Source: https://guthlabs.ai/docs/instruments/bode-plot-generator-generic-transfer-function/
instrument / verified-clean
# Bode Plot Generator (generic transfer function)
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]()[02**Mechanism**Method and assumptions]()[03**Implementation**Binding and validation]()[04**Qualification**Evidence and errata]()
## Ledger state
The current ledger marks this instrument verified clean within the source-bound verification corpus.
**Area**: Electrical & Electronics Engineering — Circuits, Power Systems, Electronics Lab
**Tranche**: tranche-8
**Evidence ID**: t8-010
**Ledger rows**: 1
No ledger note is attached.
## Review findings
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.
### Formula and scope findings
- 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.
### Unit assumptions
- 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.
## Boundary hardening
**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.
## 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": {
"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."
}
````
## Related workflows
No source-defined multi-instrument workflow membership is recorded.
## 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-tranche8/tranche8-results.json`
- `BOUNDARY_HAZARD_CATALOG.json`