Using The Find_R Utility Program

Download the Find_R Utility Program.

There are applications of Op-Amps, such as in active filter circuits, that require a precise gain. Such circuits often use the non-inverting configuration as shown in Figure 1 below. The gain of the amplifier is given by the equation below. Note that the gain must be greater than unity (i.e. Av greater than 1).

 
                                         Ra
                              Av = 1 + ------
                                         Rb

There are two ways to achieve a precise gain:

Use a potentiometer
For example, a 10k Ohm, 20-turn trimmer type potentiometer could be used to set almost any value of gain. But such potentiometers are expensive relative to the cost of other components. And they need to be adjusted by a technician while measuring the gain. For a circuit being made in large quantities, that's a very expensive thing to do.
Use two precision resistors for Ra and Rb
If an accuracy of 1% is sufficient, then using two 1% precision resistors is very cost effective. But for arbitrary values of gain (e.g. 1.414) it can be tedious to find the pair of resistor values that will come closest to achieving the desired value. Of course, you would need to try every likely combination of values and see which pair comes closest. There are so many values of 1% resistors, where do you start? But hey, that's why they make computers!

The FIND_R program is small and quick. It runs in a DOS box under Windows. When run, FIND_R prompts you for the gain you want to achieve. It then finds the best combination of values to give you that gain. It also calculates the actual gain you achieve using those values, as well as the percent error between the desired gain and the actual gain. The percent error is typically in the range of 0.00 % to 0.03 %, which is well within the tolerance of 1% resistors.

If you find this program to be useful, please let us know. If you have any suggestions for other utility programs, please pass them along. Someone on our engineering team just might write a program to do it.

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