Johnson Noise Calculator

Formula used

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Effective temperature option

When noise figure is included, the calculator converts it to equivalent input noise temperature using T_e = T₀(F − 1) with F = 10^(NF/10), then uses T_eff = T + T_e.

How to use this calculator

1. Enter the resistor value and select its unit.
2. Enter temperature in kelvin or Celsius.
3. Set bandwidth as your filter’s equivalent noise bandwidth.
4. Choose load mode for available or delivered power.
5. Optionally add noise figure to model front-end noise.
6. Press compute to view results above the form.
7. Use the download buttons to export CSV or PDF.

Example data table

Technical article

1) What Johnson noise represents

Johnson (thermal) noise is the random voltage and current created by thermal motion of charge carriers in any resistor. It exists even with zero bias and is approximately white over wide frequency ranges. This calculator uses k = 1.380649×10⁻²³ J/K to connect temperature, resistance, and bandwidth to measurable noise.

2) Key inputs and typical ranges

The key inputs are resistance R, absolute temperature T, and equivalent noise bandwidth B. Typical ranges are 50 Ω to 1 MΩ, 250–350 K (−23 to 77 °C), and 20 kHz up to about 100 MHz. Example: 10 kΩ at 300 K is ~12.9 nV/√Hz.

3) Voltage noise density in practice

Open-circuit voltage noise density follows e_n = √(4kT_effR). A useful reference is 50 Ω at 290 K: ~0.9 nV/√Hz, versus 10 kΩ: ~12.6 nV/√Hz. If a front end contributes 2 nV/√Hz, it dominates low-impedance sources but not high-value resistors.

4) Bandwidth and equivalent noise bandwidth

Integrated RMS voltage is v_n,rms = e_n√B = √(4kT_effRB). Use equivalent noise bandwidth (ENBW), not just the −3 dB cutoff. For a one‑pole low‑pass, ENBW ≈ 1.57×f_c. Noise rises with √B.

5) Current noise and low-impedance systems

The Norton equivalent gives i_n = √(4kT_eff/R). As R drops, current noise increases, which matters for current sensing and transimpedance stages. For 1 Ω at 300 K, i_n is ~4.1 pA/√Hz while the voltage density is ~0.13 nV/√Hz.

6) Noise power and dBm intuition

With a matched load, available noise power is P = kT_effB. At 290 K, the density is approximately −174 dBm/Hz. Over 1 MHz, add 60 dB to get about −114 dBm.

7) Adding amplifier noise figure as T_e

The noise figure option converts NF to F = 10^(NF/10), then computes T_e = T₀(F−1). With NF = 2 dB and T₀ = 290 K, T_e ≈ 170 K. The calculator then uses T_eff = T + T_e in every formula.

8) Common design checks and pitfalls

Start with unit checks (kΩ vs Ω, MHz vs Hz). Celsius is converted to kelvin by +273.15, so negative Celsius is fine, but T_eff must remain > 0 K. For delivered power, set the load realistically; mismatch reduces power via the (R+R_load)² divider. Add 1/f and other noise terms separately.

FAQs

1) Does Johnson noise depend on applied voltage or current?

No. It is thermal agitation noise and exists even with zero bias. Bias can introduce other noise sources, but the thermal component depends mainly on resistance, absolute temperature, and measurement bandwidth.

2) What bandwidth should I enter for a real filter?

Enter the equivalent noise bandwidth (ENBW). For simple filters, ENBW can be larger than the −3 dB cutoff. For a one‑pole low‑pass, ENBW is about 1.57 times the cutoff frequency.

3) Why does matched-load noise power equal kTB?

A resistor can be modeled as a Thevenin noise source. When the load equals the source resistance, maximum noise power is transferred. Under that condition the available noise power simplifies to kT_effB.

4) When should I use voltage noise versus current noise?

Use voltage noise for high-impedance nodes and current noise for low-impedance or transimpedance designs. They are two equivalent representations of the same resistor noise and relate through the resistance value.

5) What does the noise figure option change?

It adds an equivalent input noise temperature T_e derived from noise figure. The calculator then uses T_eff = T + T_e, increasing voltage, current, and noise power consistently.

6) Can I use Celsius inputs safely?

Yes. The calculator converts Celsius to kelvin internally using T(K)=T(°C)+273.15. Temperatures below 0 °C are fine; only non-physical values that result in ≤0 K are rejected.

7) Why might measured noise exceed this prediction?

Real measurements include amplifier input noise, 1/f (flicker) noise at low frequency, interference pickup, and bandwidth misestimation. Ensure shielding, correct ENBW, and account for front-end noise or noise figure.