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. 

MEMS Thermal Effect Sensors

Xiang Zheng Tu

Several MEMS thermal effect sensors have been developed by our company (POSIFA Microsystems). Among them are thermal flow sensors, thermal conductivity sensors, thermal vacuum sensors, thermal motion sensors and thermal humidity/carbon dioxide sensors. These sensors are given a first name as “thermal”, because their behaviors are related to thermal effects. Thermal effects mean the physical or chemical quantities measured by the sensors are caused by heat transfer processes.

All gases conduct heat to differing degrees, and the amount of heat transferred by a gas is determined by its 'Thermal Conductivity' (TC). The thermal conductivity sensor uses this property to accurately measure one of the two gases present in a sample of a binary or pseudo-binary mixture. In order to do so a micro-heater is created in a silicon wafer by MEMS technologies. The micro-heater is suspended over a cavity that is recessed in the silicon wafer. There is a temperature gradient between the micro-heater and the bottom of the cavity, which drives the heat energy generated by applying electrical power to the micro-heater transferring across the cavity by conduction. This results the change in the temperature of the micro-heater, which expresses a certain composition of the binary mixture in the cavity.

On the other hand, the thermal flow sensors operate based on a different type of heat transfer: convective heat transfer. More exactly the thermal flow sensors take advantages of laminar flow. This is why the thermal flow sensor is normally installed on the wall of a tube. When a fluid is forced to flow through the tube laminar flow will occur. The fluid tends to flow parallel in layers without lateral mixing, and adjacent layers slide past one another like playing cards. There are no cross-currents perpendicular to the direction _of flow, nor eddies or swirls of fluids.

Recall that a thermal flow sensor comprises a silicon chip, a resistive heater, one or two thermopiles, and a thermal insulating base. The heater and the hot junctions of the thermopiles are disposed on the surface layer of the base that is burred in the silicon chip and the cold junctions of the thermopiles are disposed outside of the base area. When a fixed electrical power is provided to the heater a temperature difference will be built up between the surface layer of the base and the outside area of the silicon chip. The thermopiles measure the temperature difference and output a voltage signal correspondingly. The temperature difference will be reduced by the forced laminar flow because convective heat transfer will take place.

This is a case of constant heat rate per unit surface area for steady, laminar, fully developed flow. The heat transfer from the surface layer of the thermal flow sensor through convection was first described by Newton and the relation is known as the Newton's Law of Cooling. The equation for convection can be expressed as:

q = h_c A dT,                                     (1)

where q = heat transferred per unit time, A = heat transfer area of the heated surface layer, h_c= convective heat transfer coefficient, and dT = temperature difference between the surface layer and the bulk fluid.

The convection heat transfer coefficient h_c for the surface layer is related to the heated surface layer Nusselt Number Nu_L by,

h_c = ( k/L) Nu_L                                        (2)

In this equation, k is the fluid's thermal conductivity, and L is the length of the heated surface layer.

The Nussult Number for this problem is given by,

Nu_L = 0.664 (Pr)1/3 (Re_L)1/2          (3)

where Pr is the fluid Prandtl Number, and Re_L is the fluid/heated surface layer Reynolds Number.

The Prandtl Number is given by,

Pr = c_p μ/k,                                         (4)

where c_p is the fluid’s thermal capacity and μ is the fluid’s viscosity.

The Reynolds Number is given by,

Re_l = ρu_fL/k,                                        (5)

where ρ is the fluid’s density and u_f  is the fluid’s velocity.

It can be seen that each fluid’s velocity corresponds a certain a certain heat transferred from the heated surface layer of the thermal flow sensor or a fixed input electrical power, because in the above equations only the fluid’s velocity is variable and the others are physical parameters of the fluid or geometrical parameters of the heated surface layer of thermal flow sensor.   

As well known all objects with a temperature above absolute zero emit heat energy in the form of radiation. Usually this radiation isn't visible to the human eye because it radiates at infrared wavelengths, but it can be detected by electronic devices such as MEMS infrared sensors. The MEMS infrared sensors measure temperature by converting infrared energy radiated from target objects into heat with MEMS thermopiles and then measuring the thermo-electromotive force resulting from temperature differences that occur across the contact points of two different types of metal.

