EC-6.6 The Bipolar Transistor: Operation and Models

What this is and why it exists

This is the device the analog course has always started after.

Two junctions back to back would ordinarily do nothing useful — two diodes in series, facing opposite ways, conduct in neither direction. The transistor works because of one construction decision: the middle region is made thin.

Thin compared with what? Compared with the diffusion length from two topics ago. Make the base thin enough and most carriers injected into it survive the crossing. They arrive at the far junction instead of recombining on the way.

Everything else — the current gain, the four operating regions, the small-signal model an amplifier is designed from — follows from that.

The vocabulary

• Emitter — the heavily doped region that injects carriers into the base.
• Base — the thin middle region that controls the flow.
• Collector — the region that receives the carriers that cross the base.
• Active region — emitter junction forward biased, collector junction reverse biased. This is where amplification happens.
• Saturation — both junctions forward biased; the device behaves as a closed switch.
• Cut-off — both reverse biased; the device is off.
• Current gain — the ratio of collector current to base current.
• Early effect — the slight rise of collector current with collector voltage, from base-width modulation.
• Transconductance — how much output current changes per volt of input.
• Hybrid-pi model — the small-signal model used to design amplifiers.

The mental model

Start with why the geometry matters, because the rest is bookkeeping.

The emitter is doped heavily and the base lightly. So when the emitter junction is forward biased, carriers flood from emitter into base and few go the other way. Once in the base those carriers are minority carriers, and they diffuse across it.

The base is thin, so most of them make it to the collector junction, where the reverse-biased field sweeps them straight through. Only the small fraction that recombine on the way have to be replaced by the base terminal.

That fraction is the base current, and that is where the gain comes from. Collector current is large because almost everything crosses; base current is small because little recombines. The gain is a consequence of geometry and doping, not a property that was specified and then achieved.

The four operating regions are named by which junction is biased which way, and naming the two biases identifies the region every time:

• Emitter forward, collector reverse: active. Amplification.
• Both forward: saturation. A closed switch, with a small voltage across it.
• Both reverse: cut-off. An open switch.
• Emitter reverse, collector forward: reverse active. Poor gain; nothing uses it deliberately.

On the output characteristics, collector current is almost flat against collector voltage in the active region. That flatness is what makes the device behave as a current source, which is exactly what you want in an amplifier. The slight upward slope is the Early effect. Increasing collector voltage widens the collector depletion region, which narrows the base, so fewer carriers recombine and the current rises. That slope sets the largest voltage gain a single stage can reach.

Now the move that connects all this to circuit design.

A transistor is nonlinear, and the circuits you know how to solve are linear. The small-signal idea resolves that: for a signal small enough, a curve behaves like the straight line touching it at the operating point. Replace the device by that tangent and the circuit becomes linear again.

The key number is transconductance — how much output current moves per volt of input. It depends on the operating current, not on which transistor you bought. That is worth pausing on. The same device biased at two different currents has two different gains, which is why biasing is a topic in its own right.

The hybrid-pi model is transconductance plus an input resistance and an output resistance. Three components, and it is what every amplifier in the analog course is designed from. Meeting it here, attached to the device it describes, is the difference between a model and a set of symbols.

What you should now be able to explain or do

• Explain why the base must be thin, in terms of diffusion length.
• Say where the current gain physically comes from.
• Name the four regions from the two junction biases.
• Explain the Early effect and what it limits.
• State what transconductance depends on, and what the hybrid-pi model contains.

Check yourself