1D analog behavioral SPICE model for hot wire sensors in the continuum regime

We have developed an efficient 1D electrothermal SPICE model for hot-wire sensors simulation which takes into account self-heating and temperature gradients generated by the electrical contacts, regardless of the operating regime of the hot-wire. Our approach, based on the ability of SPICE to calculate the inverse Laplace transform by convolution, leads to a very fast, accurate and compact model where both time and space could be considered as continuous variables. A test of our model is by simulating the operation of a hot-wire anemometer in the constant temperature mode and in the 3ω mode. Our simulated results reproduce very closely the experiments and confirm the relevance of such an approach.