## Y-configuration of resistors

```
V_in - V_out = I_in * R_in
V_ref - V_out = I_ref * R_ref
V_out = (I_in + I_ref) * R_gnd

I_in = (V_in - V_out) / R_in
I_ref = (V_ref - V_out) / R_ref
V_out / R_gnd = I_in + I_ref =
    = (V_in - V_out) / R_in + (V_ref - V_out) / R_ref
(V_in - V_out) / R_in = V_out / R_gnd - (V_ref - V_out) / R_ref
V_in - V_out = (V_out / R_gnd - (V_ref - V_out) / R_ref) * R_in
V_in = (V_out / R_gnd - (V_ref - V_out) / R_ref) * R_in + V_out =
     = V_out * (1 + R_in / R_gnd + R_in / R_ref) - V_ref * R_in / R_ref
```

for `V_out=0`:
```
V_in = -V_ref * R_in / R_ref
```

for `V_out=Vref`:
```
V_in = V_ref * R_in / R_gnd + V_ref
```

## alternatives:

[rgco: Multichannel Arduino Oscilloscope](https://www.instructables.com/Another-Arduino-Oscilloscope/)

> The 16MHz Arduino clock is too fast for the ADC to operate properly, therefore it needs to be prescaled.
> Prescale factors of 1 (no prescale) to 128 can be selected.
> By default, the Arduino IDE sets the prescale to 128,
> resulting in an ADC-clock period of 128/16MHz=8 microseconds,
> and thus a sampling period of `13*8=104` microseconds.
> Many tests have shown reducing the prescale to 16 results in only a slight loss of precision,
> while even faster clocks result in garbage.

> The Arduino ADC can be operated in single acquisition or free running mode.
> The standard analogRead() function does a single acquisition and returns the value when the ADC is ready.
> […], it is also possible to use a loop and poll for the ADIF flag which indicates that the ADC reading is complete, […]


[pcscope](https://www.electronicsforu.com/electronics-projects/pc-based-oscilloscope-using-arduino)
([source](http://efymag.com/admin/issuepdf/PCBasedOscilloscopeUsingArduino.zip))

> By default, the ADC configuration of the Arduino gives samples every 116µs.
> So here the ADC is configured with additional lines of code to get samples faster than 85µs by setting the prescaler to 16.
> With this, you get ADC conversion every 20µs, […]