In a bipolar-input operational amplifier, the input offset current I_os is defined in terms of the input bias currents into the two input transistors. Which expression matches I_os?

Introduction:
Two key DC parameters of bipolar-input op-amps are input bias current and input offset current. Distinguishing these improves DC error budgeting in precision analog design.

Given Data / Assumptions:

• Two nominally matched input transistors draw base currents IB1 and IB2.
• Definitions are according to standard op-amp terminology.
• We consider magnitudes; signs indicate which input draws slightly more current.

Concept / Approach:
The input bias current I_b is defined as the average of the two base currents: I_b = (IB1 + IB2) / 2. The input offset current I_os is the absolute difference: I_os = |IB1 − IB2|. These definitions separate common DC loading from mismatch-related error.

Step-by-Step Solution:
1) Identify IB1 and IB2 as currents entering the op-amp inputs.2) Form the average: I_b = (IB1 + IB2)/2.3) Compute the difference: I_os = |IB1 − IB2|.4) Compare to options; the difference between the two base currents matches the definition of input offset current.

Verification / Alternative check:
Consult any op-amp datasheet glossary: bias current and offset current are always defined as average and difference, respectively, validating the selection.

Why Other Options Are Wrong:
Average of two base currents: That is the input bias current, not I_os.

Collector current divided by current gain: That relates to estimating a single transistor base current, not the definition of I_os.

Difference between two base-emitter voltages: Defines input offset voltage mechanisms, not currents.

Sum of base currents: Not a standard DC error metric for op-amps.

Common Pitfalls:
Mixing up I_b and I_os, or assuming offset current is negligible. In precision circuits with high source resistance, even nanoamp differences can create millivolt-level errors.

Final Answer:
difference between two base currents