Bode Plot Generator (generic transfer function) mechanism

Model scope

The core equations are correct under the stated assumptions, but the specification is not sufficiently precise for an unconditional PASS. Exact review items are: frequency input units and conversion, coefficient ordering and polynomial variable, phase units, phase wrapping/unwrapping, and behavior at zeros and poles.

• The stated formulas are standard only when the polynomial variable is s and the frequency substitution is s=jω with ω in rad/s. The spec does not state whether the frequency-range input is in Hz or rad/s, nor whether the implementation performs ω=2πf.
• Polynomial coefficient ordering is unspecified; vectors below assume descending powers of s.
• phase=arg(H) is ambiguous at zeros/poles and does not specify principal phase versus unwrapped phase, radians versus degrees, or phase-continuity behavior across the sweep.
• The implementation should explicitly handle denominator zeros on the sweep, numerator zeros, and H=0; magnitude may be -∞ dB and phase may be undefined.
• The output description says phase plot but does not define phase units or whether phase wrapping is applied.

Units and conventions

• Inputs below use real polynomial coefficients in descending powers of s, with H(s)=N(s)/D(s).
• Frequency inputs below are in Hz and are converted by ω=2πf rad/s before evaluating H(jω).
• Magnitude is 20 log10(|H(jω)|) in dB.
• Phase is the principal complex argument arg(H(jω)) in radians, in the interval (-π,π].
• For a production Bode plot, frequency samples should be strictly positive on a logarithmic axis unless zero-frequency handling is explicitly implemented.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "numerator_coefficients": [
      1
    ],
    "denominator_coefficients": [
      1,
      1
    ],
    "frequency_hz": [
      0.15915494309189535,
      0.3183098861837907
    ]
  },
  "expected_outputs": {
    "canonical_exact": "H(s)=1/(s+1); H(jω)=1/(1+jω); |H(jω)|=1/sqrt(1+ω^2); magnitude_dB=20log10(1/sqrt(1+ω^2)); phase=-atan(ω)",
    "samples": [
      {
        "frequency_hz": 0.15915494309189535,
        "omega_rad_s": 1,
        "magnitude_db": "-10log10(2)",
        "magnitude_db_numeric": -3.010299956639812,
        "phase_rad": "-π/4",
        "phase_rad_numeric": -0.7853981633974483
      },
      {
        "frequency_hz": 0.3183098861837907,
        "omega_rad_s": 2,
        "magnitude_db": "-10log10(5)",
        "magnitude_db_numeric": -6.989700043360188,
        "phase_rad": "-atan(2)",
        "phase_rad_numeric": -1.1071487177940904
      }
    ],
    "spot_checks": [
      {
        "at": {
          "frequency_hz": 0.15915494309189535,
          "omega_rad_s": 1,
          "quantity": "magnitude_db"
        },
        "input_side": -3.010299956639812,
        "answer_side": -3.010299956639812
      },
      {
        "at": {
          "frequency_hz": 0.15915494309189535,
          "omega_rad_s": 1,
          "quantity": "phase_rad"
        },
        "input_side": -0.7853981633974483,
        "answer_side": -0.7853981633974483
      },
      {
        "at": {
          "frequency_hz": 0.3183098861837907,
          "omega_rad_s": 2,
          "quantity": "magnitude_db"
        },
        "input_side": -6.989700043360188,
        "answer_side": -6.989700043360188
      },
      {
        "at": {
          "frequency_hz": 0.3183098861837907,
          "omega_rad_s": 2,
          "quantity": "phase_rad"
        },
        "input_side": -1.1071487177940904,
        "answer_side": -1.1071487177940904
      }
    ]
  },
  "reference_data": {
    "system": "first-order unity-gain low-pass",
    "expected_behavior": "-3.010299956639812 dB and -45 degrees at the pole frequency ω=1 rad/s",
    "phase_degrees_at_omega_1": -45
  },
  "working": "At f=1/(2π) Hz, ω=2πf=1. Then H(j)=1/(1+j). Multiply by the conjugate: H=(1-j)/2, so |H|=1/sqrt(2), magnitude=20log10(1/sqrt(2))=-10log10(2)=-3.010299956639812 dB, and phase=arg(1-j)=-π/4=-0.7853981633974483 rad. At f=2/(2π) Hz, ω=2. Then |H|=1/sqrt(1+2^2)=1/sqrt(5), magnitude=-10log10(5)=-6.989700043360188 dB, and phase=-atan(2)=-1.1071487177940904 rad."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The specification exposes several unsafe edges: zero frequency creates an undefined logarithmic plot coordinate, a j-axis pole causes division by zero, a transfer-function zero creates a phase/magnitude branch singularity, and Hz versus rad/s interpretation produces materially different results. The instrument should validate these cases and make frequency and phase conventions explicit.

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-tranche8/tranche8-results.json
• BOUNDARY_HAZARD_CATALOG.json