Page 73 - Power Electronics Handbook

66 Thermal design
starting at fl and -Prn starting at f2. The junction temperature rise at time r3
is then given by equation (2.5).
d T(ts) = pm Rth(t,) - pm Rth(b)
= pin [Rth(t,) - &h(k)] (2.5)
The case of multiple-power pulses, shown in Figure 2.5(b), can be
considered as a series of single superimposed pulses, and the temperature
rise at time f7 is given by equation (2.6).

dT(,) = pm1 [Rth(t,) - R*h(tJI + pm2 [4h(t3) - Rth(t,)l
f pm3 [Rth(b) - Rth(Ql (2.6)
In the pulse train situation, shown in Figure 2.5(c), the last few pulses
are the only ones making individual contributions, and the rest can be
averaged, so that the temperature rise is given by equation (2.7).

The last example of transient operation to be considered here is that of a
non-rectangular pulse. This can be approximated into a series of
rectangular pulses, as in Figure 2.5(d). The temperature rise at time fm is
now given by equation (2.8).
dT(a prnl Rth(t,) + (pm2 - pml) Rth(tJ + (pm3 - pm2) Rth(Q) +
=
= {pm(n) - Pm(n - I))Rth(f) (2.8)

2.4 Heatsinks
The thermal capacity (cth) of a device, which provides a measure of its rate
of change of thermal energy with temperature, is given by equation (2.9).

cth = C.m (2.9)
where m is the mas of the device and C its specific heat.
Heatsinks are usually used to improve the thermal capacity of power
semiconductors and therefore to enable them to dissipate the heat
generated when they are in operation. This section first looks at thermal
equations, which provide a guide to the various methods of cooling power
devices, and then describes the heatsinking methods which may be used.

2.4.1 Thermal equations
Three methods exist for removing heat from a power semiconductor,
conduction, convection, and radiation, and these are described by thermal
equations.
Conduction. The rate of heat flow across a heatsink, having a
cross-sectional area of a, a thickness of d, and a thermal conductivity of kT,
is given by equation (2.10), where dT is the temperature difference across