Source: https://guthlabs.ai/docs/instruments/phasor-impedance-calculator/

instrument / verified-clean

# Phasor / Impedance 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/phasor-impedance-calculator/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/phasor-impedance-calculator/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/phasor-impedance-calculator/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/phasor-impedance-calculator/qualification/>)

## 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**: t8-001

**Ledger rows**: 1

No ledger note is attached.

## Review findings

The element formulas are correct, but the claimed instrument scope is underspecified because topology, frequency units, phase convention, and phasor-addition input semantics are not defined. Resolve those ambiguities before release.

### Formula and scope findings

- The individual element formulas are standard under sinusoidal steady-state convention: Z_R=R, Z_L=jωL, and Z_C=1/(jωC)=-j/(ωC).

- The specification does not define how topology is represented or how series and parallel combinations are calculated. For series circuits, impedances add; for parallel circuits, admittances add or Z_total=(Z1Z2)/(Z1+Z2).

- The polar representation Z=|Z|∠θ is incomplete as an algorithm: magnitude should be |Z|=sqrt(Re(Z)^2+Im(Z)^2), and phase should use atan2(Im(Z),Re(Z)), not a one-argument arctangent.

- Phasor addition is claimed but no explicit input convention or algorithm is specified. Standard addition is rectangular-component addition after converting polar inputs to rectangular form.

- The specification does not state whether frequency is ordinary frequency f in hertz, angular frequency ω in radians per second, or whether the user supplies ω directly. The formulas require ω=2πf when frequency is in hertz.

### Unit assumptions

- R is in ohms, L is in henries, C is in farads, and frequency is in hertz unless explicitly documented otherwise.

- Angular frequency is ω=2πf in radians per second when the input frequency is in hertz.

- The engineering phase convention is e^(jωt), so inductors have positive imaginary impedance and capacitors have negative imaginary impedance.

- Reported phase angles in these vectors are in degrees and use the range (-180°,180°].

- Component values are ideal, linear, frequency-independent values; parasitic resistance, ESR, and inductor losses are excluded.

## Boundary hardening

**BREAK_CLAIMED** · SELF_FLAGGED

The ideal parallel-LC resonance vector makes the parallel admittance exactly zero, so impedance requires division by zero. The calculator must reject the input or explicitly represent an infinite, phase-undefined result.

## 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": {
    "topology": "series",
    "frequency_hz": 60,
    "R_ohm": 10,
    "L_henry": 0.0265258238486492,
    "C_henry": null
  },
  "expected_outputs": {
    "Z_rect_ohm": {
      "real": 10,
      "imaginary": 10
    },
    "Z_polar_ohm": {
      "magnitude": 14.14213562,
      "phase_deg": 45
    },
    "working_note": "C is unused for this RL series case."
  },
  "reference_data": {
    "omega_rad_per_s": "2π(60)=120π",
    "exact_result": "Z=10+j10=10sqrt(2)∠45° Ω"
  },
  "working": "ω=2πf=2π(60)=120π rad/s. X_L=ωL=(120π)(1/(12π))=10 Ω. Z_R=10 Ω. Z_L=j10 Ω. Series addition: Z=Z_R+Z_L=10+j10 Ω. Magnitude=sqrt(10^2+10^2)=sqrt(200)=10sqrt(2)=14.14213562 Ω. Phase=atan2(10,10)=45°."
}
````

## 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`