Source: https://guthlabs.ai/docs/instruments/passive-crossover-frequency-calculator/

instrument / verified-clean

# Passive Crossover Frequency Calculator

The current ledger marks this instrument verified clean within the source-bound verification corpus.

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

## Inspectable records

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

## Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

**Area**: Audio, Music, Photography & Color

**Tranche**: tranche-2

**Evidence ID**: t2-037

**Ledger rows**: 1

No ledger note is attached.

## Review findings

The first-order RC and RL arithmetic is standard under the stated ideal resistive-load assumptions. The specification needs an explicit second-order Butterworth topology and complete normalized component equations. It should also consistently call the inductive first-order case RL unless a genuine LC network is intended.

### Formula and scope findings

- The stated first-order inductive formula fc=R/(2πL) is the standard RL-filter formula, not an LC-filter formula. A true ideal LC resonance uses fc=1/(2π√(LC)) and cannot be determined from driver impedance alone.

- The second-order Butterworth L/C-pair formula is missing. Exact component values require the topology, low-pass or high-pass configuration, source and load termination assumptions, and normalized Butterworth prototype coefficients.

- The first-order RC and RL formulas are valid only for an ideal single-pole filter with a frequency-independent, purely resistive load. They do not by themselves guarantee the acoustic crossover frequency or slope of a real driver system.

### Unit assumptions

- Driver impedance is a positive resistance in ohms (Ω), not a complex or frequency-dependent impedance.

- Target frequency is interpreted in hertz (Hz) internally.

- Capacitance is calculated in farads (F) and reported in microfarads (µF), where 1 µF=10^-6 F.

- Inductance is calculated in henries (H) and reported in millihenries (mH), where 1 mH=10^-3 H.

- The RC formula assumes an ideal resistor-load and capacitor single-pole network; the RL formula assumes an ideal resistor-load and inductor single-pole network.

- For second-order Butterworth calculations, the source/load impedance and exact filter topology must be explicitly defined before units and component formulas can be verified.

## Boundary hardening

**BREAK_CLAIMED** · SELF_FLAGGED

Zero target frequency produces a division-by-zero undefined result, and zero or negative driver impedance exposes invalid or ambiguous inputs. The instrument should validate impedance and target frequency before calculation and explicitly define whether impedance magnitude or signed impedance is used.

## Errata and corrections

No applied erratum is attached to this unique-name record.

## Inspectable example

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

````
{
  "inputs": {
    "filter_order": 1,
    "filter_type": "RC low-pass",
    "driver_impedance_ohm": 8,
    "target_fc_hz": 2000
  },
  "expected_outputs": {
    "capacitance_uF": 9.947184
  },
  "working": "C=1/(2πRC)=1/(2×π×8×2000)=1/(100530.9649)=0.000009947184 F. Convert to µF: 0.000009947184×1,000,000=9.947184 µF."
}
````

## Related workflows

[Audio Engineer's Rackspeakers](<https://guthlabs.ai/docs/instrument-workflows/audio-rack/>)

## Sources and evidence

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

- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`

- `evidence-tranche2/tranche2-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`