Source: https://guthlabs.ai/docs/instruments/rlc-resonance-response-solver/mechanism/

instrument mechanism / verified-clean

# RLC Resonance & Response Solver mechanism

The inspectable method record for RLC Resonance & Response Solver, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The specification is not verifiable as a complete series/parallel solver. The four vectors are valid series-RLC checks; parallel-RLC outputs cannot be verified from the supplied formulas without specifying the parallel circuit model and adding its Q, bandwidth, and damping equations.

- Q=ω0L/R is the standard quality factor for a series RLC circuit only; no parallel-RLC Q formula is supplied despite the instrument claiming parallel support.

- For a parallel RLC circuit, Q and bandwidth depend on the exact topology and on whether the resistor represents a parallel loss, a source/load resistance, or another equivalent model.

- BW=f0/Q is valid for the standard series-RLC 3 dB bandwidth when Q is defined consistently, but it is not universally valid for unspecified parallel models.

- No formula or criterion is supplied for damping classification. For a series RLC, the usual criterion compares α=R/(2L) with ω0: underdamped if α<ω0, critical if α=ω0, and overdamped if α>ω0.

- The resonance formula assumes an ideal lumped RLC model and the natural resonance frequency; loaded, lossy, or non-ideal circuits can have a different measured peak frequency.

## Units and conventions

- R is in ohms (Ω), L is in henries (H), and C is in farads (F).

- f0 and BW are returned in hertz (Hz), while ω0 is in radians per second (rad/s).

- All test calculations use topology=series because the supplied Q formula is series-only.

- The damping labels in these vectors use the conventional series-RLC criterion α=R/(2L) versus ω0=1/√(LC).

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "R_ohm": 10,
    "L_H": 0.1,
    "C_F": 0.0001,
    "topology": "series"
  },
  "expected_outputs": {
    "f0_Hz": 50.329212,
    "Q": 3.162278,
    "BW_Hz": 15.915494,
    "damping": "under"
  },
  "working": "LC=0.1×0.0001=0.00001; √LC=√0.00001=0.003162278. f0=1/(2π×0.003162278)=1/0.019869177=50.329212 Hz. ω0=2πf0=316.227766 rad/s. Q=ω0L/R=(316.227766×0.1)/10=31.622777/10=3.162278. BW=f0/Q=50.329212/3.162278=15.915494 Hz. α=R/(2L)=10/(2×0.1)=50 s^-1; since 50<316.227766, damping is under."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

Inputs at C = 0 or R = 0 produce undefined arithmetic and should be rejected. The specification also claims series/parallel support but supplies only the series Q formula, leaving parallel-Q behavior undefined.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/rlc-resonance-response-solver/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/rlc-resonance-response-solver/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/rlc-resonance-response-solver/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-tranche2/tranche2-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`