AHDL-Model for System Simulations

In case of a homogeneous temperature distribution in the heated area, h corresponds to the temperature coefficient of the heater material, otherwise h includes the effects of temperature gradients on the hotplate. As a consequence of the aheady mentioned self-heating, the applied power is not constant over time, and the hotplate cannot be simply modelled using a thermal resistance and capacitance. Replacing the right-hand term in Eq. (3.28) by Eq. (3.35) leads to a new dynamic equation  

The coupling of the hotplate to the electronics via a resistive heater consequently alters the equation, and a change in the effective time constant occurs  

Inclusion of the self-heating effect yields an additional temperature dependence of the thermal time constant. Differences in the time constants for heating and cooling are evident, and the real thermal time constant can be observed only in the cooling cycle with 4eat = 0. 

Examples for such descriptions were reported recently. Starting with the lumped-model equations explained in Sect. 3.4, a matrix formulation can be found that supports the system optimization [19]. 

A first description of the microhotplate in AHDL was developed, which calculates the power dissipated by the polysilicon heater as shown in Fig. 3.3 [89]. The calculated power serves as input for a look-up table with the measured values of the power dissipated by a normalized polysilicon resistor, which then provides the corresponding microhotplate temperature. The model extracts the microhotplate temperature from the table. This microhotplate temperature is subject to temporal delay 

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