Source: https://guthlabs.ai/docs/instruments/bjt-amplifier-gain-estimator-common-emitter/mechanism/

instrument mechanism / verified-with-binding-errata

# BJT Amplifier Gain Estimator (Common-Emitter) mechanism

The inspectable method record for BJT Amplifier Gain Estimator (Common-Emitter), kept separate from implementation and qualification.

Status: **VERIFIED_WITH_ERRATA**Lifecycle: **verified-with-binding-errata**

## Model scope

The honest label 'simplified hybrid-π small-signal model' is directionally accurate but incomplete. The UI should explicitly label the results as unloaded, emitter-AC-grounded estimates and state the IE derivation, thermal-voltage assumption, and omitted ro/RL/emitter-degeneration effects.

- re=26 mV/IE is standard only at approximately room temperature; the 26 mV thermal-voltage assumption should be stated explicitly.

- IE is not provided as an input. The specification provides IC and β, but does not state whether to approximate IE≈IC or derive IE=IC(1+1/β). The test vectors use the latter relationship.

- Av≈−RC/re is valid for an unloaded common-emitter stage with the emitter AC-grounded; it omits emitter degeneration, collector load RL, and transistor output resistance ro.

- Zout≈RC assumes ro is much larger than RC and omits any external load. A more complete approximation is RC||ro, with the load included when relevant.

- Zin≈R1||R2||βre assumes R1 and R2 are AC-grounded bias resistors and uses the simplified base-input resistance βre; it omits transistor bias-dependent parameter variation and other input loading.

## Units and conventions

- IC and IE are currents in amperes when used with 0.026 V; resistor values are in ohms; β is dimensionless.

- 26 mV is treated as the room-temperature thermal voltage VT.

- For the test vectors, IE is derived as IE=IC(1+1/β), rather than approximated as IC.

- Av is dimensionless; Zin and Zout are in ohms; the minus sign denotes common-emitter phase inversion.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "IC": "1.000 mA",
    "RC": "4700 Ω",
    "R1": "100000 Ω",
    "R2": "20000 Ω",
    "β": 100
  },
  "expected_outputs": {
    "Av": -182.576923,
    "Zin": "2229.846 Ω",
    "Zout": "4700 Ω"
  },
  "working": "IE=IC(1+1/β)=0.001(1+1/100)=0.00101 A. re=0.026/0.00101=25.742574 Ω. Av=−4700/25.742574=−182.576923. βre=100×25.742574=2574.2574 Ω. Zin=1/(1/100000+1/20000+1/2574.2574)=1/(0.00001+0.00005+0.000388461538)=1/0.000448461538=2229.846 Ω. Zout=RC=4700 Ω."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The valid-looking boundary input IC=0 makes re=26 mV/IE divide by zero, causing Av and Zin to be undefined. The estimator must reject zero collector/emitter current instead of forcing numeric results.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/bjt-amplifier-gain-estimator-common-emitter/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/bjt-amplifier-gain-estimator-common-emitter/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/bjt-amplifier-gain-estimator-common-emitter/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-tranche5/tranche5-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`