Electronic – How to calculate a simple mixed parallel/series resistor circuit

You add the conductances (reciprocal of resistance) and then convert back to resistance. For example, lets say we have 500, 1500, and 2500 ohm resistors in parallel. The total resistance is:

1 / ((1/500) + (1/1500) + (1/2500)) = 326.1 ohms.

For 2 resistors in parallel you can also use (R1 * R2) / (R1 + R2) e.g. for 500 and 700 ohms:

(500 * 700) / (500 + 700) = 291.7 ohms.

For your example of the 10, 20 and 30 ohms in a 3 x 3 network, you can either work out each row then add the results, or multiply each value by three and calculate directly:

    |
10 20 30 
10 20 30
10 20 30
    |

1 / ((1/30) + (1/60) + (1/90)) = 16.3636... ohms.

If the example is like this (in/out at top and bottom of matrix):

    |
10 10 10
20 20 20
30 30 30
    |

then the result is 20 ohms (row 1 is 3.33... row 2 is 6.66... row three is 10 - added together is 20) which agrees with the answer you have.

If you read the section regarding DLY in the datasheet for your sensor you'll see that it suggests using a simple resistive divider to set the delay. Normally, you want to drive your ADC with a low output impedance compared to your ADC's input impedance. Your resistive dividers output impedance would be R1 || R2 (assuming your voltage source is perfect with no output impedance) - so approximately 580 Ω for the circuit below - this should be OK.

But let's suppose you want to set the delay to 15 min - which corresponds to 1.8V from the datasheet. To drop 1.8 V with the divider, R2 would have to be around 5.6 kΩ. The output impedance would then be 3.5 kΩ. This might cause problems if your ADC's input impedance is just 10 kΩ.

But since the datasheet suggests a resistive divider is OK and also states that the input impedance is high, I think you'll be OK with the following (don't quote me on this, though!)

This means something like this:

R2 will drop a voltage of 0.2 V across it. Rest of the voltage (3.3 - 0.2) will be dropped on R1. If your input voltage is 5V instead of 3.3, R2 will have to be around 400 Ohms.

If you do have issues due to the output impedance you can buffer the output of the voltage divider with a unity gain buffer. A unity gain buffer has a very low output impedance and should drive your ADC very well.