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Power Electronics Notes 29 Thermal Circuit Modeling and Introduction to Thermal System Design

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## Power Electronics Notes 29 Thermal Circuit Modeling and Introduction to Thermal System Design

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**Marc T. Thompson, Ph.D.**Thompson Consulting, Inc. 9 Jacob Gates Road Harvard, MA 01451 Phone: (978) 456-7722 Email: marctt@thompsonrd.com Website: http://www.thompsonrd.com Jeff W. Roblee, Ph.D. VP of Engineering Precitech, Inc. Keene, NH www.ametek.com Power Electronics Notes 29Thermal Circuit Modeling and Introduction to Thermal System Design**Summary**• Basics of heat flow, as applied to device sizing and heat sinking • Use of thermal circuit analogies • Thermal resistance • Thermal capacitance • Examples • Picture window examples • Magnetic brake • Plastic tube in sunlight**Capacitors**• Electrolyte evaporation rate increases significantly with temperature increases and thus shortens lifetime Magnetic Components • Losses (at constant power input) increase above 100 °C • Winding insulation (lacquer or varnish) degrades above 100 °C Semiconductors • Unequal power sharing in parallel or series devices • Reduction in breakdown voltage in some devices • Increase in leakage currents • Increase in switching times Need for Component Temperature Control • All components (capacitors, inductors and transformers, semiconductor devices) have maximum operating temperatures specified by manufacturer • High operating temperatures have undesirable effects on components: 3**Temperature Control Methods**•Control voltages across and current through components via good design practices • Snubbers may be required for semiconductor devices. • Free-wheeling diodes may be needed with magnetic components • Maximize heat transfer via convection and radiation from component to ambient • Short heat flow paths from interior to component surface and large component surface area. • Component user has responsibility to properly mount temperature-critical components on heat sinks. • Apply recommended torque on mounting bolts and nuts and use thermal grease between component and heat sink. • Properly design system layout and enclosure for adequate air flow 4**Heat Transfer**• Heat transfer (or heat exchange) is the flow of thermal energy due to a temperature difference between two bodies • Heat transfers from a hot body to a cold one, a result of the second law of thermodynamics • Heat transfer is slowed when the difference in temperature between the two bodies reduces 5**Intuitive Thinking about Thermal Modeling**• Heat (Watts) flows from an area of higher temperature to an area of lower temperature • Heat flow is by 3 mechanisms • Conduction - transferring heat through a solid body • Convection - heat is carried away by a moving fluid • Free convection • Forced convection - uses fan or pump • Radiation • Power is radiated away by electromagnetic radiation • You can think of high- thermal conductivity material such as copper and aluminum as an easy conduit for conductive power flow…. i.e. the power easily flows thru the material**Thermal Circuit Analogy**• Use Ohm’s law analogy to model thermal circuits • Thermal resistance • k = thermal conductivity (W/(mK)) • Thermal capacitance: analogy isn’t as straightforward • cp = heat capacity of material (Joules/(kg-K))**Thermal Circuit Analogy**• Heat transfer can be modeled by thermal circuits • Using Ohm’s law analogy: Reference: M. T. Thompson, Intuitive Analog Circuit Design, Newnes, 2006. 8**Thermal Circuit Analogy**• Elementary thermal network Reference: M. T. Thompson, Intuitive Analog Circuit Design, Newnes, 2006. 9**Thermal Resistance**• Thermal resistance quantifies the rate of heat transfer for a given temperature difference • k = thermal coefficient (W/(mK)) • A = cross section (m2) • l = length (m) 10**Thermal Capacitance**• Thermal capacitance is an indication of how well a material stores thermal energy • It is used when transient phenomena are considered • Analogy isn’t as straightforward • M = mass (kg) • cp = heat capacity of material (Joules/(kg-K)) 11**Heat Flow Mechanisms**• Heat flows by 3 mechanisms; the driving force for heat transfer is the difference in temperature • Conduction • Convection • Free convection • Forced convection • 3. Radiation Reference: R. E. Sonntag and C. Borgnakke, Introduction to Engineering Thermodinamics, John Wiley, 2007 12**Conduction**• Heat is transferred through a solid from an area of higher temperature to lower temperature • To have good heat conduction, you need large area, short