Formula Used
The calculator uses independent rms noise addition. Each source is squared, summed, and square rooted.
Effective bandwidth: B = (fhigh - flow) x equivalent noise bandwidth factor.
Thermal resistor noise: VR = sqrt(4kTRB).
Voltage noise: Ve = en x sqrt(B + fc ln(fhigh / flow)).
Current noise through resistance: Vi = inRs x sqrt(B + fc ln(fhigh / flow)).
Total input noise: Vn = sqrt(VR2 + Ve2 + Vi2 + Vexternal2).
Output noise: Vout noise = Vn x noise gain.
SNR: SNR = 20 log10(output signal rms / output noise rms).
How To Use This Calculator
Enter source resistance, temperature, frequency range, and bandwidth factor. Add voltage noise density and current noise density from the amplifier data sheet. Add flicker corner frequencies when available. Enter noise gain and signal gain. Press the calculate button. Review total input noise, output noise, equivalent density, and SNR. Use CSV or PDF to save the result.
Example Data Table
| Use Case |
Rsource |
Bandwidth |
Voltage Noise |
Current Noise |
Noise Gain |
Expected Note |
| Sensor preamp |
1 kOhm |
10 Hz to 100 kHz |
5 nV/root Hz |
0.5 pA/root Hz |
10 |
Balanced voltage and resistor noise |
| High impedance buffer |
100 kOhm |
1 Hz to 20 kHz |
8 nV/root Hz |
2 pA/root Hz |
1 |
Current noise can dominate |
| Audio gain stage |
600 Ohm |
20 Hz to 20 kHz |
3 nV/root Hz |
0.2 pA/root Hz |
20 |
Output noise affects headroom |
Understanding Total Integrated Noise
Total integrated noise shows the actual rms noise present across a defined bandwidth. It is more useful than a single noise density value. Analog circuits rarely operate at one frequency. A sensor amplifier, filter, or data converter front end gathers noise from every active part of its passband. This calculator joins those parts into one input referred value. It also estimates output noise after noise gain.
Why Bandwidth Matters
Noise density is usually listed as volts per square root hertz. That value must be integrated across bandwidth before it becomes rms voltage. A wider passband produces more noise. A narrow filter lowers noise, but it can also remove useful signal content. The equivalent noise bandwidth factor helps approximate real filters. A single pole response has more noise than its simple cutoff width suggests.
Main Noise Sources
Resistors create thermal noise from temperature and resistance. Op amp voltage noise appears in series with the input. Op amp current noise flows through source resistance and becomes voltage noise. Flicker noise rises at low frequency and is modeled with a corner frequency. These independent sources are squared, summed, and square rooted. This gives a realistic combined rms result.
Using Results
Use input referred noise when comparing parts, sensors, or source impedances. Use output rms noise when checking converter range, gain staging, and measurable floor. The SNR result compares the output signal level with output noise. A negative or low SNR means the noise is close to the signal. Increase signal level, reduce bandwidth, lower resistance, or select a quieter amplifier.
Design Notes
The calculator is an engineering estimator. It assumes independent random noise sources. It does not replace bench measurement. Real layouts add pickup, grounding errors, supply ripple, and interference. At high impedance, current noise and resistor noise can dominate. At low impedance, voltage noise often matters more. Always test the finished circuit with proper shielding, source conditions, and bandwidth limits.
Practical Example
For example, a quiet sensor path may use ten kilohertz bandwidth and moderate gain. The integrated value can look small at the input, yet large at the output. This is why designers review both numbers before choosing filter corners, converter resolution, and amplifier gain during prototyping.
FAQs
What is total integrated noise?
It is the rms noise found by integrating noise density across a selected frequency band. It shows the usable noise floor for that circuit bandwidth.
Why is bandwidth required?
Noise grows with bandwidth. A larger frequency span collects more random noise, so a density value alone cannot describe the final rms noise.
What is noise gain?
Noise gain is the gain applied to input referred voltage noise at the amplifier output. It may differ from signal gain in some feedback circuits.
What does flicker corner mean?
The flicker corner is where low frequency noise begins rising above the flat white noise region. It matters most near DC and low frequencies.
Can I use this for audio circuits?
Yes. Use 20 Hz to 20 kHz for a common audio band. Adjust gain, resistance, and device noise from the real design.
Why include source resistance?
Source resistance creates thermal noise. It also converts amplifier current noise into voltage noise, which can be important in high impedance designs.
Is equivalent noise bandwidth exact?
It is an estimate unless the exact filter response is known. Use a factor that matches the filter type or a measured bandwidth value.
Does this replace lab measurement?
No. It supports design estimates. Final circuits should be measured because layout, shielding, supplies, and interference can change real noise.