I want to understand the circuit of the triferential subtractor:
in the context of Anderson loop based signal conditioning, found in this resource here.
This is just an inverting amplifier with a voltage reference at the positive input terminal:
but I do not understand the role of balancing resistors in parallel with the input and feedback resistances. The paper discusses something about "trimming" but I cannot find anything about it on the internet.
Trimming generally means adjusting the component values or circuit parameters to match requirements. It’s not usually possible to make circuit elements exactly to spec – there is variability in the manufacturing and assembly processes.
In the circuit you show, the trimming potentiometer is used to set the ratio of feedback to input resistance exactly where it should be, in spite of random spread of resistor values. Rbal is used to modify the resistive network so that the ratio between the effective Rfb and Rin values is closer to the desired gain value that would be possible using affordable resistors. 1% and 0.5% resistors perform well and are not expensive. In small volume applications, a trim potentiometer and a trimming procedure will be cheaper than using ultra-precision resistors.
