IGBT Modules - Technologies, Driver and Application (Second Edition) - page 178

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Thus the thermal capacities of components in power electronics can be calculated using
thematerial constants of the specific thermal capacity c
th
, the relative density
ρ
and the
volumes.
th
th
⋅ ⋅ρ⋅
=
Eq. 4.8
4.1.2.3 Thermal impedance
Using the resistances R
th
and C
th
, it is possible to construct a thermal model that
behaves like an electrical RC low-pass. This thermal model is described as transient
thermal resistance or thermal impedance Z
th
. It takes into account that every real object
possesses a thermal resistance and a thermal capacity. Taking an electric hotplate as
an example, this can be demonstrated in terms of physics. The hotplate is made of
steel, which has a good thermal conductivity and dissipates heat or heat flowwell. The
hotplate therefore has a very low thermal resistance. Nevertheless, it takes a while
before the hotplate heats up, even when it is being supplied with constant thermal
energy. This is because of the hotplate thermal capacity. The larger the hotplate, the
longer it takes to heat up. To put it another way: The greater the mass of the hotplate,
the greater its thermal capacity. The thermal energy is stored in the hotplate. Once the
heat storage is full, the hotplate heats to the maximum temperature. If the stove is
turned off, the energy in the hotplate is again given off. This phenomenon can be seen
everywhere in the environment and forms the basis for the following principles of
physics.
Fig. 4.7
Transient thermal resistanceZ
th
, comprisingR
th
andC
th
of a flat plate
The behaviour of the thermal impedance Z
th
is described in the time domain, whereby
the temperature difference
T now shows chronological behaviour because of the
thermal capacity.
) e1(
T )t(T
t
max
τ
− ⋅
∆= ∆
Eq. 4.9
The time constant in which the thermal capacity loads up with thermal energy is named
τ
as in electrical engineeringand is alsodescribed that way in physics:
th
th
CR
Eq. 4.10
The transient range extends from 0
τ
to 5
τ
, which represents 0% to 99.3% coverage of
the final value. The time period of more than 5
τ
or 99.3% is regarded as static (thermal
equilibrium), i.e. identical to the final value, in which, if
T
max
does not change, the
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