Noise in op-amp circuits and its reduction

Noise is any unwanted random signal that appears at the output of an op-amp circuit and is not part of the input signal. It sets the smallest signal the amplifier can handle and limits the signal-to-noise ratio. It can be external (pickup from power lines, motors, radio sources, ground loops) or internal (generated inside resistors and transistors).

Types of noise in op-amp circuits:

• Thermal (Johnson) noise: random motion of electrons in every resistor. RMS voltage vn = √(4kTRB), where k = 1.38 × 10⁻²³ J/K, T in kelvin, R in ohms and B the bandwidth. A 1 kΩ resistor at 300 K gives about 4 nV/√Hz. It is white (flat with frequency).
• Shot noise: due to random crossing of charge carriers across a junction; noise current in = √(2qIB·B), q = 1.6 × 10⁻¹⁹ C. It is present in the bias currents of the input transistors.
• Flicker (1/f) noise: power increases as frequency falls; dominant below the corner frequency (about 10 Hz to 1 kHz), caused by surface defects.
• Popcorn (burst) noise: sudden step changes in bias current due to contamination; heard as popping in audio.

Noise model: an op-amp's internal noise is represented by a noise voltage source en (nV/√Hz) in series with the input and noise current sources in (pA/√Hz) at each input, driving a noiseless op-amp.

              Rf (noise 4kTRf)
        +-----/\/\/-----+
        |  in           |
 R1 ----+-----(-)       |
 (4kTR1)          >-----+---- eno
 Rs --[en]--+--(+)
 (4kTRs)    in

All the input-referred noise sources are amplified by the noise gain (1 + Rf/R1), not by the signal gain. The independent sources add as root-sum-of-squares:

eni² = en² + (in·Rs)² + (in·R1‖Rf)²
       + 4kT(Rs + R1‖Rf)          per Hz
Eno  = (1 + Rf/R1) · eni · √B     (rms)

Measures to minimize noise:

1. Use low-value resistors (thermal noise and in·R terms grow with R); use metal-film resistors, not carbon.
2. Limit the bandwidth to what the signal needs (noise ∝ √B): add a small capacitor across Rf or a filter.
3. Choose a low-noise op-amp: low en (bipolar input, e.g. OP27) for low source resistance; low in (FET input) for high source resistance.
4. Keep the noise gain low; take gain in the first stage so later-stage noise is less significant.
5. Balance the resistances at the two inputs but bypass Rcomp with a capacitor so its noise is not amplified.
6. Decouple power supply pins with 0.1 µF capacitors near the IC; use proper grounding (star ground) and shielded cables against pickup.
7. Keep the circuit cool and away from noisy (switching) sources; use ac coupling or chopper op-amps to avoid 1/f noise at low frequencies.