length and high thermal conductivity • Example: aluminum plate, l = 10 cm, A=1 cm2, T2 = 25C (298K), T1= 75C (348K), k = 230 W/(m-K)**Thermal Conductivity of Selected Materials**References: 1. B. V. Karlekar and R. M. Desmond, Engineering Heat Transfer, pp. 8, West Publishing, 1977 2. Burr Brown, Inc., “Thermal and Electrical Properties of Selected Packaging Materials”**Chip T**j R R R q cs q sa q jc T T T T j c s a Case T c Heat sink T s Ambient Temperature T a Thermal Equivalent Circuits • Thermal equivalent circuit simplifies calculation of temperatures in various parts of structure. • Heat flow through a structure composed of layers of different materials Case Junction Sink Ambient + + + + P - - - - Isolation pad • Ti = Pd (Rjc+ Rcs + Rsa) + Ta • If there parallel heat flow paths, then thermal resistances combine as do electrical resistors in parallel. 15**Thermal Conductivity of Selected Materials**Reference: International Rectifier, Application note N-1057, “Heatsink Characteristics”**Heat Capacity of Selected Materials**• Heat capacity is an indication of how well a material stores thermal energy Reference: B. V. Karlekar and R. M. Desmond, Engineering Heat Transfer, West Publishing, 1977**Heat Capacity of Alloys**Reference: http://www.engineeringtoolbox.com/specific-heat-metal-alloys-d_153.html**Convection**• Convection can be free (without a fan) or forced (with a fan) Reference: International Rectifier, Application note N-1057, “Heatsink Characteristics”**Free Convection**Reference: http://www.freestudy.co.uk/heat%20transfer/convrad.pdf 20**Heat Transfer Coefficient for Convection**• Heat is transferred via a moving fluid • Convection can be described by a heat transfer coefficient h and Newton’s Law of Cooling: • Heat transfer coefficient depends on properties of the fluid, flow rate of the fluid, and the shape and size of the surfaces involved, and is nonlinear • Equivalent thermal resistance: Reference: B. V. Karlekar and R. M. Desmond, Engineering Heat Transfer, pp. 14, West Publishing, 1977**Free Convection**• Heat is drawn away from a surface by a free gas or fluid • Buoyancy of fluid creates movement • For vertical fin: • A in m2, dvert in m • Example: square aluminum plate, A=1 cm2, Ta = 25C (298K), Ts = 75C (348K)**Free Convection Heat Transfer Coefficient (h)**• For vertical fin: • Area A in m2, fin vertical height dvert in m**Forced Convection**• With a fan Reference: International Rectifier, Application note N-1057, “Heatsink Characteristics”**Forced Convection**• In many cases, heat sinks can not dissipate sufficient power by natural convection and radiation • In forced convection, heat is carried away by a forced fluid (moving air from a fan, or pumped water, etc.) • Forced air cooling can provide typically 3-5 increase in heat transfer and 3-5 reduction in heat sink volume • In extreme cases you can do 10x better by using big fans, convoluted heat sink fin patterns, etc.**Thermal Performance Graphs for Heat Sinks**• Curve #1: natural convection (P vs. Tsa) • Curve #2: forced convection curve (Rsa vs. airflow) 1 2 Reference: http://electronics-cooling.com/articles/1995/jun/jun95_01.php 26**Radiation**• Energy is transferred through electromagnetic radiation Reference: International Rectifier, Application note N-1057, “Heatsink Characteristics”**Radiation**• Energy is lost to the universe through electromagnetic radiation • = emissivity (0 for ideal reflector, 1 for ideal radiator “blackbody”); = Stefan-Boltzmann constant • = 5.6810-8 W/(m2K4) • Example: anodized aluminum plate, = 0.8, A=1 cm2, Ta = 25C (298K), Ts = 75C (348K)**Radiation**• Incident, reflected and emitted radiation; e.g. body in sunlight Reference: http://www.energyideas.org/documents/factsheets/PTR/HeatTransfer.pdf 29**Emissivity**Reference: International Rectifier, Application note N-1057, “Heatsink Characteristics”**Emissivity**Reference: International Rectifier, Application note N-1057, “Heatsink Characteristics”**Comments on Radiation**• In multiple-fin heat sinks with modest temperature rise, radiation usually isn’t an important effect • Ignoring radiation results in a more conservative design • Effective heat transfer coefficient due to radiation for ideal blackbody ( = 1) at with surface temperature 350K radiating to ambient at 300K is hrad = 6.1 W/(m2K), which is comparable to free convection heat transfer coefficient • However, radiation between heat sink fins is usually negligible (generally they are very close in temperature)**IC Mounted to Heat Sink**• Interfaces • Heat sink-ambient: convection (free or forced) • Heat sink-case of IC: conduction • Case – junction: conduction**Multiple