Offset voltage/current and bias current compensation

Input offset voltage

Input offset voltage (Vio) is the dc differential voltage that must be applied between the two input terminals to make the output zero when both inputs are grounded. It arises from mismatch of the input transistors (VBE). For the 741, Vio ≈ 1 mV typical, 6 mV maximum.

Input offset current

Input offset current (Ios) is the difference between the bias currents flowing into the two inputs when the output is zero: Ios = |IB1 − IB2|. For the 741, Ios ≈ 20 nA typical, 200 nA maximum. (Input bias current IB = (IB1 + IB2)/2.)

Compensating the effect of input bias currents

The input transistors need base currents IB1 and IB2. These flow through the external resistors and produce an output voltage even with zero input.

                 Rf
          +----/\/\/----+
          |             |
 Vi --R1--+--> IB1 -(-) |
                     >--+---- Vo
     +-----> IB2 ---(+)
     |
   Rcomp
     |
    GND

Take Vi = 0 (only bias currents act). IB1 flows into the inverting input and IB2 into the non-inverting input.

Without compensation (Rcomp = 0): the non-inverting input is at 0 V, so the inverting input is also at 0 V (virtual ground). No current flows in R1, so all of IB1 comes through Rf:

Vo = IB1 · Rf

e.g. IB = 500 nA, Rf = 1 MΩ gives 0.5 V of output error with no input.

With compensation resistor Rcomp at the non-inverting input:

V+ = -IB2·Rcomp = V-
KCL at inverting node:
  (0 - V-)/R1 + (Vo - V-)/Rf = IB1
  Vo = IB1·Rf + V-(1 + Rf/R1)
     = IB1·Rf - IB2·Rcomp(1 + Rf/R1)
Choose Rcomp(1 + Rf/R1) = Rf, i.e.
  Rcomp = R1·Rf/(R1 + Rf) = R1 ‖ Rf
Then
  Vo = Rf (IB1 - IB2) = Rf · Ios

Since Ios is only a fraction of IB (for the 741, 20 nA against 80 nA typical), the error falls a lot. The rule is: both inputs should see the same dc resistance to ground.

Other ways to reduce the effect of bias currents:

• Use op-amps with low IB (FET-input or super-β types, e.g. LF351, CA3140 with IB in pA).
• Keep Rf (and all resistors) low, since the error is IB·Rf or Ios·Rf.
• Use a T-network feedback to get high gain with smaller resistors.
• Use the offset-null terminals (pins 1 and 5 on the 741 with a 10 kΩ pot) or an external balancing network to trim the remaining output offset to zero.
• For ac amplifiers, use capacitor coupling so the dc gain is 1.