Transistor Amplifier: Small Signals Made Large

The transistor as a controlled valve

A bipolar junction transistor (BJT) is, electrically, a current-controlled current source. In the common NPN device, a small current flowing into the base, across the forward-biased base-emitter junction, permits a much larger current to flow from collector to emitter. The ratio between them is the current gain β (also written hFE), typically somewhere between 50 and a few hundred for a small-signal transistor. This is not free power — the extra current comes from the collector supply — but the base is doing the controlling, and the base current needed to control it is tiny by comparison.

Turn that current-controlled valve into a voltage amplifier by making the collector current flow through a resistor. As the base voltage wiggles up and down, the collector current wiggles with it, and the voltage dropped across the collector resistor wiggles too — by a much larger amount, because a modest change in current across a few kilohms is a large voltage swing.

Biasing: finding the sweet spot

Before any signal arrives, the transistor needs a DC operating point (the quiescent point, or Q-point) sitting away from both rails, usually near half the supply voltage at the collector. This is class-A biasing: it wastes some power holding the transistor partway on at all times, but it buys symmetric headroom for the output to swing both up and down around the resting value without hitting the supply rail on one side or the saturation voltage on the other.

The standard scheme is voltage-divider bias: two resistors set a fixed voltage at the base, an emitter resistor sets the emitter voltage roughly one diode drop below that, and Ohm's law across the emitter resistor fixes the collector current — largely independent of the individual transistor's exact β, which varies significantly between parts of the same type.

Vb  = Vcc * R2 / (R1 + R2)      // divider sets the base voltage
Ve  = Vb - 0.7                  // one diode drop below the base
Ie  = Ve / Re                   // Ohm's law fixes the current
Ic  ≈ Ie                        // base current is small, Ic ≈ Ie
Vc  = Vcc - Ic * Rc              // resting collector voltage, aim ≈ Vcc/2

The small-signal model and where gain comes from

Once biased, the transistor's response to small wiggles around the Q-point is well approximated as linear. The key parameter is the transconductance gm — how much collector current changes per volt of base-emitter change — and for a BJT it depends only on the bias current: gm = Ic / VT, where VT is the thermal voltage, about 26 mV at room temperature. For a common-emitter stage with a collector resistor Rc, the small-signal voltage gain is approximately -gm·Rc, and the minus sign is real: the output is inverted relative to the input, because more base current pulls more current through Rc, which drops more voltage and leaves less at the collector.

If an emitter resistor is left undecoupled, the gain drops to roughly -Rc/Re — much less sensitive to the exact transistor, more predictable, and lower distortion, at the cost of raw gain. A common trick is to bypass the emitter resistor with a capacitor at signal frequencies, which restores the full gm·Rc gain for AC while keeping the DC bias stability the resistor provides.

Common-emitter, common-collector, common-base

The three basic single-transistor configurations trade gain, impedance and phase differently. The common-emitter stage described above gives large voltage gain and moderate impedances, at the cost of an inverted output. The common-collector (emitter follower) has voltage gain just under 1, but very high input impedance and very low output impedance, making it the standard choice as a buffer between a weak source and a demanding load. The common-base stage has low input impedance, high output impedance, good gain and no phase inversion, and is prized in radio-frequency work for its wide bandwidth, since it has no Miller-effect capacitance multiplication between input and output.

Distortion, clipping and the limits of linearity

The linear small-signal model only holds for signals small enough that the transistor's exponential base-emitter characteristic looks locally straight. Push the input harder and two things eventually happen: the collector voltage runs out of room and clips flat against the supply rail or the saturation voltage, or the base-emitter junction stops conducting on the negative half-cycle and clips at cutoff. Either failure flattens part of the waveform, adding harmonic distortion that a spectrum analyzer sees as extra energy at multiples of the input frequency. Real amplifier design is largely the art of choosing the bias point and feedback so the signal you actually expect stays inside that linear window, with margin to spare.

Frequently asked questions

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