---
title: "Offset/bias definitions; closed-loop input resistance"
subject: "Advanced Electronics"
chapter: 2
key: "semester_4/advanced_electronics:offset-bias-closed-loop-input-resistance"
source: https://www.bctengineer.com/q/semester_4/advanced_electronics/offset-bias-closed-loop-input-resistance
site: BCT Engineering
---

# Offset/bias definitions; closed-loop input resistance

Advanced Electronics · Chapter 2: Operational Amplifier Characterization

- Asked in: 2074 Chaitra, 3+4 marks
- Video: [Op-Amp: Input Offset Voltage Explained](https://www.youtube.com/watch?v=hUu3SqRSYyA) — ALL ABOUT ELECTRONICS
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/advanced_electronics/offset-bias-closed-loop-input-resistance
- Whole chapter: https://www.bctengineer.com/md/semester_4/advanced_electronics/chapter-2

## Question

Define input offset voltage, input offset current and input bias current of an operational amplifier. Find the input resistance of closed loop op-amp circuit.

## Short answer

Input offset voltage is the dc differential voltage needed to null the output. Input bias current is the average of input currents; input offset current is their difference. Inverting closed-loop input resistance is Rin = R1 + Rf/(1+A) ≈ R1; non-inverting input resistance is Rif = Ri(1+Aβ), very high.

## Answer

#### Definitions
- **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.
- **Input bias current (IB):** the average of the currents flowing into the two input terminals when the output is zero, IB = (IB1 + IB2)/2. It is the base current of the input transistors. 741: 80 nA typical, 500 nA max.

#### Input resistance of the closed-loop op-amp
The answer depends on the configuration; both are shown.

**Inverting amplifier (voltage-shunt feedback):**

```text
                Rf
       +------/\/\/-----+
       |                 |
 vin --R1--+--(-)        |
  -> i1    |        >----+---- vo
       GND-+--(+)
```

The input current i1 flows through R1 into node v− (the op-amp input current is negligible since Ri is very large).

```text
vo = -A·v-          (v+ = 0)
Current through Rf:
  iF = (v- - vo)/Rf = v-(1 + A)/Rf
So, seen from node v-, Rf looks like
  Rf/(1 + A)        (Miller effect)
Node v- to ground: Ri ‖ Rf/(1 + A) ≈ Rf/(1 + A)
Input resistance:
  Rin = vin/i1 = R1 + Rf/(1 + A)
Since A is very large:
  Rin ≈ R1
```

So the input resistance of the inverting amplifier is set by R1, because the inverting input is a **virtual ground**. Example: R1 = 10 kΩ, Rf = 100 kΩ, A = 2 × 10⁵: Rin = 10 kΩ + 0.5 Ω ≈ 10 kΩ.

For the **non-inverting amplifier** (voltage-series feedback), vin drives the + input directly:

```text
vd  = vin - β·vo ,   vo = A·vd ,   β = R1/(R1 + Rf)
vin = vd(1 + Aβ)
iin = vd/Ri
Rif = vin/iin = Ri(1 + Aβ)
```

Example: Ri = 2 MΩ, A = 2 × 10⁵, β = 0.1 gives Rif = 2 MΩ × 20 001 ≈ 40 GΩ, practically infinite.

| Configuration | Closed-loop input resistance |
|---|---|
| Inverting | Rin ≈ R1 (low, set by R1) |
| Non-inverting | Rif = Ri(1 + Aβ) (very high) |
| Voltage follower (β = 1) | Rif = Ri(1 + A) |

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Input bias current IB is defined as:
   A. (IB1 + IB2)/2, the average of the two input currents
   B. |IB1 - IB2|
   C. IB1 x IB2
   D. The dc voltage that nulls the output
   Answer: A. The difference is the offset current; the average is the bias current. (Key point: Input bias current)

2. The closed-loop input resistance of the inverting amplifier is approximately:
   A. Ri(1 + A*beta)
   B. R1, because the inverting input is a virtual ground
   C. Rf
   D. Ri
   Answer: B. Rin = R1 + Rf/(1 + A), and with very large A this is about R1. (Key point: Inverting Rin)

3. Seen from the inverting node, the feedback resistor Rf looks like:
   A. Rf(1 + A)
   B. Rf x A
   C. Rf/(1 + A)
   D. Rf
   Answer: C. Current through Rf is v-(1 + A)/Rf, so the effective resistance to ground is Rf/(1 + A). (Key point: Miller effect)

4. The closed-loop input resistance of the non-inverting amplifier is:
   A. Rif = R1
   B. Rif = Ri/(1 + A*beta)
   C. Rif = Rf/(1 + A)
   D. Rif = Ri(1 + A*beta), very high
   Answer: D. Series feedback multiplies the input resistance by (1 + A*beta), e.g. 2 Mohm gives about 40 Gohm. (Key point: Non-inverting Rif)

## Close variants set in other exams

- [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 Advanced Electronics

- [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
- [Offset voltage/current and bias current compensation](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Aoffset-voltage-bias-compensation) — Advanced Electronics, chapter 2, asked 2×
- [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
- [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

- [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
- [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
- [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
- [Voltage gain of non-inverting op-amp](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Aopamp-noninverting-gain) — Basic Electronics Engineering, chapter 4, asked 2×