Source: https://guthlabs.ai/docs/instruments/thermal-johnson-nyquist-noise-calculator/mechanism/

instrument mechanism / verified-with-binding-errata

# Thermal (Johnson-Nyquist) Noise Calculator mechanism

The inspectable method record for Thermal (Johnson-Nyquist) Noise Calculator, kept separate from implementation and qualification.

Status: **VERIFIED_WITH_ERRATA**Lifecycle: **verified-with-binding-errata**

## Model scope

The voltage expression is correct under the stated SI and bandwidth assumptions, but the spec is incomplete because it promises an rms current output without specifying its formula and leaves temperature and bandwidth conventions ambiguous. The honest label should state that outputs are resistor-equivalent thermal noise over a one-sided equivalent noise bandwidth, not total system noise.

- The voltage formula Vn=sqrt(4kTRΔf) is standard for a resistor when T is in kelvin, R in ohms, and Δf is a one-sided equivalent noise bandwidth in hertz.

- The specification declares an In (rms) output but provides no current formula. The standard corresponding formula is In=sqrt(4kTΔf/R), equivalently In=Vn/R for an ideal resistor.

- The specification does not define whether bandwidth means rectangular bandwidth or equivalent noise bandwidth, nor whether a one-sided or two-sided noise-bandwidth convention is intended.

## Units and conventions

- Use the exact SI Boltzmann constant k=1.380649e-23 J/K.

- Resistance R is positive and measured in ohms.

- Temperature T is absolute temperature in kelvin; Celsius inputs must be converted using T_K=T_C+273.15.

- Bandwidth Δf is nonnegative and measured in hertz.

- The 4kTRΔf expression uses a one-sided equivalent noise bandwidth and produces mean-square voltage in V^2.

- The current output is interpreted as the Norton-equivalent rms noise current in amperes.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "R_ohm": 1000,
    "temperature_K": 300,
    "bandwidth_Hz": 10000
  },
  "expected_outputs": {
    "Vn_rms_V": 1.2871592e-8,
    "In_rms_A": 1.2871592e-11
  },
  "working": "4kTRΔf = 4×(1.380649e-23)×1000×300×10000 = 1.6567788e-16 V^2. Vn = sqrt(1.6567788e-16) = 1.2871592e-8 V rms. In = Vn/R = (1.2871592e-8)/1000 = 1.2871592e-11 A rms."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The specification does not state the current-noise formula or input units explicitly. R=0 produces an undefined current result, negative temperature produces a non-real square-root argument, and an unlabelled temperature such as 25 is ambiguous between kelvin and Celsius.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/thermal-johnson-nyquist-noise-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/thermal-johnson-nyquist-noise-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/thermal-johnson-nyquist-noise-calculator/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche5/tranche5-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`