BJT/MOSFET Small-Signal Models & Oscillators
Hybrid-π analysis, bias-point stability, the Barkhausen criterion and the RC/LC oscillator line-up interviewers expect you to know cold.
Key formulas
|Aβ| = 1, ∠Aβ = 0° (mod 360°)
Barkhausen criterion: The only condition needed for sustained oscillation — every oscillator question reduces to checking loop gain and phase.
f = 1 / (2πRC), with R1 = R2 = R, C1 = C2 = C
Wien bridge frequency: Wien bridge gives 0° phase at f; the non-inverting amp needs gain ≥ 3 to sustain oscillation.
Cheat sheet
- ▸Hybrid-π parameters: gm = IC/VT (BJT), ro = VA/IC; a MOSFET has gm = 2ID/(VGS−Vth) and near-infinite gate input resistance.
- ▸BJT is a transconductance device too: Av = −gm·Rc for a common-emitter stage (with ro ignored).
- ▸BJT bias stability: fixed-bias is worst, voltage-divider with emitter resistor is standard — RE gives negative feedback that pins the Q-point.
- ▸Barkhausen criterion for oscillation: loop gain |Aβ| = 1 and total phase shift = 0° (or 360°) at the oscillation frequency; |Aβ| > 1 to start, settling to 1.
- ▸RC oscillators (Wien bridge ~1 Hz–1 MHz), LC (Colpitts capacitive divider, Hartley tapped inductor) for RF; crystal when frequency stability matters.
- ▸Three BJT amplifier configs: CE (high A_v, medium Z), CC/emitter-follower (buffer, A_v≈1), CB (current buffer, good HF response).
BJT vs MOSFET small-signal behaviour
| Aspect | BJT | MOSFET |
|---|---|---|
| Transconductance | gm = IC/VT (exponential device) | gm = 2ID/Vov (square-law) |
| Input resistance | Moderate (rπ = β/gm) | Nearly infinite (gate insulated) |
| Output resistance | ro = VA/IC | ro = 1/(λID) |
| Bias sensitivity | VBE drops ~2 mV/°C — needs emitter degeneration | Threshold varies widely — needs feedback or current mirror bias |
Top 4 campus interview questions
MCQ mastery quiz
1. For a BJT, gm = IC/VT. If IC doubles at constant temperature, gm…
2. The Barkhausen criterion requires loop gain magnitude…
3. A Wien bridge oscillator with R = 16 kΩ, C = 10 nF oscillates at about…
4. Which configuration is best as a buffer between a high-impedance source and a low-impedance load?
5. Compared with LC oscillators, crystal oscillators offer…