An integrated 3D sound intensity sensor using four-wire particle velocity sensors: II. Modelling

Abstract

The sensitivity of a micromachined acoustic sensor consisting of four hot-wire particle velocity sensors is analysed theoretically and experimentally. The device and its fabrication have been presented in part 1 of this paper (Yntema et al 2010 J. Micromech. Microeng. 20 015042). A relatively straightforward analytical model is presented that describes both the air flow around the probe and the temperature profile around the heated wires. The presence of the chip surface near the heated wires influences the fluid flow around the wires, while it also affects the temperature distribution in the probe by altering the direction of heat transport. Both effects result into a modified angular dependence of the sensor sensitivity with respect to the normal 'figure-of-eight' figure of the response. By means of finite elements software, the thermal and the acoustic flow behaviour of the sensor are also investigated numerically, both effects together and each apart, and the results are compared to the analytical model. Comparison with the experimental data is presented, showing that the model is appropriate to describe the angular dependence and the magnitude of the sensor response. It is concluded that the perturbed air flow due to the chip surface is the dominant reason for the observed angular sensitivity.

An integrated 3D sound intensity sensor using four-wire particle velocity sensors: I. Design and characterization

“…The wire length is 1.5 mm, which was also used in previous designs. The design shown in figure 3 was designed specifically for modelling and characterization of the fourwire structure, the results of which are presented in [8]. For a complete three-dimensional particle velocity sensor, another sensor should be integrated on the same chip, for example as indicated in figure 4.…”

“…This influences the temperature distribution of the 'heat bubble' around the sensor wires and might result in an increased sensitivity in a specific direction. Both explanations are analysed and discussed in detail in part 2 of this paper [8].…”

“…Measurements have revealed a deviation of the sensitivity direction due to the presence of the silicon substrate. A thorough analysis of this effect is given in a separate paper in this issue [8]. In practice, the deviation can be corrected easily because it is almost independent of frequency and the sensor locations are virtually the same.…”

“…However, measurements have shown that the sensitive direction is actually shifted by more than 10 • . The exact origin of this deviation has been investigated and a detailed sensor model explaining this behaviour is presented in part 2 of this paper [8]. Because of the fact that the deviation is almost frequency independent, it can easily be compensated for as explained below.…”

A 2D acoustic particle velocity sensor with perfectly orthogonal sensitivity directions

“…This temperature difference causes a change in resistance of the two sense wires which is a measure for the particle velocity. This principle has been extended to multiple dimensions by using multiple parallel wire configurations [21][22][23].…”