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0082-01 Page 6 Wednesday, August 23, 2000 9:51 AM Therefore, increasing the surface area, A, of a given heat sink reduces sa. Consequently, increasing the heat transfer coefficient, hc, also reduces the thermal resistance. When we mount a semiconductor on a heat sink, the relationship between junction temperature rise above ambient temperature and power dissipation is given by: T q ( jc cs sa ) The focus of the remaining chapters is to explore and expand on these basic resistances to heat transfer, and then predict and minimize them (cost-effectively) wherever possible. 1.2 THEORETICAL POWER DISSIPATION IN ELECTRONIC COMPONENTS 1.2.1 THEORETICAL POWER DISSIPATION Electronic devices produce heat as a by-product of normal operation. When electrical current flows through a semiconductor or a passive device, a portion of the power is dissipated as heat energy. The quantity of power dissipated is found by: Pd VI where: Pd power dissipated (W) V direct current voltage drop across the device (V) I direct current through the device (A) If the voltage or the current varies with respect to time, the power dissipated is given in units of mean power Pdm : t 1 2 P dm --- V ( t )I ( t ) dt t t1 where: Pdm mean power dissipated (W) t waveform period (s) I(t) instantaneous current through the device (A) V(t) instantaneous voltage through the device (V) t1 lower limit of conduction for current t2 upper limit of conduction for current © 2001 by CRC PRESS LLC 0082-01 Page 7 Wednesday, August 23, 2000 9:51 AM 1.2.2 HEAT GENERATION 1.2.2.1 IN ACTIVE DEVICES CMOS Devices The power that is dissipated by bipolar components is fairly constant with respect to frequency. The power dissipation for CMOS devices is a first-order function of the frequency and a second-order function of the device geometry. Switching power constitutes about 70 to 90% of the power dissipated by a CMOS. The switching power of a CMOS device can be found by: 2 CV Pd ---------- f 2 where: C input capacitance (F) V peak-to-peak voltage (V) f switching frequency (Hz) Short-circuit power, caused by transistor gates being on during a change of state, makes up 10 to 30% of the power dissipated. To find the power dissipated by these dynamic short circuits, the number of on gates must be known. This value is usually given in units of W/MHz per gate. The power dissipated is found by: Pd Ntot Non q f where: Ntot Non q f 1.2.2.2 total number of gates percentage of gates on (%) power loss (W/Hz per gate) switching frequency (Hz) Junction FET The junction FET has three states of operation: on, off, and linear transition. When the junction FET is switched on, the power dissipation is given as: 2 Pd ON ID R DS ( ON ) where: ID drain current (A) RDS(ON) resistance of drain to source () In the linear and off states the dissipated power is again found by VI. © 2001 by CRC PRESS LLC 0082-01 Page 8 Wednesday, August 23, 2000 9:51 AM 1.2.2.3 Power MOSFET The power dissipated by a power MOSFET is a combination of five sources of current loss:2,3 a. Pc : conduction losses while the device is on, b. Prd : reverse diode conduction and trr losses, c. PL : power loss due to drain-source leakage current (IDSS) when the device is off, d. PG: power dissipated in the gate structure, and e. PS: switching function losses. Conduction losses, Pc, occurring when the device is switched on, can be found by: 2 Pc I D R DS ( ON ) where: ID drain current (A) RDS(ON) drain to source resistance () Conduction losses when the device is in the linear range are found by VI, as are leakage current losses, PL, and reverse current losses, Prd. Switching transition losses, PS, occur during the transition from the on to off states. These losses can be calculated as the product of the drain-to-source voltage and the drain current; therefore: t t S2 S1 P S f S 0 VDS ( t )I D ( t ) dt 0 VDS ( t )ID ( t ) dt where: fS VDS ID tS1 tS2 switching frequency (Hz) MOSFET drain-to-source voltage (V) MOSFET drain current (A) first transition time (s) second transition time (s) The MOSFET gate losses are composed of a capacitive load with a series resistance. The loss within the gate is RG PG VGS QG ------------------RS RG where: VGS gate-to-source voltage (V) QG peak charge in the gate capacitance (coulombs) RG gate resistance () © 2001 by CRC PRESS LLC 0082-01 Page 9 Wednesday, August 23, 2000 9:51 AM The total power dissipated by the gate structure, PG(TOT), is found by: PG ( TOT ) V GS QG fS 1.2.3 1.2.3.1 HEAT GENERATED IN PASSIVE DEVICES Interconnects The steady-state power dissipated by a wire interconnect is given by Joule’s law: 2 PD I R where: I steady-state current (A) R steady-state resistance () The resistance of an interconnect is L R ----Ac where: material resistivity per unit length (/m) (see Table 1.1) L connector length (m) Ac cross-sectional area (m2) TABLE 1.1 Resistance of Interconnect Materials Material Alloy 42 Alloy 52 Aluminum Copper Gold Kovar Nickel Silver Resistivity, , /cm 66.5 43.0 2.83 1.72 2.44 48.9 7.80 1.63 Source: King, J. A., Materials Handbook for Hybrid Microelectronics, Artech House, Boston, 1988, p. 353. With permission. © 2001 by CRC PRESS LLC 0082-01 Page 10 Wednesday, August 23, 2000 9:51 AM Table 1.2 shows the maximum current-carrying capacity of copper and aluminum wires in amperes:5 TABLE 1.2 Maximum Current-Carrying Capacity of Copper and Aluminum Wires (in Amperes) Copper MIL-W-5088 Aluminum MIL-W-5088 Underwriters Laboratory National Size, Single Bundled Single