Source: https://guthlabs.ai/docs/instruments/decoupling-capacitor-selector/

instrument / verified-with-binding-errata

# Decoupling Capacitor Selector

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

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

## Inspectable records

[01**Overview**Purpose and lifecycle](<https://guthlabs.ai/docs/instruments/decoupling-capacitor-selector/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/decoupling-capacitor-selector/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/decoupling-capacitor-selector/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/decoupling-capacitor-selector/qualification/>)

## 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**: t5-081

**Ledger rows**: 1

No ledger note is attached.

## Review findings

The declared honest label correctly identifies a simplified series RLC decoupling-capacitor model, but the product needs an explicit series impedance equation, explicit output definitions, SI-unit validation or documented unit conversions, and a defined method for calculating effective useful range before it can receive PASS.

### Formula and scope findings

- The self-resonant-frequency formula fSRF=1/(2π√(L_ESL·C)) is correct for an ideal series LC model with positive L_ESL and C in SI units; ESR does not change the series-resonance frequency in this simplified model.

- The impedance formula is underspecified. For the declared simplified series RLC model, it should explicitly be Z_complex(f)=ESR+j(2πfL_ESL−1/(2πfC)) and |Z(f)|=√(ESR²+(2πfL_ESL−1/(2πfC))²).

- The phrase "effective useful range" has no defined formula or acceptance criterion. It must specify a maximum impedance, target impedance, frequency band, or other engineering criterion.

- The specification does not state whether the impedance output is complex impedance, magnitude, phase, or all three; the plot title only says |Z| versus frequency in ios27_notes.

### Unit assumptions

- C is entered in farads, L_ESL in henries, ESR in ohms, frequency in hertz, and all angular-frequency calculations use ω=2πf.

- The calculations assume a series RLC capacitor model: ESR, ESL, and capacitive reactance are in series.

- All capacitance and inductance values must be positive for a finite, physically meaningful SRF.

- The package ESL table values are estimates and should not be treated as universal; mounting geometry, vias, planes, and current-loop area can materially change ESL.

## Boundary hardening

**BREAK_CLAIMED** · SELF_FLAGGED

Zero capacitance and zero frequency produce undefined arithmetic, and the specification does not state explicit input rejection or phasor-sign conventions. The selector should guard C=0, f=0, negative or nonphysical values, and document the complex-impedance convention.

## Errata and corrections

### Tranche errata

**SRF_Hz** · vector 4

3558812700

112539539.5

reciprocal exponent slip; contradicts her own correct √(LC)=1.414e-9 in step 3

## Inspectable example

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

````
{
  "inputs": {
    "C_F": 1e-7,
    "ESL_H": 1e-9,
    "ESR_ohm": 0.02,
    "frequency_Hz": 10000000
  },
  "expected_outputs": {
    "SRF_Hz": 15915494.31,
    "impedance_magnitude_ohm": 0.09838
  },
  "working": "1. LC=(1e-9)(1e-7)=1e-16 H·F. 2. √(LC)=1e-8. 3. SRF=1/[2π(1e-8)]=1/(6.2831853e-8)=15,915,494.31 Hz. 4. ω=2π(10,000,000)=62,831,853.07 rad/s. 5. XL=ωL=(62,831,853.07)(1e-9)=0.06283185 Ω. 6. XC=1/(ωC)=1/[(62,831,853.07)(1e-7)]=0.15915494 Ω. 7. Net reactance=XL−XC=0.06283185−0.15915494=−0.09632309 Ω. 8. |Z|=√[0.02²+(−0.09632309)²]=√(0.0004+0.00927814)=√0.00967814=0.09838 Ω."
}
````

## 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`