1. Introduction

Two-dimensional wind sensors play an important role in human productive activity, environment monitoring and prevention of natural disasters. Compared to the traditional wind sensors, 2-D solid thermal wind sensors have a significant advantage of portability, accuracy and reliability.

The vast majority of solid thermal wind sensors^[1-6] are fabricated on silicon substrates by CMOS process. Due to the high thermal conductivity of the silicon material, the sensitivity of silicon thermal wind sensors is not high. Besides, the fabrication processes of the silicon chips are complex and the accuracy of the silicon chips' package is difficult to control, such as classical attaching to ceramic package, which was proposed by Oudheusden^[2] and perfected by Matova^[4]. A direct chip attaching (DCA) packaged wind sensor fabricated on a ceramic substrate was presented by our group^{[7, 8]}.

But there is a fatal flaw in the DCA packaged wind sensor. The position of the chip is easily mounted off-center, which will weigh heavily against the consistency and performance of the sensors. In this paper, an advanced DCA packaged wind sensor is presented, which could avoid the above-mentioned flaw. The CFD model simulation results of advanced DCA packaged sensors are in line with the wind tunnel testing results.

2. Chip structure and package

The chip of the ceramic thermal wind sensor is designed on a ceramic substrate. Firstly, titanium and platinum are deposited on the ceramic substrate by electron beam evaporation; then detectors and heaters are fabricated by metal lift-off processes. Finally, a layer of gold is deposited on the pad by the same processes. Laser cutting is used to form the circular chip, which is shown in Fig. 1(a). The microscopic structure of the ceramic chip is shown in Fig. 1(b).

The temperature difference-detecting resistors ($R_{x11}$-$R_{x22}$, $R_{y11}$-$R_{y22})$, the heating resistors ($R_{\rm h1}$-$R_{\rm h4})$ and the chip's temperature detecting resistors ($R_{\rm s1}$, $R_{\rm s2})$ on the chip are shown in Fig. 1(a). The advanced direct chip attaching packaged ceramic thermal wind sensor, which combines the package of the silicon thermal wind sensor^[9] and the DCA packaged sensor, is shown in Fig. 2. Due to the air gap between the ceramic square chip and the aluminum shell, the asymmetry of the sensor is easily caused by some uncontrollable factors like attaching errors and slicing errors. Firstly, a flexible print circuit (FPC) is attached to the circular chip and wires are bonded to achieve electric connection between the sensor and the signal processing circuits, then the bonding wires are capsulated with bonding glue. Finally, the chip is glued to the aluminum oxide metab with the window of the same shape as the chip. This advanced DCA packaged thermal wind sensor avoids the deviation of the chip mounting position completely and simplifies the processes of thermal wind sensor packaging further. The simplification of packaging processes improves the reliability and consistency of the wind sensor. The cross-section view, top view and bottom view of the advanced DCA packaged sensor are shown in Figs. 3(a), 3(b) and 3(c), respectively. The radius of the circular advanced DCA packaged ceramic chip is about twice the size of the length of the square chip side. We assume that the radius of the DCA packaged chip is 2$a$, the slicing error of the chip is $b$, $a \gg b$. Then the relative area error of the circular chip is $e_1=(b^2+4ab)/(2a+b)^2 \approx b/(a+b)$. In the same way, the relative area error of the square chip is $e_2=2b/(a+2b)$. Obviously, we can conclude that $e_1 < e_2$. So the advanced DCA packaged chip could be more accurate than the DCA packaged chip.

3. Operating principle

In this paper, constant temperature difference (CTD) control mode is adopted in this two-dimensional ceramic thermal wind sensor and temperature differences in the chip surface are detected to measure the wind speed and wind direction.

