Download 1.2 theoretical power dissipation in electronic components

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
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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.
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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 ()
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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.
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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
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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)
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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 )
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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.
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