---
title: Operational Amplifier (Op-Amp)
url: https://doc.liz6.com/en/hardware/04-analog-circuits/02-operational-amplifier-op-amp
locale: en
area: hardware
tags:
- hardware
- analog-circuits
date: 2026-06-30
modified: 2026-07-16
description: Operational Amplifier (Op-Amp) Basic Concepts Operational Amplifier — A high-gain differential amplifier, originally used in analog computers for mathematical o…
---

# Operational Amplifier (Op-Amp)

## Basic Concepts

**Operational Amplifier** — A high-gain differential amplifier, originally used in analog computers for mathematical operations (addition, integration, etc.), and now the most versatile analog IC.

```
Symbol:
      V+  ──┤+        ┌── Vout
             │  ────
      V-  ──┤- 

Or:
         ┌──────┐
  V- ────┤-     │
         │   ───┼── Vout
  V+ ────┤+     │
         └──────┘
```

---

## Ideal Op-Amp Characteristics

### Two Golden Rules
```
1. No current enters the input terminals:  Iin+ = Iin- = 0
   (Input impedance = ∞)

2. Virtual Short:
   With negative feedback, V+ = V-
   (Open-loop gain Ao = ∞, forcing the differential voltage → 0)
```

### Ideal vs. Real
| Parameter | Ideal | Real (LM358) | Real (NE5532) |
|------|------|-------------|---------------|
| Open-loop Gain Ao | ∞ | 100dB | 100dB |
| Input Impedance Rin | ∞ | 1MΩ | 300kΩ |
| Output Impedance Rout | 0 | Tens of Ω | 0.5Ω |
| Bandwidth BW | ∞ | 1MHz (GBW) | 10MHz |
| Input Bias Current | 0 | 45nA | 200nA |
| Input Offset Voltage | 0 | 2mV | 0.5mV |

---

## Basic Circuits

### Inverting Amplifier
```
        Rf
    ┌──┤├─────┐
    │         │
Rin │    ┌────┤
Vin─┤├───┤-   │
         │ ───┼── Vout
GND ─────┤+   │
         └────┘

Av = -Rf / Rin
Rin_eff = Rin  (Input impedance = Rin)

Example: Rin=10k, Rf=100k → Av = -10
```

### Non-Inverting Amplifier
```
    ┌──────────┐
    │    ┌─────┤
Vin─┼────┤+    │
    │    │ ───┼── Vout
    │    ├-    │
    │   ┌┴┐   │
    │   │R2   │
    │   └┬┘   │
    │    ├────┘
    │   ┌┴┐
    │   │R1
    │   └┬┘
    │    │
   GND  GND

Av = 1 + R2/R1
Rin = Op-amp input impedance (Very high, in MΩ range)
```

### Voltage Follower (Buffer)
```
Vin ────┤+ 
         │ ───┬── Vout
         ├-    │
         └─────┘

Av = 1 (Vout = Vin)
Use: Impedance matching — driving a low-impedance load from a high-impedance source
```

### Differential Amplifier
```
          R2
    ┌───┤├─────┐
    │          │
R1  │    ┌─────┤
V1─┤├────┤-    │
         │ ───┼── Vout
V2─┤├────┤+    │
    R3   └─────┘
    │
    R4
    │
   GND

If R1=R3, R2=R4:
Vout = (R2/R1) × (V2 - V1)

This is the basis for an Instrumentation Amplifier
```

### Integrator
```
         C
    ┌────┤├────┐
    │          │
    R    ┌─────┤
Vin─┤├───┤-    │
         │ ───┼── Vout
GND ─────┤+    │
         └─────┘

Vout = -(1/RC) × ∫Vin dt

Used for: Waveform generation, ramp generators, PID control
```

---

## Non-Ideal Characteristics

### Input Offset Voltage (Vos)
```
When the op-amp inputs are shorted, the output is not zero.
Equivalent to a small voltage source at the input (~mV).

Impact: Output saturation in high-gain circuits
Solution: Select low Vos op-amps or use a zero-adjustment circuit
```

### Slew Rate
```
Maximum rate of change of the output (V/μs)

SR = dVout/dt(max)

If the signal changes faster than the SR → Waveform distortion (becomes triangular)
Example: LM358 SR=0.5V/μs → Max amplitude for 20kHz sine wave = SR/(2πf) = 4Vpp
         NE5532 SR=9V/μs → Sufficient for audio
```

### Gain-Bandwidth Product (GBW)
```
GBW = Open-loop Gain × Bandwidth (Constant)

Example: LM358 GBW=1MHz
    If Av=100 → BW = GBW/Av = 10kHz
    If Av=1  → BW = 1MHz

Higher gain results in narrower bandwidth!
```

### Input and Output Swing
```
Old op-amps (LM358): Output can only reach Vcc-1.5V
Rail-to-Rail (RRIO): Both input and output can reach the supply rails
  Choose based on application requirements
```

---

## Common Models

| Model | Channels | Features | Application |
|------|------|------|------|
| LM358 | Dual | Cheap, single supply, slow | General purpose, low speed |
| TL072 | Dual | JFET input, low noise | Audio |
| NE5532 | Dual | Extremely low noise, strong drive | Professional audio |
| LM324 | Quad | 4x LM358 | Multi-channel, low speed |
| OPA2134 | Dual | High-fidelity audio | HiFi |
| MCP6002 | Dual | RRIO, low power | Battery powered |

---

## Usage Notes

1. **Power Decoupling**: Place 0.1μF ceramic capacitors close to the power pins.
2. **Input Common-Mode Range**: Do not exceed the allowed range.
3. **Avoid Floating Inputs**: Connect unused op-amps as followers.
4. **Feedback Loop**: Ensure stability; add compensation capacitors if necessary.
5. **Single-Supply Bias**: When using a single supply, create a virtual ground (typically Vcc/2).

---
*Keywords: Op-amp, Inverting Amplifier, Non-Inverting Amplifier, Virtual Short, GBW, Slew Rate, Offset Voltage*