Source: https://guthlabs.ai/docs/instruments/filter-designer-active-sallen-key-2nd-order/implementation/

instrument implementation / implementation-contract

# Filter Designer — Active Sallen-Key (2nd order) implementation

A source-bound implementation contract for Filter Designer — Active Sallen-Key (2nd order); deployment and executable qualification remain separate.

Status: **VERIFIED_CLEAN**Lifecycle: **implementation-contract**

## Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

**Record owner**: Guth Instruments

**Lifecycle**: verified-clean

**Evidence ID**: t6-013

**Effect**: Computation or source lookup only

## Input and validation requirements

The advertised input Q is not independently realizable in the stated unity-gain equal-component approximation: that topology fixes Q at 0.5, so any requested Q other than 0.5 cannot be met without changing component ratios or adding gain. The engine also reaches an undefined division at fc=0 and can misdesign by a factor of 2π if Hz versus rad/s is not explicit.

## Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

## Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

````
{
  "inputs": {
    "fc_hz": 1000,
    "Q": 0.5,
    "filter_type": "LP",
    "design_assumption": "C1=C2=10 nF; unity gain K=1; R1=R2"
  },
  "expected_outputs": {
    "R1_ohm": 15915.494309,
    "R2_ohm": 15915.494309,
    "C1_F": 1e-8,
    "C2_F": 1e-8,
    "achieved_fc_hz": 1000,
    "achieved_Q": 0.5
  },
  "working": "Set C1=C2=C=10 nF=10×10^-9 F and R1=R2=R. Then fc=1/(2πRC), so R=1/(2πfcC)=1/(2×3.141592653589793×1000×10×10^-9)=1/(0.0000628318530718)=15915.494309 Ω. For unity gain K=1, Q=1/(3-K)=1/(3-1)=0.5. Therefore R1=R2=15915.494309 Ω and C1=C2=10 nF."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/filter-designer-active-sallen-key-2nd-order/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/filter-designer-active-sallen-key-2nd-order/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/filter-designer-active-sallen-key-2nd-order/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-tranche6/tranche6-results.json`