That mysterious extra input resistor

My caller last week admitted that analog circuit design was a new field of study for him. He had inherited an older design to maintain and perhaps improve. As we reviewed the total system it became obvious that he had done his homework until we hit a stage that had an extra resistor. The stage is shown here.

This circuit appeared in several places within the system. Theory says that with an ideal op amp there is no current flow through the input pin so adding a resistor in that circuit would have no effect, yet each stage had the resistor. I have seen this circuit in many systems where the engineer had no idea why it was there but as long as the system worked no effort was spent to investigate.

Adding this resistor was standard practice in the days when all input stages were bipolar transistors without bias current cancellation. Under these conditions the op amp bias currents ranged from a few nanoamps to the micro amp region. With some modern op amps this range of bias current is still normal.

The reason for this resistor comes from the error budget. The input stage error at the output due to bias currents can be expressed as:

If we set R?? equal to the parallel combination of Ri and Rf then the expression reduces to:

This is the mathematical relationship but for a quick determination just look at the data sheet. To illustrate the variation that can be seen between op amps, the bias and offset currents are listed in the following table for three devices.

The OPA132 is a FET input stage device while the other two have bipolar transistors in the input stage. It can be deduced that the OPA277 has a bias current cancellation circuit because the bias current may be either positive or negative and is the same value as the offset current. The OPA241 does not have this cancellation circuit because the bias current is only negative.

The compensation resistor should only be used with the OPA241, but then only if the added offset voltage caused by the bias current causes a significant error. For the other devices including the extra resistor in the circuit adds cost, uses more board space and gives an additional noise source in the system for no improvement in performance.