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@@ -1,3 +1,30 @@
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+## Y-configuration of resistors
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+
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+```
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+V_in - V_out = I_in * R_in
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+V_ref - V_out = I_ref * R_ref
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+V_out = (I_in + I_ref) * R_gnd
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+
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+I_in = (V_in - V_out) / R_in
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+I_ref = (V_ref - V_out) / R_ref
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+V_out / R_gnd = I_in + I_ref =
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+ = (V_in - V_out) / R_in + (V_ref - V_out) / R_ref
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+(V_in - V_out) / R_in = V_out / R_gnd - (V_ref - V_out) / R_ref
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+V_in - V_out = (V_out / R_gnd - (V_ref - V_out) / R_ref) * R_in
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+V_in = (V_out / R_gnd - (V_ref - V_out) / R_ref) * R_in + V_out =
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+ = V_out * (1 + R_in / R_gnd + R_in / R_ref) - V_ref * R_in / R_ref
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+```
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+
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+for `V_out=0`:
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+```
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+V_in = -V_ref * R_in / R_ref
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+```
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+
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+for `V_out=Vref`:
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+```
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+V_in = V_ref * R_in / R_gnd + V_ref
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+```
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+
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## alternatives:
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[rgco: Multichannel Arduino Oscilloscope](https://www.instructables.com/Another-Arduino-Oscilloscope/)
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