Classic back-EMF acquisition circuit explains BLDC back-EMF zero-crossing detection calculation

In the figure below, PHASE_A, PHASE_B, PHASE_C are connected to the A, B, C lines of the motor respectively, and after a voltage divider network, they are NULL_A, NULL_B, NULL_C respectively, and then connected to the ADC0, ADC1, ADC2 pins of the microcontroller. MITTEL is the estimated midpoint voltage after deformation, connected to the AIN0 pin of the microcontroller. As long as the comparison between NULL_C and MITTEL is turned on during the AB power-on period; the comparison between NULL_B and MITTLE is turned on during the AC power-on period; and the comparison between NULL_A is turned on during the BC power-on period, the zero-crossing event of each phase can be successfully detected.

Let's talk about what this voltage divider network is all about. This is a classic back-EMF collection circuit. It is copied in many brushless motor textbooks. I don't think it was originally created by the German in the MK project. Now let's analyze it. Ignore the capacitors in the figure and treat it as a pure resistance network. Assume that when the AB phase starts to be powered on, the voltage of PHASE_A is about 12V, the voltage of PHASE_B is about 0V, and the C coil generates a 6V reverse induced electromotive force at this time. After superimposed on the midpoint of the winding, the voltage output at PHASE_C should be about 12V. Question: What is the voltage value of the MITTEL point at this time? What is the voltage value of the NULL_C point?

Given that the voltages at each point are as shown in the figure above, how can you calculate the voltage at point C and point M?

1. Current at point A: (VA-A)/R7 = A/R18 + (AM)/R20 =》 12 + M = 3A

2. Current at point C: (VC-C)/R13 = C/R1 + (CM)/R22 =》 12 + M = 3C

3. Current at point B: (MB)/R21 = B/R12 + B/R4 =》 M = 3B

4. Current at point M: (MB)/R21 = (AM)/R20 + (CM)/R22 =》 3M = A + C + B

5. From 1 and 2, we can calculate that =》 A = C

6. From 3, 4, and 5, we can calculate that =》 3C = 4M

7. From 2 and 6, we can calculate that =》 M = 4V, C = 5.3V