Offset definitions; closed-loop output resistance

Input offset voltage and input offset current

• Input offset voltage (Vio): the dc voltage that must be applied between the two inputs to make the output zero when both inputs are at ground potential. It comes from mismatch of the input transistors. 741: 1 mV typical, 6 mV max.
• Input offset current (Ios): the difference between the currents flowing into the two inputs when the output is zero, Ios = |IB1 − IB2|. 741: 20 nA typical, 200 nA max.

Output resistance of the closed-loop op-amp

Model the op-amp by its open-loop gain A, input resistance Ri (very large, ignored) and output resistance Ro. To find the closed-loop output resistance, set the input source to zero, apply a test voltage vx at the output and find the current ix drawn.

                    Rf
      +-----------/\/\/-----------+
      |                           |
 v- --+-----(-)                   |
      |         >--(A·vd)---Ro----+----o vx (test source,
      R1   +---(+)                         ix flows in)
      |    |
     GND  GND

Feedback voltage at inverting input:
  v- = vx·R1/(R1 + Rf) = β·vx
  vd = v+ - v- = -β·vx
Current through Ro:
  io = (vx - A·vd)/Ro = vx(1 + Aβ)/Ro
Current through R1 + Rf:
  iF = vx/(R1 + Rf)   (very small, neglected)
  ix ≈ io = vx(1 + Aβ)/Ro
Rof = vx/ix = Ro / (1 + Aβ),   β = R1/(R1 + Rf)

Because the output voltage is sampled and fed back (voltage feedback), the output resistance is divided by (1 + Aβ). Example: 741 with Ro = 75 Ω, A = 2 × 10⁵ and β = 0.1 gives Rof = 75/(1 + 2 × 10⁴) ≈ 3.75 mΩ, practically zero. The same result holds for the inverting and non-inverting amplifiers, since with the input grounded both have the same feedback network.