BJT Amplifier Gain Estimator (Common-Emitter) mechanism

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

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