## 5 Experimental Results  
Prototypes of the CTA circuit were fabricated and experimentally characterized using CMOS FD-SOI 28-nm technology. The total chip area including pads was 0.266 mm\({}^{2}\). The die photograph of the CTA circuit is shown in Figure 6.  
The supply voltage of the sensitive resistor is \(V_{DD}\) = 3 V and of the CTA circuit is \(V_{CC}\) = 1.2 V. A miller operational transconductance amplifier (OTA) was used with the resistors \(R_{A}\) and \(R_{B}\) equal to 1 k\(\Omega\) to minimize the input thermal noise. Moreover, these resistors allowed reduction of energy consumption. Finally, resistors \(R_{A}\) and \(R_{B}\) also allowed the minimizing of  
Figure 5: CTAcircuit with \(R_{\text{NL}}R_{\text{w2}}\), \(R_{\text{w3}}\) and \(R_{\text{w4}}\) are the wire resistances. Figure 6: Chip microphotograph of the CTA circuit in CMOS FD-SOI 28-nm technology and 0.266-mm\({}^{2}\) area. resistances of the connection wires of the CTA circuit, which were \(R_{w1}\) to \(R_{w4}\). Capacitors values were chosen as \(C_{1}=C_{2}=C_{3}=12\) pF. A ratio of \(N=20\) between the transistors N4/N6 and N5/N7 was set to reduce the power consumption. To test the CTA circuit, the nominal resistance of the sensitive resistor was 750 \(\Omega\) at 0 \({}^{\circ}\)C. The measurement result when different target voltages \(V_{TR}=\) {0.5 V, 1 V, 1.5 V, 2 V} were applied to the sensitive resistor with the digital signals \(\phi_{1}\), \(\phi_{2}\) and \(\phi_{3}\) is shown in Figure 7. We set references \(V_{ref1}=3\) V, \(V_{ref3}=0.5\) V and we varied the reference \(V_{ref2}=\) {2.5 V, 2 V, 1.5 V, 4 V}. The curves show that the applied reference voltages were stable. In addition, after each calibration phase, there was a change in voltage \(V_{RS}\). Figure 8 shows the transient response of the sensitive resistor for a voltage \(V_{RS}=2\) V. By setting the reference voltages \(V_{ref1}=3\) V, \(V_{ref2}=1\) V and \(V_{ref3}=\)\(0.5\) V, we can see that the increase in sensitive resistor temperature ensured a decrease in current flowing through the heat resistor \(R_{H}\). For this transient response, the steady state current reached the value \(I_{RH}\) of 3 mA and a sensitive resistor of 750 \(\Omega\) after 30 s.  
To find the cut-off frequency of the CTA circuit, a 1-kHz frequency and 50-mV amplitude square wave signal was used to optimize its frequency response. This square wave signal was applied to the non-inverting input of the differential amplifier A1. Figure 9 shows the square wave response of the CTA circuit: The cut-off frequency at \(-3\) dB of the CTA circuit is defined as \(f_{cut}=1/(1.3\tau)\)[8], where \(\tau\) is the pulse width. Therefore, our CTA circuit has a cut-off frequency of 60 kHz. Figure 8: Transient response of the CTA circuit with \(V_{TR}=1.5\) V.  
Figure 7: Measurement results for target voltage (\(V_{TR}\)) = {0.5 V, 1 V, 1.5 V, 2 V}. The fabricated MEMS calorimetric sensor was packaged into a printed-circuit board (PCB). The PCB was polished with a chamfer to reduce the possible flow separation and make sure a stable boundary layer was generated. The packaged flow sensor was tested at the test-section of an open-loop suction type wind tunnel (LW-8233, LonGwin, Taiwan), which was attached to a gantry as shown in Figure 10. The wind tunnel has a pitot tube (DP-Calc 8710, TSI, MN, USA) based reference flow meter for the free stream airflow measurement. With the heater resistor \(\mathrm{R_{H}}\) working on the temperature of 40 K, the measured power consumption P of \(\mathrm{R_{H}}\) under the input airflow of 0-26 m/s was 3-3.5 mW. More power was needed to maintain a constant overheated temperature due to the cooling effect of fluids flow. Accordingly, the required heater current \(\mathrm{I_{H}}\) was increased with the enhanced joule heating. The measurement of the MEMS calorimetric sensor was performed with an input airflow from 0 m/s to 26 m/s. The calorimetric sensor had a high sensitivity of 0.35 V/(m/s) at the linear low velocity region.