Miniaturized Thermal Wind Sensors

Tu Xiang Zheng

A miniaturized thermal wind sensor produced by POSIFA Microsystems is shown in the above figure. The sensor is fabricated in a silicon substrate using popular CMOS and proprietary MEMS technologies. As shown in the figure, on the upper face of the silicon substrate there are four thermopiles and heaters indicated respectively by thermopile (W), thermopile (E), thermopile (N) and thermopile (S) and heater (W), heater (E), heater (N) and heater (S). They are arranged in symmetrical positions with the central point of the upper face of the silicon substrate. It should be noted that the hot junctions of the thermopiles and the heaters are disposed on a thermal insulating base that recessed into the silicon substrate. The heat generated by the heater is almost restricted in the top layer of the base because the conductive heat transfer is minimized. It is easy to understand that when wind flows over the sensor the temperature of the top layer will be reduced significantly by convective heat transfer. Since the cold junctions of the thermopiles are positioned in the outside of the base the temperature change will be detected by the thermopiles which represent the velocity of the wind.    

As can be seen, the thermal wind sensors operate by heat transfer from the heater to the flowing fluid. The term thermal implies the use of the resistive heaters within the fluid flow and the thermopiles measuring the temperature difference between the heaters and the fluid flow. As the fluid flow past the heaters increases, convective heat loss increases from the heaters. The relationship between increasing fluid flow and forced convective cooling of the heaters can be determined and used as a baseline calibration for sensing wind applications. Appropriately the heat transfer can be expressed by King’s Law that describes heat transfer from a cylinder of infinite length in terms of the resulting voltage difference and is useful for hot-wire anemometry characterization.

V = a + b * ν ^0.5                                 (1)

where: V = flow induced voltage difference; υ= wind velocity; a,b = constants.

The constants are a complex combination of fluid thermal conductivity properties and flow geometry and should be found empirically.

Combination of King’s law and Kinematics knowledge the following equations can be obtained for solving the direction and magnitude of the wind shown in the above figure.

υ_x = υ * sin(θ)                                   (2)

υ_y = υ * cos(θ)                                   (3)

V_x = a_x + b_x * υ_x^0.5                            (4)

V_y = a_y + b_y * υ_y^0.5                            (5)

 υ = (υ_x² + υ_y² )^0.5                              (6)

θ = tan​⁻¹​​(​υ_{x /} υ_y ​​​​)                              (7) 

where : υ – wind velocity, υ_x – horizontal component of wind velocity, υ_y – vertical component of wind velocity,  θ - incident airflow angle,  V_x – amplified differential signal of thermopiles responding to υ_x, V_y – ampilified differential signal of thermopiles responding to υ_y, a_x, a_y, b_x and b_y – constants of fluid thermal conductivity properties and flow geometry properties.

In the equation (2) to (7) υ and θ are variables, V_x and V_y are measured values of thermal flow sensor, and the others are constants. After getting the values of the by test and calculation the variables υ and θ can be found by solving the equations (2) to (7).

It has been subjected that the interface electronics of the thermal flow sensor operates in an offset free mode. This means that when there is no fluid flow the static (no flow) two signals of the thermopile (W)-thermopile (E) pair and the thermopile (N)-thermopile (S) pair are compensated each other and the static differential signal becomes offset free. This can be done in this way: the two heaters of a thermopile pair are derived with a fixed voltage and then the lower static output of the thermopile is compensated by a DAC modulated higher static output of the thermopile. As a result, the static differential signal of a thermopile pair is maintained constantly zero. 

When operated in this mode, the offset of the thermopiles is no longer problem. Operation in this should lead to canceling all common mode noise of the thermopiles.

A further advantage of operation in this mode is that, since the thermopiles have a same temperature coefficient, the temperature drift of the output signal of the thermopiles is also automatically compensated for.