Source: https://guthlabs.ai/docs/instruments/op-amp-summing-integrator-differentiator-designer/mechanism/

instrument mechanism / verified-clean

# Op-Amp Summing/Integrator/Differentiator Designer mechanism

The inspectable method record for Op-Amp Summing/Integrator/Differentiator Designer, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The three displayed equations are recognizable standard ideal-op-amp formulas under stated topology and unit assumptions. The specification is not complete enough to verify a deterministic component-value designer because target-gain handling, time-constant selection, waveform/integration interval, initial conditions, supply limits, and practical bandwidth constraints are unspecified. The honest-label statement correctly identifies the ideal model but should explicitly mention the missing initial condition and the ideal differentiator's unbounded high-frequency behavior.

- The summing formula is standard for an ideal inverting summing amplifier with the non-inverting input at ground, but that topology constraint is not stated in the inputs.

- The integrator formula is incomplete as written because the output also depends on the capacitor initial condition: Vout(t)=Vout(t0)−(1/RC)∫ from t0 to t Vin(t)dt.

- The differentiator formula is the standard ideal inverting differentiator formula, but its valid frequency range and practical stabilization requirements are unspecified.

- The instrument claims to compute component values from target gains or time constants, but no explicit design formulas or constraints are provided for selecting Ri, Rf, R, and C.

- Input definitions are too vague to determine integration interval, initial output, waveform derivative, resistor values, capacitor values, or whether values are SI units.

## Units and conventions

- Voltages are in volts, resistances are in ohms, capacitances are in farads, time is in seconds, and derivatives are in volts per second.

- For the summing formula, all input voltages are measured relative to the op-amp ground reference and the non-inverting input is grounded.

- For the integrator, the stated integral is definite over the supplied time interval and the initial output voltage is supplied separately.

- For the differentiator, dVin/dt is an instantaneous slope in volts per second and R and C are frequency-independent ideal components.

- Component values must be positive and finite unless an explicitly defined limiting case is supported.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "mode": "summing",
    "Rf_ohm": 100000,
    "V1_V": 0.25,
    "R1_ohm": 25000,
    "V2_V": -0.1,
    "R2_ohm": 50000
  },
  "expected_outputs": {
    "Vout_V": -0.8
  },
  "working": "V1/R1 = 0.25/25000 = 0.00001 A = 10 microA. V2/R2 = -0.1/50000 = -0.000002 A = -2 microA. Sum = 10 microA - 2 microA = 8 microA. Vout = -Rf times sum = -100000 ohm times 0.000008 A = -0.8 V."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

A zero input resistance produces an undefined division and should be rejected. The specification also leaves signed-voltage versus magnitude conventions unstated, allowing a polarity error in the computed output.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/op-amp-summing-integrator-differentiator-designer/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/op-amp-summing-integrator-differentiator-designer/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/op-amp-summing-integrator-differentiator-designer/qualification/>)

## 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`