An investigation of the constant-temperature hot-wire anemometer

An algorithm is developed for deriving the transfer functions of the constant-temperature hot-wire anemometer of arbitrary complexity. The only restriction is that the bridge elements, including the hot-wire filament, must be modeled by lumped components. A minimum of two equivalent amplifiers are required to model the feedback amplifier properly. The poles of the transfer functions for electronic and velocity perturbations are shown to be identical regardless of the frequency response characteristics of the feedback amplifier and the nature and quantity of components used to model the bridge impedances. Computer simulations are used to explore the behavior of representative configurations. It is shown that the frequency response characteristics of the feedback amplifier must be included in addition to the offset voltage and cable and balance inductance to fully account for the behaviour observed in real systems. This leads to an optimum system response when the balance inductor is in excess of that required for ac bridge balance. Increasing the frequency response and gain of the feedback amplifier have the rather surprising effect of increasing the damping of the dominant poles. It is the higher order poles that are responsible for the instabilities under these conditions. With subminiature wires it is shown that insufficient frequency response of the feedback amplifier is the most likely cause of instabilities. Operating modes are demonstrated that are misleading, in the sense that the operator can be deceived into interpreting an erroneous frequency response. Examples are provided to help operators of the instrument to identify and avoid these rather subtle and undesirable modes of operation. A brief description is given of a new high-performance anemometer design that is based on these considerations.