While the airflow goes through the back side of the chip, it could cause the variation of the temperature gradient in the chip surface. Then the Wheatstone bridges, which consist of Pt resistors, could detect the temperature differences in the chip surface and convert them into the voltage values. From these values, the microprocessor can calculate the wind speed and wind direction. In Fig. 1(a), when wind direction is $\beta$, the temperature gradients can be decomposed as follows: $\Delta T_y=\Delta T_0 \cos \beta$, $\Delta T_x=\Delta T_0 \sin \beta$. While $\Delta T_0$ is relative to wind speed $U$ and the temperature difference $\Delta T$ between the chip and the airflow, which can be expressed as $\Delta T_0 =\Delta TF(U)$, $F(U)$ depends on the material properties of the fluid and sensor^[1]. The ideal output voltages in $y$ and $x$ directions are expressed as respectively^[1]:

$\begin{equation} V_y=s\Delta TF(U)\cos \beta, \end{equation}$

(1)

$\begin{equation} V_x=s\Delta TF(U)\sin \beta, \end{equation}$

(2)

where $s$ is the sensitivity of the sensor, the unit is V/K. The wind speed $U$ and wind direction $\beta$ are expressed as:

$\begin{equation} U=F^{-1} \left(\sqrt{V_x^2+V_y^2}/s\Delta T\right), \end{equation}$

(3)

$\begin{equation} \beta=\tan^{-1}(V_x/V_y). \end{equation}$

(4)

4. CFD simulation of packaged structure

The characteristics of the advanced DCA packaged structures could be analyzed by the CFX simulation. The CFD model of the advanced DCA packaged sensor is shown in Fig. 4. In the CFD model of the advanced DCA packaged sensor, there is a 21 mm diameter circular chip in the center. The chip is attached to a metab with a window, and the size of the window is the same as the chip. The air-shed of this CFD model is 60 $\times$ 60 $\times$ 12 mm$^{3}$, which is on the ceramic chip. Then the air-shed can be rotated to different degrees to achieve the simulation of this advanced DCA sensor in different wind directions.

A professional mesh generation software ICEM-CFD is used to generate a full-hexahedral grid of these models^[10]. Then the meshed models are imported to CFX-Pre to define air domain, solid domain, boundary conditions, fluid solid interface and material parameters, then they are imported to CFX solver manager to carry out the solutions. The results of the solutions could be looked into in the CFD-post^[11]. The major parameters of the materials in the simulation are listed in Table 1. The simulated velocity profiles of two DCA packaged sensors under the wind speed of 5 m/s, 10 m/s are shown in Fig. 5. From the figure, the steady speed of the advanced DCA packaged sensor is a little smaller than that of the DCA packaged sensor, but the thickness of the velocity boundary layer of DCA and advanced DCA packaged sensors is almost the same. So the advanced DCA sensor can obtain a wider range in constant power mode. Then the simulations with the different wind speeds from 0 to 360 degree are carried out to verify the performance of the advanced DCA packaged sensor. The simulated temperature difference outputs in $x$ and $y$ axis directions with the speeds of 7m/s and 15 m/s are shown in Fig. 6. The results show the advanced DCA packaged sensor can detect wind speed and wind direction effectively.

5. Results and discussion

The advanced DCA packaged sensor system is designed, which is shown in Fig. 7. The CTD control circuit, calorimetric measurement circuit and the MCU processing system are included in this system. The calorimetric measurement circuit is designed to detect the voltages $V_x$ and $V_y$ in two directions. The wind speed and direction are calculated in the MCU. The wind tunnel for calibration and measurement and the sensor system mounting position, wind speed and direction controller in the wind tunnel are shown in Fig. 8. The measured output curves of the advanced DCA packaged sensor in $x$ axis and $y$ axis directions with the wind speed of 7 m/s and 15 m/s are shown in Fig. 9. From the curves in Figs. 6 and 9, the testing results are in line with the simulated results. The advanced DCA packaged sensor can achieve the error of wind speed from 0 to 20 m/s of about 0.5 m/s, which is much smaller than the error of the old DCA packaged sensor. From the testing results which is shown in Fig. 10, we can conclude that the advanced DCA packaged sensor is a better choice.

