## 5 Applied Magnetic Linkage Estimation Methods
### Input of Analogue Circuit  
The voltage signal generated by the Omicron CMC-type tester was fed to the input of an analogue conditioning circuit. This circuit adjusts the measured voltage signal so that it can be fed to the input of the analogue-to-digital converter in the STM32 microcontroller. An electronic schematic of the analogue voltage input circuit implementing the signal conditioning is shown in Figure 12.  
Figure 10: Waveforms (from top): red color is secondary voltage \(3u_{0}\), blue color is phase secondary voltage \(u_{21(1)}\) of phase L1, green color is associated flux \(\Psi_{12(1)}\) of phase L1 for the assumed value of the network capacitance to earth equal to \(C_{0}=9\) nF.  
The analogue voltage input circuit has two pairs of input terminals:  
1. Galvanically isolated input terminals IN_Tr, isolated by a voltage reduction transformer. This input is not marked on the diagram as it was not used;
2. Input terminals without galvanic isolation IN_F, connected directly to the low-pass filter. This input is dedicated to the connection of a voltage divider with a buffer. The  
Figure 11: Prepared measurement system consisting of an analogue integrator, analogue voltage input and a NUCLEO-H7A3 ZI-Q development board.  
Figure 12: Schematic diagram of the analogue voltage input electronic circuit that performs input signal conditioning.  
described divider mediated the signal exchange between the voltage output of the Omicron CMC-type tester and the IN_F input terminals. In addition, the analogue voltage input circuit consists of five subcircuits:  
1. Input a low-pass filter with a cut-off frequency equal to the following: \[f_{\text{c\_IN}}=\frac{1}{2\cdot\pi\cdot(R_{\text{f\_IN}}\cdot\text{C\_IN})}= \frac{1}{2\cdot\pi\cdot(5\text{ k}\Omega\cdot 10\text{ nF})}=3183\text{ Hz}\] (39) This filter provides pre-filtering of the voltage input signal, suppressing high-frequency noise.
2. Non-inverting active amplifier with adjustable voltage gain in the following range: \[G_{u1}=1+\frac{R_{\text{f}}}{R}=1+\frac{(0\div 20)\text{ k}\Omega}{3.3\text{ k}\Omega}=(1\div 7.06)\] (40)
3. DC voltage source (offset) separated by a buffer, with adjustable voltage gain in the following range: \[U_{\text{offset}}=U_{\text{Ref}}\cdot\left(1+\frac{R_{\text{1}}}{R_{\text{2}}} \right)\cdot\frac{R_{\text{4}}}{R_{\text{3}}+R_{\text{4\_max}}}=2.495\text{ V}\cdot\left(1+\frac{10\text{ k}\Omega}{10\text{ k}\Omega}\right)\cdot\frac{(0\div 20)\text{ k}\Omega}{10\text{ k}\Omega+20\text{ k}\Omega}=(0 \div 3.33)\text{ V}\] (41) The preset fixed voltage \(U_{\text{offset}}\) is used to artificially raise the AC voltage of the input signal so that it can be applied to the input of the analogue-to-digital converter, which processes voltages in the range of 0 V to 3.3 V. The preset DC voltage is as follows: \[U_{\text{offset}}=1.65\text{ V}\] (42)
4. Non-inverting summing active amplifier with constant voltage gain equal to the following: \[G_{u2}=1\] (43) This circuit sums a voltage input signal (alternating) and a fixed voltage \(U_{\text{offset}}\), creating a variable positive voltage signal.
5. An output low-pass filter with a cut-off frequency is equal to the following: \[f_{\text{c\_OUT}}=\frac{1}{2\cdot\pi\cdot(R_{\text{f\_OUT}}\cdot\text{C\_ GUT})}=\frac{1}{2\cdot\pi\cdot(10\text{ k}\Omega\cdot 10\text{ nF})}=1592\text{ Hz}\] (44)  
This filter provides final filtration of the output voltage signal, suppressing fast-changing interference (noise) from the electronic circuit. The cut-off frequency \(f_{\text{c\_OUT}}\) has been selected in such a way as to suppress signals with a frequency higher than that defined by the sampling theorem, also known as the Nyquist-Shannon theorem [27; 28], for the assumed sampling frequency \(f_{\text{P}}\):  
\[f_{\text{c\_OUT}}\leq\frac{f_{\text{P}}}{2} \tag{45}\]  
The adjusted output signal is finally passed to the input of the analogue-to-digital converter of the STM32 microcontroller on the NUCLEO-H7A3 ZI Q development board.