Small Signal Gain Calculator
Calculate BJT transconductance, intrinsic emitter resistance, effective collector loading, voltage gain, and gain in dB around a selected DC operating point.
Compare bypassed and unbypassed emitter configurations when estimating common-emitter amplifier gain and load sensitivity.
Engineering tool
Small Signal Gain Calculator
Estimate BJT transconductance, intrinsic emitter resistance, loaded voltage gain, and gain in dB.
Quiescent current used to calculate gm and re.
Collector resistance before external load interaction.
External AC load connected to the amplifier output.
Unbypassed emitter resistance in the AC signal path.
Approximately 26 mV near room temperature.
Result console
- Transconductance (gm)
- 38.461538mS
- Small-signal emitter resistance (re)
- 26Ω
- Effective collector load (RC || RL)
- 4.489016kΩ
- Voltage gain (Av)
- -4.375259V/V
- Gain magnitude
- 12.820076dB
Inverting voltage gain
Negative gain indicates that the common-emitter output is inverted by approximately 180° relative to the input.
Formula reference
Small Signal Gain Formulas
These first-order equations assume a properly biased transistor in its forward-active region and omit transistor output resistance and frequency-dependent parasitics.
Transconductance: gm = IC / VTEmitter resistance: re = VT / IC = 1 / gmEffective load: RC,parallel = RC || RLBypassed gain: Av ≈ -gm × RC,parallelUnbypassed gain: Av ≈ -RC,parallel / (re + RE)Gain magnitude: dB = 20 log10(|Av|)Variable definitions
- IC
- quiescent collector current in amperes
- VT
- thermal voltage, approximately 26 mV near room temperature
- RC || RL
- effective AC collector load
- A negative Av indicates an inverted output
Worked Example
IC = 1 mA, RC = 4.7 kΩ, RL = 100 kΩ, RE = 1 kΩ, VT = 26 mV, emitter not bypassed.
gm = 0.001 / 0.026 ≈ 38.46 mS
re = 0.026 / 0.001 = 26 Ω
RC || RL ≈ 4.489 kΩ
Av ≈ -4489 / (26 + 1000) ≈ -4.38 V/V
Gain magnitude ≈ 20 log10(4.38) = 12.82 dB
Engineering Notes
Current controls gm
Transconductance gm depends directly on collector current at a given thermal voltage.
Current reduces re
Small-signal emitter resistance re decreases as collector current increases.
Emitter degeneration
Emitter degeneration reduces gain but improves linearity, stability, and gain predictability.
Output loading
Load resistance appears in parallel with RC and reduces the effective gain.
Signal inversion
Common-emitter stages invert the signal, so voltage gain is shown with a negative sign.
Support reference
FAQ
What is small-signal gain?
Small-signal gain is the incremental ratio of output voltage change to a small input voltage change around a fixed DC bias point. It is valid while the transistor remains approximately linear around that operating point.
How do you calculate gm?
For a BJT, transconductance is approximated by gm = IC / VT. At 1 mA collector current and 26 mV thermal voltage, gm is approximately 38.46 mS.
What is re in a BJT amplifier?
The intrinsic small-signal emitter resistance is re = VT / IC, which is also approximately 1 / gm. It represents the transistor emitter-junction response near the selected bias current.
Why does emitter degeneration reduce gain?
An unbypassed emitter resistor adds local negative feedback. This increases the effective emitter-path resistance, reducing gain while improving linearity, bias stability, and predictability.
Why is common-emitter gain negative?
A higher input voltage increases collector current and the drop across the collector load, lowering collector output voltage. The output is therefore inverted by approximately 180 degrees.
Documentation
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