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Output offset voltage of 741 inverting amplifier

Short answer

i) Output offset from I_B: 5 V. ii) From V_ios: 0.606 V. iii) Compensation resistor R_comp = 99.01 kΩ (R1∥Rf). iv) With R_comp, maximum total output offset is 2.606 V (2 V from I_os plus 0.606 V from V_ios).

For the inverting amplifier shown in figure below, R1 = 100 KΩ and Rf = 10 MΩ. Calculate: i) Maximum output offset voltage caused by the input bias current IB. ii) Maximum output offset voltage caused by the input offset voltage, Vios. iii) The value of compensation resistor Rcomp needed to eliminate the effect of input bias current. iv) The maximum output offset voltage even if the Rcomp is connected in the circuit. The op-amp used is 741 with Vios = 6 mV, IB = 500 nA and Ios = 200 nA. [Figure: inverting amplifier: source Vi through R1 to the inverting input, feedback resistor Rf from output V0 to the inverting input, non-inverting input grounded.]

Given: R1 = 100 kΩ, Rf = 10 MΩ, 741 with Vios = 6 mV, IB = 500 nA, Ios = 200 nA (maximum values).

Noise gain: 1 + Rf/R1 = 1 + 10 MΩ/100 kΩ = 101

(i) Output offset due to input bias current

With the + input grounded, the − input is at virtual ground, so IB flows through Rf:

Vo(IB) = Rf · IB = 10 × 10⁶ × 500 × 10⁻⁹ = 5 V

(ii) Output offset due to input offset voltage

Vios is amplified by the noise gain:

Vo(Vios) = (1 + Rf/R1) · Vios = 101 × 6 mV = 0.606 V

(iii) Compensating resistor

To cancel the effect of IB, both inputs must see the same dc resistance:

Rcomp = R1 ‖ Rf = (100 kΩ × 10 MΩ)/(100 kΩ + 10 MΩ)
      = 10¹² / 10.1 × 10⁶ = 99.01 kΩ

(A standard 100 kΩ resistor would be used.)

(iv) Maximum output offset with Rcomp connected

With Rcomp = R1‖Rf, the bias-current error becomes Ios·Rf:

Vo(Ios) = Rf · Ios = 10 × 10⁶ × 200 × 10⁻⁹ = 2 V

The offset voltage error is still present, so in the worst case both add:

Vo(total, max) = Vo(Ios) + Vo(Vios) = 2 + 0.606 = 2.606 V

Answers: (i) 5 V, (ii) 0.606 V, (iii) Rcomp = 99.01 kΩ, (iv) 2 V due to Ios, or 2.606 V total including Vios. Without Rcomp the worst-case total would be 5 + 0.606 = 5.606 V. The remaining offset can be removed with the 741 offset-null pot.

✓ Answer checked by Claude Opus 5.5 (high effort)

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