Bundled Electrical AWG Wire Wirea Wire Wirea Code 60°C 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2 1 0 00 – – – – 9 11 16 22 32 41 55 73 101 135 181 211 245 283 – – – – 5 7.5 10 13 17 23 33 46 60 80 100 125 150 175 – – – – – – – – – – – 58 86 108 149 177 204 237 – – – – – – – – – – – 36 51 64 82 105 125 146 – – – – – – 6 10 20 30 35 50 70 90 125 150 200 225 0.2 0.4 0.6 1.0 1.6 2.5 4.0 6.0 10.0 16.0 – – – – – – – – American Insurance 500 80°C Association cmilA 0.4 0.6 1.0 1.6 2.5 4.0 6.0 10.0 16.0 26.0 – – – – – – – – – – – – – 3 5 7 15 20 25 35 50 70 90 100 125 150 0.20 0.32 0.51 0.81 1.28 2.04 3.24 5.16 8.22 13.05 20.8 33.0 52.6 83.4 132.8 167.5 212.0 266.0 Rated ambient temperatures: 57.2°C for 105°C-rated insulated wire 92.0°C for 135°C-rated insulated wire 107°C for 150°C-rated insulated wire 157°C for 200°C-rated insulated wire a Bundled Wire indicates 15 or more wires in a group. Source: Croop, E. J., in Electronic Packaging and Interconnection Handbook, Harper, C.A., Ed., McGraw-Hill, New York, 1991. With permission. These values can be rerated at any anticipated ambient temperature by the equation: Tc T I I r -----------------Tc T r © 2001 by CRC PRESS LLC 0082-01 Page 11 Wednesday, August 23, 2000 9:51 AM where: I current rating at ambient temperature (T) Ir current rating in rated ambient temperature (Table 1.2) T ambient temperature (°C) Tr rated ambient temperature (°C) Tc temperature rating of insulated wire or cable (°C) 1.2.3.2 Resistors The steady-state power dissipated by a resistor in given by Joule’s law: 2 PD I R where: I steady-state current (A) R steady-state resistance () The instantaneous power, PD(t), dissipated by a resistor with a time-varying current, I(t), is 2 P D ( t ) I ( t )R where I(t) IM sin( t) and IM peak value of the sinusoidal current (A). The average power dissipation when a sinusoidal steady-state current is applied is 2 PD 0.5I M R 1.2.3.3 Capacitors Although capacitors are generally thought of as non-power-dissipating, some power is dissipated due to the resistance within the capacitor. The power dissipated by a capacitor under sinusoidal excitation is found by: PD ( t ) 0.5 CV M sin 2 t 2 where: C VM f capacitance (F) peak sinusoidal voltage (V) radian frequency, 2f frequency (Hz) © 2001 by CRC PRESS LLC 0082-01 Page 12 Wednesday, August 23, 2000 9:51 AM TABLE 1.3 Typical Resistances of Capacitors6–9 Dielectric Material Capacitance (F) RES @ 1 kHz, m 0.1 0.1 0.18 1.0 3.3 2.2 22 33 33 68 19.0 k 16.0 k 10.0 k 2.0 k 0.60 k 1.0 k 0.20 k 0.20 k 0.26 k 0.168 k BX X7R X7R BX Z5U Tantalum Tantalum Tantalum Tantalum Tantalum The equivalent series resistance of a capacitor in an AC circuit can lead to significant power dissipation. The average power in such a circuit is given as: t 1 2 PD --- I 2 ( t )R ES dt T t1 where RES equivalent series resistance (). Table 1.3 shows the typical resistance of commercial capacitors. 1.2.3.4 Inductors and Transformers Inductors and transformers generally follow the power dissipation of resistors, 2 PD I R L where RL direct current resistance of the inductor or winding (). If the high-frequency component of the excitation current is significant, the winding resistance will increase due to the skin depth effect. The power dissipated by the sinusoidal resistance of an inductor is found by: PD ( t ) 0.5LI M sin 2 t 2 where: L inductance (Henry) IM peak sinusoidal current (A) radian frequency (2f ) © 2001 by CRC PRESS LLC 0082-01 Page 13 Wednesday, August 23, 2000 9:51 AM When a ferromagnetic core is used, the loss consists of two sublosses: hysteresis and eddy current. The rate of combined core power dissipation can be found by: n m Ṗ D ( CORE ) 6.51 f B MAX where: PD(CORE ) power dissipation (W/kg) n, m constants of the core material f switching frequency (Hz) BMAX maximum flux density (Tesla) The power dissipation is then found by: P D Ṗ D ( CORE ) M where M mass of the ferromagnetic core (kg). 1.3 THERMAL ENGINEERING SOFTWARE FOR PERSONAL COMPUTERS The past 10 years have seen a major change in the way we evaluate heat transfer. Whereas mainframe computers were once used to calculate large thermal resistance networks for conduction problems, we now perform FEA (finite element analysis) on desktop personal computers. Ten years ago CFD (computational fluid dynamics) was largely experimental and was almost exclusively used only in research laboratories; it is now also used to provide quick answers on desktop computers. The convective coefficient of heat transfer, the most difficult value to assign in heat transfer, is regularly being estimated within 10%, whereas 30% was formerly the norm. Once we construct and verify a computer model, we can evaluate hundreds of changes in a short time to optimize the model. In the future, as the underlying CFD code becomes more advanced, even the tedious model verification step may be eliminated. As with physical designs, computer models can be a combination of conduction, convection, and radiation modes of heat transfer. Convection problems have the largest variety of permutations, and this has given the CFD engineers the most difficulty: laminar flow changes to turbulent flow, energy dissipation rates change with velocity, at slow velocity natural convection may override the expected forced convection effects, etc. When additional factors such as multiphase flow, compressibility, and fine model details such as semiconductor leads are added, it is easy to see why convective computer modeling is so complex. © 2001 by CRC PRESS LLC