Dynamic compensation of temperature sensors using a continuum model

Most temperature sensors are known to have slow dynamic response. Dynamic compensation has been used to expand the sensor frequency bandwidth using the known sensor frequency responses. There has been extensive literature on the temperature sensor dynamic compensation using the first order model which ignores the heat conduction within the sensor itself. This paper proposes a continuum model that includes the heat conduction. The resulting mathematical model is analyzed using Laplace transform from which a non-polynomial transfer function is obtained. This non-polynomial transfer function is further used to obtain approximations that can be implemented in the time domain for sensor dynamic compensation. The effectiveness of the compensation is illustrated with the data obtained from numerical simulations for random sensor input.