# Resistors in an instrumentation amplifier

I'm designing a circuit where I'm using instrumentation amplifier to amplify my input voltage The formula for the amplifier is $$\frac{V_{\text{out}}}{V_{\text{in}}} = \left(1 + 2\frac{R_1}{R_{\text{gain}}}\right)\frac{R_3}{R_2}$$

In the circuit, there are an overall 7 resistors but only one controls the gain. From what I can find online, to find the gain of the amplifier what they did is they set all 6 resistors equal to each other and hence only one variable is left.

What I don't understand is why did they all equal to each other? What determines the value of the resistors? Why didn't they randomise the resistors and if they did what effect would it have on the amplifier?

• They don't need to be the same but they do need to be mirrored for COMMON mode rejection. All same is just simpler equation and more convenient when it comes to physical parts you need to have on-hand. May 20, 2020 at 13:41
• If you want a gain of 100 for example you can set R3/R2=10, and set R1 and Rgain to get 100 overall. Then each stage operates with the same gain of 10 which usually helps to maximise bandwidth. May 20, 2020 at 14:52 