Transistor Bias Explorer
Toggle between BJT and FET, adjust bias resistors, and watch the DC circuit transform into its hybrid-π (BJT) or small-signal FET equivalent. The Q-point guide coaches you toward optimal bias.
Adjust the bias
Q-point
Vʙ = 2.8 V
Iᴄ = 2.1 mA
Vʙᴇ = 0.7 V
Vᴄᴇ = 5.3 V
Q-point Guide
Small-signal BJT model
The small-signal model replaces the nonlinear BJT with linear equivalent components valid for small AC signals around the DC operating point (Q-point). It is the tool used to calculate voltage gain, input impedance, and output impedance of amplifier stages.
Key parameters
- gm = IC / VT — transconductance; VT ≈ 26 mV at room temperature
- rπ = β / gm — small-signal base–emitter resistance
- ro = VA / IC — output resistance (Early effect); VA ≈ 50–200 V for typical BJTs
Common-emitter voltage gain
Av = −gm × RC (ignoring ro). Negative sign = inverting. Higher IC increases gm and gain — but also shifts the Q-point and reduces headroom.
Learn more → Small-Signal Models — Learn
Quick experiments
- Put the Q-point in the middle. Adjust the bias resistors until VCE sits near half the supply. That is the point of maximum symmetrical swing — the output can move equally far in both directions before it runs out of room.
- Bias too low and watch it clip. Push the Q-point down toward cutoff. The transistor stops conducting on negative half-cycles, so the waveform flattens on one side only — asymmetric clipping is the signature of a bias problem rather than an over-driven input.
- See where gain comes from. Gain tracks gm, and for a BJT gm = IC / VT. Raise the collector current and gain rises with it, in direct proportion — no device parameter required.
- Compare BJT and FET. Switch device types at similar bias. The BJT gives far more transconductance for the same current; the FET gives an essentially infinite input resistance. That trade-off is why the two are chosen for different jobs rather than one being better.
Biasing and small-signal models — reference
Amplifier analysis splits into two problems that are solved separately. The DC bias decides where the transistor idles with no signal present. The small-signal model then describes how it responds to a tiny wiggle around that idle point. Superposition is what lets you separate them: capacitors are open circuits to DC and short circuits to the signal, so the two analyses barely interact.
Why the Q-point decides everything
The quiescent point sets the available output swing, the gain, and the distortion. Too close to saturation and positive peaks clip; too close to cutoff and negative peaks clip. Roughly mid-rail maximises the undistorted swing, and it is the reason a working amplifier burns current with no input applied.
The hybrid-π model
For a BJT the small-signal model is a transconductance gm = IC / VT with an input resistance rπ = β / gm. Note what is absent: gm depends only on bias current and temperature, not on β. That is what makes a well-biased stage predictable despite β varying by three to one between parts from the same reel.
The FET model
A FET has no gate current, so the input resistance is effectively infinite and there is no rπ. Its transconductance rises only as the square root of drain current, so buying gain by raising current is far less effective than with a BJT. The compensation is the input impedance, which is why FET front ends dominate where the source cannot supply current.
Emitter degeneration — trading gain for stability
An un-bypassed emitter resistor drops the gain to roughly −RC / RE, a ratio of two resistors. That is worth doing: the raw gain depends on temperature and on the individual device, while a resistor ratio does not. It is local negative feedback, and the same bargain the op-amp configurations make on a larger scale.
Common mistakes
Applying the small-signal model to large signals.
The model linearises around the Q-point and holds only for signals well under the 26 mV thermal voltage. Large swings need the full non-linear analysis.
Forgetting that gm depends on bias current.
Transconductance is Ic/Vt, so gain moves with the operating point. Changing the bias resistor changes the gain even with the load untouched.
Neglecting the emitter bypass capacitor's effect.
Bypassing the emitter resistor restores full gain at signal frequencies but leaves DC stability intact. Omit it and gain drops to roughly Rc/Re.
Ignoring output resistance ro.
The Early effect gives the transistor a finite output resistance in parallel with the collector load. With a large Rc, ro can dominate and cap the achievable gain.
Using the DC model to find input impedance.
Small-signal input impedance is beta divided by gm, not the DC bias network alone. The bias resistors appear in parallel with it and often dominate.
Frequently asked questions
What is transconductance in a BJT?
Transconductance gm is the collector current divided by the thermal voltage, about 26 millivolts at room temperature. At 1 milliamp of collector current gm is roughly 38 millisiemens.
How do I find the voltage gain of a common-emitter amplifier?
Gain is minus gm times the collector load resistance. At 1 milliamp with a 5 kilohm collector resistor the gain is about minus 190 — before any emitter degeneration is added.
Why does an emitter resistor reduce gain?
The emitter resistor introduces local negative feedback, making gain approximately minus Rc divided by Re. This trades raw gain for a Q-point and gain that no longer depend on beta or temperature.
What is the small-signal model used for?
It linearises the transistor around its DC operating point so gain, input impedance and output impedance can be calculated with ordinary linear circuit analysis. It is only valid for signals small enough that the linearisation holds.
What is the Early effect?
Collector current rises slightly with collector-emitter voltage because the effective base width narrows. It appears in the small-signal model as a finite output resistance ro, which limits the maximum achievable gain.
Related tools
CE / CS Amplifier Bench
Design a common-emitter or common-source stage — bias, load line, gain, impedance.
Open →Differential Pair Playground
Sweep the differential input and watch current redistribute — gains and CMRR live.
Open →Diode Lab
I-V plotter, half-wave, full-wave (bridge / center-tapped) — one widget.
Open →Zener Regulator Playground
Live Zener regulator + 4-curve compare (Zener / LED / Schottky / photodiode).
Open →BJT Simulator
Switch (cutoff / active / saturation) + Q-point stability across β and temperature.
Open →FET Simulator
JFET (Shockley) and MOSFET (square-law) transfer and output curves side by side.
Open →Browse the full circuit toolkit or start a guided lesson in topics.