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

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

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