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

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

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