# calculate input resistance with known adc value

I am fairly new in the electronics world, but I would really like to learn it. The problem I'm facing right now, is that I miss the insight to be able to tackle this specific problem.

I have to calculate the input resistance of a system on the basis of a given ADC value. There will be an temperature sensor connected to the input, which will give some resistance, depending on the temperature. What I want to know / calculate, is the given resistance, so that I can calculate the right temperature. I know how to convert the ADC value to the correct voltage, but I do not know what the next steps are.

I calculate the voltage as follows: $\text{Result}_{\text{mV}} = (\text{Reference}_{\text{mV}} / \text{BitSteps}) \times \text{ADC}$

That gives the correct voltage at the input of the ADC.

Given the following diagram, which follow up steps should I take to calculate the input resistance?

74HC4052 Dual 4-channel analog multiplexer/demultiplexer data sheet

MCP6L04T/E/SL operational amplifier data sheet

• The more complete diagram makes more sense - your simplified diagram does not take account of the ADC being a differential input (I have made this assumption based on the 2nd diagram) and is therefore flawed for the purpose of analysis. Can you also be clear that you wish to translate the ADC reading to a value of unknown resistance placed between the input and 0 volts? Your question reads as if you are trying to calc the input resistance of your circuit rather than an unknown value placed at the input. Jun 27 '18 at 10:37
• @Andyaka, thank you for your comment. I must say that I never had heard of the term differential input, so I already learned something new. The case is that I have a temperature sensor which "gives" a certain resistance depending on the temperature. What I'm trying to do, is calculate / translate the given ADV value back to the resistance coming from the sensor. Does that clarify your question? Jun 27 '18 at 11:08
• I think a key step you need to consider is converting the sensor resistance into a corresponding voltage, and I can't tell how you plan to do that. I suspect you want a voltage divider. Please try to provide a more complete schematic that shows how the sensor is connected to the ADC, and includes the sensor itself. Jun 27 '18 at 12:11
• @ElliotAlderson The sensor is directly connected to the left, which is a NTC sensor. The labels on the right directly connect to the ADC. So I think that this schema is complete? Or am I overlooking something? Jun 27 '18 at 12:25
• I see what looks like a 12.4K pullup. I don't know what's driving the FET, but I assume it's just on/off. If you read the voltage at the center of the voltage divider driven between 5V and 0V with 12.4K on the top and X on the bottom, you should be able to determine X. Jun 27 '18 at 12:40

The voltage at the output of the mux is $\frac{5.0R_X}{R_X+12.4K +Rds(on)}$, and we can ignore Rds(on) since it's typically a couple tenths of an ohm.
The voltage at the input to the ADC is $\frac{5.0\cdot 0.4\cdot R_X}{R_X+12.4K +Rds(on)}$ because of the divider resistors R149/R150.
• Thank you very much... It took me some time to solve Rx (it's been a while since I did that), but this gives the correct resistance indeed. Jun 28 '18 at 6:20