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