There are many tedious aspects of designing electronic circuits, and one of these is determining which parallel combination of standard off-the-shelf stock value resistors will come closest to a predetermined value. The issue usually arises when you are faced with an existing circuit assembly where an internal resistance is a little too high and needs some "tweaking" to lower its value. It can also occur when you are specifying the gain resistors of an operational amplifier or designing a voltage divider circuit which needs to be trimmed to some value.
The formula for the equivalent value of two resistances in parallel is well known and easily handled with a basic calculator:
The difficulty is, of course, that stock resistors are only supplied in discrete values, in any of several tolerance levels. Since you no doubt have an exact target value in mind for the end result, you need to determine which standard value resistor, when added in parallel with the existing circuit resistance, will bring you closest to that target.
Also, when designing a circuit which will be produced in quantity you might like to know the range of the equivalent value of two parallel resistors, based on the nearest standard values and the manufacturer's tolerance.
In order to save yourself a great deal of punching numbers into a calculator and poring through lists of standard value components you can use the program supplied here to carry the load. This program allows you to select the tolerance level of resistors you will be working with and then enter the real-world values into two text boxes, "Resistor 1" and "Resistor 2". These "real values" might result from in-circuit measurements or from idealized calculations.
You also have the option of supplying a value for one resistor only (leaving the other one blank) and entering a value for the Parallel Equivalent you are aiming for.
Clicking on the button labeled "Calculate missing resistor value" displays the parallel equivalent of the resistances entered in the "real value" boxes; or, if you have supplied a value for the Parallel Equivalent, it will fill in the value of the resistor you need to achieve that value. The program then goes on to calculate the nearest standard value resistors and (probably more importantly) the maximum and minimum values of the parallel combination you can expect based on the tolerance level of the resistors listed in the "Nearest standard value" boxes.
The program will not accept a value of resistors less than 1. It expects that two of the resistor boxes will have numeric values, with the third one a blank. It will give you an error message if you have too many or not enough boxes with data in them. Also, it will complain if you try to enter non-numeric data.Click here to download the program "Resistors In Parallel 2"