Source: https://guthlabs.ai/docs/instruments/filter-designer-rc-low-pass-high-pass/mechanism/

instrument mechanism / verified-clean

# Filter Designer — RC Low-Pass/High-Pass mechanism

The inspectable method record for Filter Designer — RC Low-Pass/High-Pass, kept separate from implementation and qualification.

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

## Model scope

The core cutoff formula is correct under the ideal first-order RC assumption, but the specification needs explicit inverse formulas, input units, positivity constraints, topology/transfer-function definitions, and an honest label stating that results are nominal ideal values rather than guaranteed measured cutoffs.

- fc=1/(2πRC) is the standard ideal first-order RC cutoff formula for both low-pass and high-pass filters, but the specification does not explicitly provide the inverse formulas R=1/(2πfcC) and C=1/(2πfcR) required for the claimed component-value calculation.

- The stated −3 dB output is valid only for an ideal single-pole RC network when measured relative to the passband gain; source impedance, load impedance, parasitic capacitance, and non-ideal component behavior are not addressed.

- The topology is ambiguous: low-pass and high-pass filters share the same cutoff-frequency formula, but their transfer functions and passband references differ.

## Units and conventions

- R must be entered in ohms, C in farads, and fc in hertz before applying the formula.

- The factor 2π converts angular frequency to ordinary frequency in hertz.

- All component values are positive real quantities.

- The circuit is assumed to be an ideal first-order RC network with negligible source and load impedance.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "topology": "low-pass",
    "R_ohm": 10000,
    "C_F": 1e-8
  },
  "expected_outputs": {
    "fc_Hz": 1591.54943,
    "minus_3dB_frequency_Hz": 1591.54943
  },
  "working": "C=10 nF=10×10^-9 F=1×10^-8 F. RC=10000×1×10^-8=1×10^-4 s. 2πRC=2π×1×10^-4=0.00062831853. fc=1/0.00062831853=1591.54943 Hz. For an ideal first-order low-pass, the −3 dB frequency equals fc."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The zero-resistance input produces an undefined cutoff and must be rejected; additionally, unspecified component units can produce a 1,000,000-fold cutoff-frequency discrepancy.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/filter-designer-rc-low-pass-high-pass/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/filter-designer-rc-low-pass-high-pass/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/filter-designer-rc-low-pass-high-pass/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`