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

instrument mechanism / verified-with-binding-errata

# Decoupling Capacitor Selector mechanism

The inspectable method record for Decoupling Capacitor Selector, kept separate from implementation and qualification.

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

## Model scope

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.

- 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.

## Units and conventions

- 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.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "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."
}
````

## Failure boundary

**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.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/decoupling-capacitor-selector/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/decoupling-capacitor-selector/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/decoupling-capacitor-selector/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`