The heat received by the thermopiles is very little and easy to dissipate by conduction. To solve this problem a micro-plate has been used to support the hot junction of the thermopiles, which is built over a cavity using low thermal conductivity materials such as a silicon-nitride, silicon dioxide or multilayered combination of these materials. 

Design of Thermal Flow Sensor Circuit

Being Offset Free, Temperature Drift Free, Noise Free and Interchangeable

Xiang Zheng Tu

1.    Schematic diagram of POSIFA thermal flow sensor

Reference to figure 1, a thermal flow sensor compromises a heater and two thermopiles 1 and 2. Suppose there is no fluid flow passing over the sensor.  The heater is heated by a filtered PWM output converted voltage generated by a microcontroller such as a PIC16 (L) F1704/8. The thermopiles will produce static outputsV_T1 and V_T2, respectively. If the filtered PWM converted voltage is set at 3V, the value of the static outputs is ranging from 30mv to 50mv and the V_T2 is always higher than V_T2 about 1.5mv. It should be noted that the filtered PWM output converted voltage contains a noise signal that is in the form of ringing with a periodic repetition. Since this noise signal is common mode to both the thermopiles, they can be canceled each other by sending to a differential amplifier for signal processing.

 

   

2.  Selecting a PWM output converted voltage for fixing the output V_T2 of the thermopile 2 at 30mv

Reference to figure 2, a comparator of the microcontroller is used to compare the output V_T2 of the thermopile 2 with a 30mv reference voltage V_Ref  provided by the microcontroller for sending out a digital output signal for adjusting PWM output converted voltage. When the thermopile 2 produces the output V_T2 equal to the reference voltage V_Ref, the PWM output converted voltage is fixed and the selection is finished.

According to our experience the thermal flow sensors with same static output have a similar sensitivity. They can be interchangeable for most of applications. 

  

3.    Creating a DAC output replacing the output of thermopile 2

Reference to figure 3, there is still no fluid flow passing over the sensor. A digital-to-analog converter (DAC) of the microcontroller is used to convert the output V_T2 of the thermopile 2 into a variable voltage V_DAC. The variable voltage V_DAC is derived by a resistor ladder and can be ratiometric with the input source. Moreover its all electrical properties maintain the same as the input source, which include the environment temperature influence and electromagnetic interference. As shown in the figure 3, the output V_T2 of the thermopile 2 is send to the DAC through an amplifier TP5552. TP5552 is used as a buffer for impedance transformation, because the recommended maximum source impedance of the input source is limited to be 10kΩ for the microcontroller, which is much lower than the impedance of the thermopiles.

4.    Adjusting the output V_DACT2 of a DAC for best match to the output V_T1 of the thermopile 1.

Reference to figure 4, the output V_DAC of the DAC is sent to the positive input of another comparator of the microcontroller and compares with the output V_T1 of the thermopile 1. The digital output of the comparator is used to change the output V_DAC of the DAC and eventually become V_DACT2 that is equal to the output V_T1 of the thermopile 1. Since them the output V_T2 is replaced by the output V_DACT2.

It should be understand that all these steps are performed without fluid flow passing over the sensor and can be done in the calibration process of the sensor and in the initiate stage of each sensor operation. 

After finishing these steps the output V_T2 of the thermopile 2 is replaced by the new reference voltage V_DACT1. The outputs of the differential output of the two thermopiles can be zero. This means the offset, temperature drift and noise of the two thermopiles can be canceled each other so that the sensor becomes the offset, temperature drift and noise free.

5.    Offset free, temperature drift free and noise free thermal flow sensor is realized by a differential amplifier

Reference to the figure 5, when a fluid flow passes over the sensor the thermopiles 1 and 2 will produce voltages -ΔV_T1 and -ΔV_T2 superimposed to the original output V_T2 and V_T1. Please note that -ΔV_T2 will be ratiomatric as V_T2 does and superimposed to the output V_DACT2, which is expressed as ΔV_DACT2. When a differential amplifier is used to multiply the difference between V_T1 - ΔV_T1 and V_T2 - ΔV_T2DAC, the common mode signals will be rejected. These common mode signals include temperature drift and electromagnetic noise. This means the thermal flow sensor becomes offset free, temperature drift free and noise free.

It can be seen in the figure that the used differential amplifier is another TP5554.  It was tolled that TP5552 is a dual chopper stabilized zero-drift operational amplifier, which features very low input offset voltage and low noise and may be operated with a relative high gain.