# Effect of bias resistor value on common-mode rejection in a differential or instrumentation amplifier

In the below schematics a source is coupled to a differential amplifier.

Rb is a bias resistor for bias currents to flow:

Since in instrumentation amplifiers it is a remedy to add resistors for bias currents to find a return path(See the middle in this link.).

So basically I wanted to see the effect of this resistor value on common mode voltage rejection in a simulation. So I simulated the above schematics in LTspice for Rb = 1 Ohm and Rb = 47k resistors. Source is a 50mV DC and the common mode voltage is 50Hz interference. Here are the results for Vo1-Vo2:

For Rb = 1 Ohm:

For Rb = 47k 0hm:

As you see above in Rb = 1 Ohm case the distortion/common mode is rejected much more than in Rb = 47k case.

On the other hand the manufacturers recommend 10k to 100k resistor for Rb. I couldn't get the logic behind if it is causing more distortion why wouldn't we just ground the negative side or use a very low resistance? And what makes 10k very recommended?

• Please give values used for V1 and V2. It's not that clear what you have used. You should have used V1 at 0 volts to look at CMR. I would also simplify analysis by getting rid of the 10n capacitor. Commented Mar 22, 2018 at 18:00
• Vin and -Vin are just terminals of V1, source voltage is V1. V1 is 50mv differential voltage which is the voltage difference Vin - (-Vin). V2 is is sine 1V 50Hz common mode. I did what you say. I removed the 10n cap and removed V1 and shorted Vin and -Vin and made a single node. And I direct coupled the 50Hz 1V commonode to that node. And now increasing the Rb reduces the common mode voltage when I plot Vo2-Vo1. You definitely are right but I don't know why this happens the other way around when I use the way in the question. Commented Mar 22, 2018 at 18:12
• Thanks a lot for this insight. This makes a lot sense now. I dont know why in my circuit it is the other way around but your way definitely checks the common mode noise rejection. How about is 10k to 100k recom a magic? Commented Mar 22, 2018 at 18:16

Please give values used for V1 and V2. It's not that clear what you have used. You should have used V1 at 0 volts to look at CMR. I would also simplify analysis by getting rid of the 10n capacitor...

I did what you say. I removed the 10n cap and removed V1 and shorted Vin and -Vin and made a single node. And I direct coupled the 50Hz 1V commonode to that node. And now increasing the Rb reduces the common mode voltage when I plot Vo2-Vo1. You definitely are right but I don't know why this happens the other way around when I use the way in the question.

I think you are getting a mix of V1 and V2 and that was clouding the issue.

Thanks a lot for this insight. This makes a lot sense now. I dont know why in my circuit it is the other way around but your way definitely checks the common mode noise rejection. How about is 10k to 100k recom a magic?

You don't want the resistor to be too high or you won't bias the inputs correctly. On the other hand you don't want it to be too low or you'll be getting earth ground fault currents (as previously explained on another question).

• 1-) The thing is this circuit does not obey the superposition principle even though it is linear. When I remove common mode and increase Rb to high yes bias is not enough. And when I remove the source and use only common mode source then yes I can see the effect of Rb. But when I simulate the total signal things do not follow. Increasing the Rb do not decrease common mode. Very peculiar. I would like to see both effects in one simulation. 2-) You wrote "you'll be getting earth ground fault currents" Will that happen by capacitive coupling? Because there is no earth ground involved in my mind. Commented Mar 22, 2018 at 19:08
• You should try it with capacitive coupling back in to see what happens. I'd want to get to the root of the reason but don't go setting V1 to anything or confusion will reign. Commented Mar 22, 2018 at 19:12
• If I set V1 to zero volt, and common-mode voltage V2 to 1V 50Hz capacitive coupled with 10n like in my question; then the value of Rb has such effect: If Rb is 1 Ohm then the peak-peak rejected common mode at the output (Vo2-Vo1) becomes 1mV. If Rb is set to 100k same result. If Rb is set to 1 Meg peak-peak becomes 0.3mV. After this it starts to act weird and if I add 100 Meg or more. Commented Mar 22, 2018 at 19:25
• I also noticed somehow common mode voltages increases with V1(when V2 kept constant). The CMR is decreasing when the V1 is increased from zero to lets say 50mV, Commented Mar 22, 2018 at 19:27
• Isn’t V1 the same frequency and therefore not easily differentiated from V2. Commented Mar 22, 2018 at 20:54