I'm designing a circuit, and I need a particular resistance. However, I don't have a resistor with that value. Therefore, I want to combine two resistors in parallel. In principle, with the parallel resistor equation:
$$ R_{//} = \frac{R_1 R_2}{R_1 +R_2} $$
I could just plug in random resistor values that I have until I get the right resistance. However, I think there must be a "correct" way to choose these resistors. Any tips?
Apart from using random resistors and this calculator, you may want to minimize the difference between the resistance across the resistors. The best way is to have equal resistance distribution.
The reason is to distribute the power evenly and minimize the chance that one resistor will blow up (usually the lesser resistance) than others due to exceeding its power rating.
So when you selected your resistors, make sure each path satisfies the maximum power rating of each resistor by calculating the power from either the expected voltage or current of that resistor:
$$ P_{rating} \ge I^2 * R $$ $$ P_{rating} \ge \frac{V^2}{R} $$
The best calculator I have found for such problems is https://jansson.us/resistors.html which allows for parallel or series connection. (It is particularly useful for ratios, which in this case is not applicable.)
I think there must be a "correct" way to choose these resistors.
Yes. Go through all combinations of two or three values from a table using a Python or Octave script would be my first approach. That's what computers are great at. Then sort them according to absolute error and choose according to your needs.
I highly suggest you put together such a script yourself. Fire up Thonny and go for it. Leverage Python's "batteries included" standard library.
I can show such a script here, but that would take all the fun out of it. If you insist I will, though. The value table is longer than the core of the script :)
There several aspects that may or may not be relevant depending on the application:
Power: You may want distribute the power dissipation evenly between the resistors, so you make them as equal as possible. Or you want the majority of power dissipated in one resistor (for whatever reason), so you make them as different as possible.
Unique Part Numbers: It's always a good idea to keep the number of unique part numbers in a design to a minimum. So you pick one resistor that's already in the BOM and you calculate the other one.
Tolerances: Maybe you need a certain tolerance for your parallel combination. The total tolerance of a parallel combination is dominated by the smaller resistor. So you might get away with buying only one instead of two precision resistors, if you make the precision resistor significantly smaller than the standard resistor.
