I'm powering the DFRobot SEN0189 with an ESP32 @ 3V3, and I'm in the same boat as you. There are 3 points on the graph, so I used multiple-variable algebra and solved.
TL;DR:
3V3 quadratic equation:
y = -2572.2x² + 8700.5x - 4352.9
I'll post my work, so you can catch me if I'm wrong.
First, we need to transform the X-axis from 5V to 3V3:
| 5V | 3.3V |
|---|---|
| 2.5V | 1.65V |
| 3.9V | 2.574V |
| 4.2V | 2.772V |
Now to transform the quadratic equation from 5V to 3V3:
y = -1120.4x² + 5742.3x - 4352.9
Replace the coefficients with a, b, and c
y = -ax² + bx - c
Now, substitute in the three points:
3000 = -a(1.650)² + b(1.650) - c
1000 = -a(2.574)² + b(2.574) - c
0 = -a(2.772)² + b(2.772) - c
Represent c, as values of a and b:
c = -a(2.772)² + b(2.772)
Replace c:
1000 = -a(2.574)² + b(2.574) - (-a(2.772)² + b(2.772))
1000 = 1.058508a - 0.198b
1000 + 0.198b = 1.058508a
a = 0.187055743b + 944.725972784
Represent c in terms of b:
c = -1.437333336b - 7259.259259259 + 2.772b
c = 1.33466664b - 7259.259259259
Substitute and solve for b:
3000 = -0.50925926b - 2572.016460904 + 1.650b - 1.33466664b + 7259.259259259
3000 = -0.1939259b + 4687.242798355
0.1939259b = 1687.242798355
b = 8700.451040088
Solve for c:
c = 1.33466664 * 8700.451040088 - 7259.259259259
c = 4352.9424969
Solve for a:
a = 0.187055743 * 8700.451040088 + 944.725972784
a = 2572.195306523
3V3 quadratic equation:
y = -2572.2x² + 8700.5x - 4352.9
The new equation works for the 3V3 points:
- 3000.11 = -2572.2×1.65² + 8700.5×1.65 - 4352.9
- 1000.14 = -2572.2×2.574² + 8700.5×2.574 - 4352.9
- 0.14 = -2572.2×2.772² + 8700.5×2.772 - 4352.9
As well as (3.5, 2000) from the original graph:
3.5V => 2.31V
2019.74 = -2572.2(2.31)² + 8700.5(2.31) - 4352.9