166

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.

Ad c C

th

th

⋅ ⋅ρ⋅

=

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.

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

−

− ⋅

∆= ∆

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

⋅

=τ

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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