## 4 Principle of the CTA Circuit  
Figure 3 shows the main architecture of the CTA circuit. It has three modes of operation; two modes for calibration and offset correction, which are M1 and M2, and an M3 mode for normal operation. Normal mode, M3, represents the state of the CTA circuit when it detects and amplifies the error signal \(V_{ER}\). This error signal represents the difference between the voltage drop \(V_{RS}\) created by the sensitive resistor \(R\)s and the target voltage \(V_{TR}\), \(V_{ER}=V_{RS}-V_{TR}\). We have two terminals of the sensitive resistor \(R\)s that are wired to nodes \(V_{A}\) and \(V_{B}\). We have also two resistors \(R_{A}\) and \(R_{B}\), which create down-level shifters, \(V_{RA}\) and \(V_{RB}\), which allow separating of nodes \(V_{A}\) and \(V_{B}\) in order to provide a high-power heating. Finally, we have cascade current sources delivering bias currents \(I_{A}\) and \(I_{B}\). To adjust currents \(I_{A}\) and \(I_{B}\), we use linear feedback loops. Two analog multiplexers, \(M_{\text{UX1}}\) and \(M_{\text{UX2}}\), are placed between resistors \(R_{A}\) and \(R_{B}\) in order to ensure different modes of operation. Moreover, they must withstand the voltages \(V_{A}\) and \(V_{B}\). When \(V_{RS}\) across the sensitive resistor is equal to target \(V_{TR}\), it must occur a zero differential voltage \(V_{TR}=0\) V across the amplifier in normal operating mode. Then, for a desired \(V_{TR}\), we must correctly adjust the two-current sources in order to cause two-voltage drops, \(V_{RA}\) and \(V_{RB}\), across resistors \(R_{A}\) and \(R_{B}\), respectively. The two calibration operation modes M1 and M2 allow defining the two currents \(I_{A}\) and \(I_{B}\). \[V_{TR}=I_{A}R_{A}-I_{B}R_{B}=V_{RA}-V_{RB} \tag{16}\]  
In fact, three digital signals are used to control the two current sources feedback loops. They allow the control of the topology of the complete circuit. Moreover, they allow selecting the corresponding operation mode, as shown in Figure 4. The adjustment of the voltage drops \(V_{RA}\) and \(V_{RB}\) is ensured  
Figure 3: Circuit of the constant temperature anemometer (CTA). by three voltage references \(V_{n\
eq 1}\), \(V_{n\
eq 2}\), and \(V_{n\
eq 3}\) during the two calibration phases. A common-mode voltage appears at the input terminal of the operational amplifier during the calibration phase of the CTA circuit. The reference voltage \(V_{n\
eq 3}\) determines this voltage. When {\(\phi_{1}\), \(\phi_{2}\), \(\phi_{3}\)} = 14, 0, 0], the first mode M1 is active, as shown in Figure 4a. During this mode, the switching of the positive input of the operational amplifier to \(V_{n\
eq 1}\) and the connection of \(V_{n\
eq 3}\) to the negative input allows the adjustment of the voltage \(V_{RA}\). Therefore, during this mode, the positive feedback loop of the operational amplifier will be closed. We set \(V_{n\
eq 1}\) to the typical value of \(V_{A}\). In the input range of the operational amplifier, we use \(V_{n\
eq 3}\) to cause a desired voltage drop \(V_{RA}\). \[V_{RA}=V_{n\
eq 1}-V_{n\
eq 3} \tag{17}\]  
The setting of the voltage to the capacitor \(C_{a}\) ensures the adjustment of the current \(I_{A}\) by this closed loop. The value of this capacitor is set to maintain the voltage gate at the transistor P1 at the end of operation of this mode. Furthermore, this capacitor also allows defining of the dominant pole of the active feedback loop. Transistors P1 and N3 compose the current mirror. It allows to reverse the phase of this loop, which ensures good stability. The second mode, M2, is active when {\(\phi_{1}\), \(\phi_{2}\), \(\phi_{3}\)} = {0, 1, 0], as shown in Figure 4b. In this case, the drop voltage \(V_{RB}\) is ensured by adjusting the current \(I_{B}\) of the CTA circuit. In this mode of operation, the voltage \(V_{n\
eq 1}\) is at the positive input terminal of our CTA circuit and the voltage \(V_{n\
eq 2}\) is at its negative input.