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In order to cofigure an ADC, I need to know the input resistance to the ADC Pin of a uC, designated as R_source in the following equivalent circuit:

R_source equivalent circuit

From R_source the acquisition time TACQ can be read from the following table:

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TACQ is what I need to find out. Now, my schematic looks like this:

enter image description here

The ADC is the grey box at the top right. My question is now, how can I calculate R_source from R3 and R4? When the switch closes, the cap looks like a short circuit to the DC. But as the charge increases, more current flows through R4, until the cap is fully charged.

ilja
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1 Answers1

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The Thevenin equivalent of this arrangement of V_BAT, GND, R3 and R4 is shown on the right:

schematic

simulate this circuit – Schematic created using CircuitLab

The effective source resistance is therefore \$R_{SOURCE}=50k\Omega \$, which puts acquisition time at a little over 5μs.

Simon Fitch
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  • Thanks for the answer. However, I still don't get how I get from the voltage at the ADC input (V_Bat/2) to the conclusion that R_source is 50kOhms. Could you explain that further? – ilja Aug 11 '23 at 11:48
  • So, after reading on Wikipedia on how to calculate `R_th` of the Thevenin Equivalent, I now know that voltage sources can be considered as short circuits. This makes it super easy as `R3` and `R4` are now parallel resistances. Can you explain why the voltage source can be considered a short circuit? – ilja Aug 11 '23 at 12:02
  • @ilja I don't like calling it a short circuit, I prefer the term "has 0Ω internal resistance" instead. That means it doesn't matter how much current you draw from it, the voltage across it remains fixed. That is, effective resistance, which by Ohm's law is change in voltage across the thing divided by the change in current through it, is zero. You can interpret that as a "short circuit", but it's not telling the whole story. Recap: an ideal voltage source has no internal resistance, and the voltage across it will not change regardless of the amount or direction of current through it. – Simon Fitch Aug 11 '23 at 12:52
  • @ilja BTW thank you for reading up on Thevenin equivalent, it tells me you're serious about learning, and makes me feel my writing here is justified. – Simon Fitch Aug 11 '23 at 13:00
  • I used the term they used in the Wikipedia article. But with your explanation it is much clearer. Thank you for following up. – ilja Aug 11 '23 at 15:44