Thermal (Johnson-Nyquist) Noise Calculator

The current ledger marks this instrument verified with errata that must be applied at binding time.

Status: VERIFIED_WITH_ERRATALifecycle: verified-with-binding-errata

Inspectable records

01OverviewPurpose and lifecycle 02MechanismMethod and assumptions 03ImplementationBinding and validation 04QualificationEvidence and errata

Ledger state

The current ledger marks this instrument verified with errata that must be applied at binding time.

Area: Electrical & Electronics Engineering — Circuits, Power Systems, Electronics Lab
Tranche: tranche-5
Evidence ID: t5-207
Ledger rows: 1

No ledger note is attached.

Review findings

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.

Formula and scope findings

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.

Unit assumptions

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.

Boundary hardening

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.

Errata and corrections

Tranche errata

Vn_rms_V / In_rms_A · vector all(1-3)

~~v1 1.287e-8, v2 5.66e-7, v3 4.07e-9 (and In)~~

v1 4.070e-7, v2 4.002e-6, v3 4.071e-7 — Vn=√(4kTRB)

systematic: R omitted under the square root (her values = √(4kTB) exactly); caught only by the floor-audit of my own gate

Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

{
  "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."
}

Related workflows

No source-defined multi-instrument workflow membership is recorded.

Sources and evidence

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

VERIFIED_LEDGER.json · VERIFIED_WITH_ERRATA
evidence-tranche5/tranche5-results.json
BOUNDARY_HAZARD_CATALOG.json