+
temperature of device #6 power of
other devices
“interaction” terms from theta matrix (off-
diagonal elements)
ambient (scalar)
device #6 “self heating”term from theta matrix
power of device #6
effective ambient“system” slope
Corporate R&D • 8-Jul-2007197 Electronics System Thermal Design and Characterization (RPS)
0.0
0.4
0.8
1.2
1.6
2.0
20 40 60 80 100Junction Temperature [C]
Dev
ice
Pow
er D
issi
patio
n [W
]
Graphically, it looks like this
device operating
curve
25°C/W system
system with “background heating” of
other devices
realrunaway margin
( )∑≠
⋅ji
iij Qψ
what you thought
was your margin
Corporate R&D • 8-Jul-2007198 Electronics System Thermal Design and Characterization (RPS)
when Q6 is zero, both of these will be zero
( ) a
5
1ii6i6a6j6j TQQT +⋅Ψ+⋅= ∑
=
θ
How does effective ambient relate to board temperature?
temperature rise, board to J6
effective ambient
“system” slope for isolated device
temperature rise, ambient to board
a6a6B6B6j TQQ ′+⋅+⋅= θθ
aa6BB6j TTT ′+∆+∆=
( ) a6a6BB6j TQ ′+⋅+= θθ
if any of these are non-zero, will be higher thanaT′ aT
when Q6 is not zero, both of these will be non-zero
Corporate R&D • 8-Jul-2007199 Electronics System Thermal Design and Characterization (RPS)
References
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 0-7918-0223-X)
On the lighter side, not “technical” as such, but very informative, accurate, and humorous:
11:55
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Thermal Test Standards3. 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, 19908. MIL-STD-883E, Method 1012.1, U.S. Department of Defense, 31 December
1996
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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, 196914. H.H. Skilling, Electric Networks, John Wiley and Sons, 197415. L. Weinberg, Network Analysis and Synthesis, McGraw Hill Book Company,
Inc., 196216. H. Wayland, Complex Variables Applied in Science and Engineering, Van
Nostrand Reinhold Company
Corporate R&D • 8-Jul-2007202 Electronics System Thermal Design and Characterization (RPS)
Thermal textbooks & references17. H.S. Carslaw & J.C. Jaeger, Conduction of Heat In Solids, Oxford Press, 195918. E.R.G. Eckert & R.M. Drake Jr., Heat and Mass Transfer, McGraw Hill, 195919. J.P. Holman, Heat Transfer, 3rd Ed., McGraw Hill, 197220. J. VanSant, Conduction Heat Transfer Solutions, Lawrence Livermore National
Laboratory, Livermore, CA, 1980
Related papers by Stout, et al21. “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
Corporate R&D • 8-Jul-2007203 Electronics System Thermal Design and Characterization (RPS)
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
Related papers by Stout, et al, cont’
Corporate R&D • 8-Jul-2007204 Electronics System Thermal Design and Characterization (RPS)
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>
web links
Corporate R&D • 8-Jul-2007205 Electronics System Thermal Design and Characterization (RPS)
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>
web links, cont’