Op-Amp Noise Analysis: Voltage Noise, Current Noise, Johnson Noise, and Bandwidth

Noise Is Spectral and Statistical

Noise density describes RMS amplitude in a one-hertz bandwidth around a frequency. Total RMS noise requires integrating power spectral density through the complete transfer function. Peak-to-peak noise is not a fixed multiple of RMS unless a probability and observation interval are stated.

Input-Referred Noise Sources

Resistor Thermal Noise

Noise Gain and Source Impedance

Use the Non-Inverting and Inverting Gain Calculators for nominal closed-loop ratios, but calculate the actual frequency-dependent noise gain separately.

White Noise, 1/f Noise, and ENBW

Op-amp voltage and current noise usually rise below their 1/f corner. At higher frequencies the white region may be approximately flat until device and circuit response shape it. Integrate manufacturer curves when low-frequency precision matters.

The Active Low-Pass Filter Calculator establishes an ideal corner; the Active Filter and Dynamic Limits Guide covers implementation limits.

Worked Noise Budget

For a 10 nV/√Hz op amp with 1 pA/√Hz current noise and a 10 kΩ source at 300 K, current noise contributes 10 nV/√Hz and resistor thermal noise contributes about 12.9 nV/√Hz. The input-referred white total is √(10² + 10² + 12.9²) = 19.1 nV/√Hz. Through noise gain 11 and a first-order 1 kHz low-pass, ENBW is 1.571 kHz and output RMS noise is approximately 19.1 nV/√Hz × 11 × √1571 = 8.33 µV. This excludes 1/f noise, feedback-resistor noise, source spectrum, reference noise, EMI, and aliasing.

Topology and Device Selection

• Choose voltage-noise and current-noise performance together with source impedance.
• Check 1/f corner for DC, bridge, thermocouple, and other low-frequency measurements.
• Keep resistor values low enough for noise and bias-current goals, but high enough for loading and power constraints.
• For differential and instrumentation stages, include both source legs, resistor networks, reference input, and CMRR.
• Verify input capacitance, stability, settling, common-mode range, output swing, and supply current alongside noise.

Measurement Workflow

1. Define input termination, gain, frequency span, filter shape, and output measurement boundary.
2. Short or terminate the input with the same impedance as the application.
3. Measure the instrument and fixture floor independently.
4. Shield electric and magnetic interference and control ground loops.
5. Record spectral density and integrate over the intended bandwidth.
6. Repeat with realistic source impedance and common-mode voltage.
7. Check multiple devices, temperature, supply, and warm-up.
8. Compare measured spectral shape, not only one RMS number, with the budget.

Common Mistakes

• Comparing only the 1 kHz voltage-noise headline.
• Ignoring current noise with a high-impedance source.
• Using signal gain instead of noise gain.
• Multiplying density by √fc instead of √ENBW.
• Ignoring 1/f noise in low-frequency measurements.
• Adding independent noise amplitudes arithmetically.
• Forgetting feedback-network and reference noise.
• Treating RMS noise as guaranteed peak-to-peak noise.
• Ignoring aliasing above the sampled Nyquist band.
• Measuring below the analyzer or fixture noise floor.

Scope Boundary

This guide covers small-signal random-noise budgeting. It does not model deterministic interference, EMI susceptibility, distortion, popcorn noise, every device correlation, ADC architecture noise, phase noise, or the full statistics of rare peaks. Use device spectra, circuit simulation, and measured data for critical designs.