In order to study the performance of the ceramic thermal wind sensor further, data fitting of the relationship between the amplitude of $V_x$ and $V_y$ voltage and wind speed is achieved in Matlab. The nonlinear fitting function lsqcurvefit based least square method in Matlab Optimization Toolbox^[12] is used in this paper. The equations of output voltages $V_x$ and $V_y$ are given in Section 3. Considering the zero drift caused by the fabrication errors and other factors, we can rewrite the equations:

$V_x=A_x\sin \beta +V_{x0}, \\[2mm]$

(5)

$V_y=A_y\cos \beta +V_{y0},$

(6)

where $A_x$ is the amplitude of the output voltage $V_x$ in $x$ direction, which is $s\Delta TF(U)$, $A_y$ is the amplitude of the output voltage $V_y$ in $y$ direction, which is $s\Delta TF(U)$. $V_{x0}$ and $V_{y0}$ are the reference voltages in $x$ and $y$ directions respectively. It is difficult for these two values to be identical due to the different performances of devices in the actual testing. From the operating principle of thermal wind sensor, $F(U) \sim U^{1/2}$^[2], we can deduce that $A_x$, $A_y\sim U^{1/2}$. The total amplitude $A=\sqrt{A_x^2+A_y^2} \sim U^{1/2}$.

Firstly, the parameters of simulated temperature differences' curves in Fig. 5 and the measured voltage curves in Fig. 8 can be fitted by using lsqcurvefit function in Matlab, which is shown in Table 2. The fitting curves show the amplitudes of the simulated temperature differences are identical, and those of measured voltage $A_x$ and $A_y$ are not exactly identical. The differences between $A_x$ and $A_y$ are mainly caused by the fabrication errors. The measured voltages' fitting functions have different reference voltages in the same direction due to the zero drift. The maximum absolute residuals of simulated and measured fitting curves are 0.0012 and 0.022.

Then we can assume that $A_x$, $A_y$ and $A$ have similar functional forms such as $BU^{1/2}+C$. The unit of $B$ is Vs$^{0.5}$/m$^{0.5}$, which indicates the sensitivity of the wind sensor. The constant $C$ indicates the output voltage variation caused by other factors, and the unit is $V$. $U$ is wind speed. Then we use lsqcurvefit function to solve the $A_x$, $A_y$ and $A$ expression in Matlab. In Fig. 11, $A_x$, $A_y$ and $A$ curves show the amplitude-wind speed relationships before fitting, $A_x$Fit, $A_y$Fit, and $A$Fit curves are the corresponding relationships of $A_x$, $A_y$ and $A$ after fitting respectively. The fitting curves are in good agreement with the original data, which are described as follows: $A_x$Fit $=$ 0.1038$U^{1/2}$ $+$ 0.0296, $A_y$Fit $=$ 0.1088$U^{1/2}$ $+$ 0.0359, $A$Fit $=$ 0.1504$U^{1/2}$ $+$ 0.0464. The fitting expressions of $A_x$Fit and $A_y$Fit show the sensitivity of sensor in $x$ direction and $y$ direction are almost identical. The maximum absolute residuals of $A_x$Fit, $A_y$Fit, $A$Fit are 0.0101, 0.0093 and 0.0136 respectively. From the parameters of $A_x$Fit, $A_y$Fit curves, we can know that the sensitivities of $x$ direction and $y$ direction are almost the same. The average sensitivity of sensor is 0.1504 Vs$^{0.5}$/m$^{0.5}$. The $A$ curve can be used as reference to calculate the wind speed in the MCU.

6. Conclusion

This paper presents an advanced DCA packaged ceramic thermal wind sensor based on the DCA package. This new package process simplifies the package procedures further. The reliability of the ceramic thermal wind sensor has been improved and the deviation of the chip position in the package could be avoided. All these would have important roles in industrialization of thermal wind sensors. In this paper, the simulated results are in accord with the testing results. With the range of the wind speed below 20 m/s, the measured error of the advanced DCA packaged sensor is about 0.5 m/s, which is smaller than the old DCA packaged sensor. The nonlinear fitting based least square method in Matlab is adopted to analyze the performance of the sensor. The fitting results show this sensor can detect the wind speed correctly.