--- title: "Bias current effect; closed-loop output impedance" subject: "Advanced Electronics" chapter: 2 key: "semester_4/advanced_electronics:bias-current-output-impedance" source: https://www.bctengineer.com/q/semester_4/advanced_electronics/bias-current-output-impedance site: BCT Engineering --- # Bias current effect; closed-loop output impedance Advanced Electronics · Chapter 2: Operational Amplifier Characterization - Asked in: 2069 Chaitra, 4+3 marks - Video: [Input Bias Current in Op-Amps (Amplifiers #9)](https://www.youtube.com/watch?v=SN8ZjCgm-EY) — Aaron Danner - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/advanced_electronics/bias-current-output-impedance - Whole chapter: https://www.bctengineer.com/md/semester_4/advanced_electronics/chapter-2 ## Question Show the effect of input bias current in op-amp circuit. Derive the expression for closed loop output impedance of inverting op-amp configuration. ## Short answer Input bias currents create output error; with no compensation Vo=IB1·Rf, while Rcomp=R1||Rf makes Vo=Rf(IB1−IB2)=Rf·Ios. For the inverting amplifier, output impedance is Rof=Ro/(1+Aβ), β=R1/(R1+Rf), because voltage feedback divides Ro by the loop gain. ## Answer #### Effect of input bias current The input transistors of an op-amp draw small dc base currents IB1 (inverting input) and IB2 (non-inverting input). These flow through external resistors and produce an output voltage even with zero input. ```text Rf +----/\/\/----+ | | Vi --R1--+--> IB1 -(-) | >--+---- Vo +-----> IB2 ---(+) | Rcomp | GND ``` With Vi = 0 and Rcomp = 0, the inverting input is at virtual ground, so all of IB1 flows through Rf: ```text Vo = IB1·Rf (e.g. 500 nA × 1 MΩ = 0.5 V) ``` Adding Rcomp = R1‖Rf at the non-inverting input makes V− = −IB2·Rcomp, and ```text Vo = IB1·Rf - IB2·Rcomp(1 + Rf/R1) = Rf(IB1 - IB2) = Rf·Ios ``` so only the much smaller offset current causes error. #### Closed-loop output impedance of the inverting amplifier 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. ```text Rf +-----------/\/\/-----------+ | | v- --+-----(-) | | >--(A·vd)---Ro----+----o vx (test source, R1 +---(+) ix flows in) | | GND GND ``` ```text 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. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. With Vi = 0 and Rcomp = 0 the output due to bias current is: A. IB1 x Rf B. IB2 x R1 C. Zero D. IB1 x R1 Answer: A. Virtual ground leaves IB1 to flow in Rf. (Key point: Uncompensated bias effect) 2. With Rcomp = R1||Rf the output becomes: A. Rf x IB B. Rf x Ios C. Zero D. R1 x Ios Answer: B. Vo = Rf(IB1 - IB2). (Key point: Compensated result) 3. To derive Rof, the input source is set to zero and: A. The output is shorted B. The feedback is removed C. A test voltage vx is applied at the output and ix is found D. A current is injected at the + input Answer: C. Rof = vx/ix. (Key point: Output impedance method) 4. The closed-loop output resistance is: A. Ro(1 + A*beta) B. Ro/A C. Ro*beta D. Ro/(1 + A*beta), beta = R1/(R1 + Rf) Answer: D. Voltage feedback reduces the output resistance by (1 + A beta). (Key point: Rof result) ## Related in Advanced Electronics - [Input impedance of inverting op-amp](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Ainverting-input-impedance) — Advanced Electronics, chapter 2 - [Offset/bias definitions; closed-loop input resistance](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Aoffset-bias-closed-loop-input-resistance) — Advanced Electronics, chapter 2, asked 2× - [Output voltage of two op-amp IA](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Atwo-opamp-ia-output) — Advanced Electronics, chapter 4 - [Find coefficients of op-amp summing circuit](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Asumming-amplifier-coefficients) — Advanced Electronics, chapter 1 - [Positive/negative bias current effect and reduction](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Apositive-negative-bias-current) — Advanced Electronics, chapter 2 - [Offset definitions; closed-loop output resistance](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Aoffset-closed-loop-output-resistance) — Advanced Electronics, chapter 2, asked 2× ## Related in other subjects - [Non-inverting op-amp voltage gain](https://www.bctengineer.com/question.md?key=semester_1%2Ffundamental_of_electrical_and_electronics_engineering%3Anon-inverting-amplifier-gain) — Fundamental of Electrical and Electronics Engineering, chapter 6 - [Ideal op-amp properties; non-inverting gain](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Aopamp-props-noninverting-gain) — Basic Electronics Engineering, chapter 4, asked 3× - [Ideal op-amp properties; inverting gain](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Aopamp-props-inverting-gain) — Basic Electronics Engineering, chapter 4, asked 3× - [Transfer function of op-amp phase-shift circuit](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Atf-opamp-allpass-r1-c-r2) — Control Systems, chapter 2, asked 2×