--- title: "Offset definitions; closed-loop output resistance" subject: "Advanced Electronics" chapter: 2 key: "semester_4/advanced_electronics:offset-closed-loop-output-resistance" source: https://www.bctengineer.com/q/semester_4/advanced_electronics/offset-closed-loop-output-resistance site: BCT Engineering --- # Offset definitions; closed-loop output resistance Advanced Electronics · Chapter 2: Operational Amplifier Characterization - Asked in: 2070 Chaitra, 2+5 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/advanced_electronics/offset-closed-loop-output-resistance - Whole chapter: https://www.bctengineer.com/md/semester_4/advanced_electronics/chapter-2 ## Question What is input offset voltage and input offset current of an operational amplifier? Find the output resistance of closed loop op-amp. ## Short answer V_io is the differential DC voltage to zero output; I_os is the difference between input bias currents. Output resistance with feedback is R_of = R_o/(1+Aβ). For a 741 with R_o=75 Ω and Aβ ≈ 2×10^4, R_of ≈ 3.75 mΩ. ## Answer #### 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. ```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. Input offset voltage is: A. The dc voltage applied between the inputs to make the output zero B. The output voltage with open inputs C. The supply difference D. The difference of two bias currents Answer: A. It compensates input transistor mismatch. (Key point: Vio definition) 2. Input offset current is: A. (IB1 + IB2)/2 B. |IB1 - IB2| C. IB1 x IB2 D. IB1 + IB2 Answer: B. It is the difference between the input currents with output at zero. (Key point: Ios definition) 3. With a test voltage vx at the output and input grounded, the voltage at the inverting input is: A. vx B. Rf x vx C. beta x vx with beta = R1/(R1 + Rf) D. Zero Answer: C. R1 and Rf form a divider across vx, giving vd = -beta vx. (Key point: Feedback voltage) 4. The closed-loop output resistance is: A. Ro x (1 + A*beta) B. Ro C. Ro*A*beta D. Ro/(1 + A*beta) Answer: D. Since io = vx(1 + A beta)/Ro, Rof = Ro/(1 + A beta), practically zero. (Key point: Rof) ## Close variants set in other exams - [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× ## Related in Advanced Electronics - [Output offset voltage of 741 inverting amplifier](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Aoutput-offset-741-inverting) — Advanced Electronics, chapter 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 - [Bias current effect; closed-loop output impedance](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Abias-current-output-impedance) — Advanced Electronics, chapter 2 - [IA features; 3 op-amp IA output voltage](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Aia-features-3opamp-output) — Advanced Electronics, chapter 4 - [Effect of input offset voltage; PSRR](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Aoffset-voltage-effect-psrr) — Advanced Electronics, chapter 2 - [Input offset voltage; proof of constant GBP](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Ainput-offset-voltage-gbp) — Advanced Electronics, chapter 2 ## Related in other subjects - [CE amplifier input, output resistance and gain (RE1, RE2)](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Ace-partial-bypass-numeric) — Electronics Devices and Circuit, chapter 2 - [Op-amp properties and summing amplifier](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Aopamp-props-summer-v1-2v2-3v3) — Basic Electronics Engineering, chapter 4 - [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 - [Summing amplifier using op-amp](https://www.bctengineer.com/question.md?key=semester_1%2Ffundamental_of_electrical_and_electronics_engineering%3Asumming-amplifier-op-amp) — Fundamental of Electrical and Electronics Engineering, chapter 6