Fin Heat Sink**Reference: http://www.oldcrows.net/~patchell/AudioDIY/AudioDIY.html 34**IC Mounted to Heat Sink**Reference: International Rectifier, Application Note AN-997**IC Mounted to Heat Sink --- Close-up**• Thermal compound is often used to fill in the airgap voids Reference: International Rectifier, Application Note AN-997**IC Mounted to Heat Sink --- Contact Resistance vs. Torque**(TO-247) Reference: International Rectifier, Application Note AN-997**IC Mounted to Heat Sink --- Contact Resistance vs. Interface**Material (TO-247) Reference: International Rectifier, Application Note AN-997**IC Mounted to Heat Sink --- Contact Resistance vs. Interface**Material (TO-247) • Dry vs. thermal compound vs. electrically-insulating pad Reference: International Rectifier, Application Note AN-997**T (t)**j R q C s T a Transient Thermal Impedance •Heat capacity per unit volume Cv = dQ/dT [Joules /oC] prevents short duration high power dissipation surges from raising component temperature beyond operating limits. •Transient thermal equivalent circuit. Cs = CvV where V is the volume of the component. P(t) •Transient thermal impedance Z(t) = [Tj(t) - Ta]/P(t) •= π R Cs /4= thermal time constant • Tj(t = ) = 0.833 Po R 42**Use of Transient Thermal Impedance**•Response for a rectangular power dissipation pulse P(t) = Po {u(t) - u(t - t1)}. • Tj(t) = Po { Z(t) - Z(t - t1) } •Symbolic solution for half sine power dissipation pulse. •P(t) = Po {u(t - T/8) - u(t - 3T/8)} ; area under two curves identical. •Tj(t) = Po { Z(t - T/8) - Z (t - 3T/8) } 43**Multilayer Structures**•Multilayer geometry •Transient thermalequivalent circuit •Transient thermal impedance (asymptotic) of multilayer structure assuming widely separated thermal time constants. 44**Heat Sinks**•Aluminum heat sinks of various shapes and sizes widely available for cooling components. • Often anodized with black oxide coating to reduce thermal resistance by up to 25%. • Sinks cooled by natural convection have thermal time constants of 4 - 15 minutes. • Forced-air cooled sinks have substantially smaller thermal time constants, typically less than one minute. •Choice of heat sink depends on required thermal resistance, Rsa, which is determined by several factors. • Maximum power, Pdiss, dissipated in the component mounted on the heat sink. • Component's maximum internal temperature, Tj,max •Component's junction-to-case thermal resistance, Rjc. •Maximum ambient temperature, Ta,max. • Rsa = {Tj,max - Ta,max}Pdiss - Rjc • Pdissand Ta,max determined by particular application. • Tj,max and Rjcset by component manufacturer. 45**Heat Conduction Thermal Resistance**•Generic geometry of heat flow via conduction • Heat flow Pcond [W/m2] =kA (T2 - T1) / d = (T2 - T1) / R cond • Thermal resistance R cond = d / [k A] • Cross-sectional area A = hb • k = Thermal conductivity has units of W-m-1-oC-1 (kAl = 220 W-m-1-oC-1 ). • Units of thermal resistance are oC/W 46**Radiative Thermal Resistance**•Stefan-Boltzmann law describes radiative heat transfer. •Prad = 5.7x10-8 EA [( Ts)4 -( Ta)4 ] ; [Prad] = [Watts] •E = emissivity; black anodized aluminum E = 0.9 ; polished aluminum E = 0.05 •A = surface area [m2] through which heat radiation emerges. •Ts = surface temperature [K] of component. Ta = ambient temperature [K]. • (Ts - Ta )/Prad = R,rad = [Ts - Ta][5.7x10-8EA {( Ts/100)4 -( Ta/100)4 }]-1 •Example - black anodized cube of aluminum 10 cm on a side. Ts = 120C and Ta =20C •R,rad = [393 - 293][(5.7) (0.9)(6x10-2){(393/100)4 - (293/100)4 }]-1 • R,rad = 2.2C/W 47**Convective Thermal Resistance**•Pconv = convective heat loss to surrounding air from a vertical surface at sea level having height dvert [in meters] less than one meter. • Pconv = 1.34 A [Ts - Ta]1.25 dvert-0.25 • A = total surface area in [m2] •Ts = surface temperature [K] of component. Ta = ambient temperature [K]. •[Ts - Ta ]/Pconv = R,conv = [Ts - Ta ] [dvert]0.25[1.34 A (Ts - Ta )1.25]-1 •R,conv = [dvert]0.25 {1.34 A [Ts - Ta]0.25}-1 •Example - black anodized cube of aluminum 10 cm on a side. Ts = 120C and Ta = 20C. •R,conv = [10-1]0.25([1.34] [6x10-2] [120 - 20]0.25)-1 •R,conv = 2.2 C/W 48**Combined Effects of Convection and Radiation**•Heat loss via convection and radiation occur in parallel. •Steady-state thermal equivalent circuit • R,sink = R,rad R,conv / [R,rad + R,conv] • Example - black anodized aluminum cube 10 cm per side • R,rad = 2.2 C/W and R,conv = 2.2C/W • R,sink = (2.2) (2.2) /(2.2 + 2.2) = 1.1C/W 49**Cost for Various Heat Sink Systems**• Note: heat pipe and liquid systems require eventual heat sink Reference: http://www.electronics-cooling.com/Resources/EC_Articles/JUN95/jun95_01.htm