Op-Amp Gain Calculator (Inverting/Non-inverting/Diff) mechanism

Model scope

The stated gain equations are standard ideal formulas, but the specification is not complete enough for an unambiguous implementation. The exact ambiguity is the differential resistor labeling and missing R3/R4 inputs, plus undefined formulas for the promised impedance notes. Verdict requires review before release.

• The inverting formula Av=-Rf/Rin and non-inverting formula Av=1+Rf/Rin are standard ideal closed-loop formulas, assuming Rin is nonzero and the op-amp remains in its linear operating region.
• The differential formula Vout=(R2/R1)(V2−V1) is standard only for a four-resistor difference amplifier with matched ratios, specifically R2/R1=R4/R3 under the usual resistor labeling. The second resistor pair and its labeling are not defined in the specification.
• The promised input/output impedance notes have no specified formulas or topology-dependent definitions. In particular, input impedance differs between inverting, non-inverting, and differential configurations.
• The specification does not define how gain and output should be reported when resistor values are zero, negative, non-finite, or supplied in inconsistent units.

Units and conventions

• All resistor ratios are dimensionless; resistor values must use the same resistance unit after conversion, such as all ohms or all kilohms.
• Vin, V1, V2, and Vout are in volts.
• For the differential formula, R1 and R2 refer to the inverting-side input and feedback resistors, while R3 and R4 refer to the non-inverting-side resistor pair, with R2/R1=R4/R3.
• The ideal-op-amp impedance interpretation is infinite input impedance at the op-amp terminals and zero output impedance; the effective source impedance seen by each external input also depends on the resistor network.
• The calculations assume negative feedback, ideal resistors, and operation within the op-amp supply rails and common-mode range.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "topology": "inverting",
    "Rf": 100000,
    "Rf_unit": "ohm",
    "Rin": 10000,
    "Rin_unit": "ohm",
    "Vin": 0,
    "Vin_unit": "V"
  },
  "expected_outputs": {
    "gain": -10,
    "Vout": 0,
    "impedance_notes": "Ideal model: source input impedance is approximately Rin = 10000 ohm; output impedance is 0 ohm."
  },
  "working": "Av = -Rf/Rin = -100000/10000 = -10. Vout = Av*Vin = (-10)*0 V = 0 V."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

A zero-valued Rin produces division by zero and an undefined gain/output; the instrument must reject that input rather than emit a numeric result.

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-tranche4/tranche4-results.json
• BOUNDARY_HAZARD_CATALOG.json