Putting the biased transistor to work
By now you can place an NPN transistor exactly where you want it. The last guide left you with a transistor held by a voltage-divider bias and an emitter resistor, its Q-point parked comfortably in the middle of the active region — the collector sitting at roughly half the supply, with plenty of room to swing both up and down. A transistor that just sits there is not yet useful. The whole point of all that careful biasing was to reach this moment: feed in a small wiggle and get a bigger one out.
The classic arrangement is the common-emitter amplifier: the signal goes in at the base, the amplified output comes off the collector, and the emitter is the terminal shared by both — that is what "common-emitter" names. Think back to the tap analogy: a tiny movement of the handle (the base voltage) controls a big flow (the collector current). Wiggle the base a little and the collector current wiggles a lot; run that wiggling current through a collector resistor Rc and it becomes a wiggling voltage — your amplified signal.
The signal rides on top of the DC bias, like ripples on a pond whose water level you already set. To get it in and out without disturbing that level, you use coupling capacitors: a cap in series at the input passes the AC wiggle but blocks any DC from the source that would otherwise shove your carefully-set Q-point around, and another at the output strips the collector's DC away so the next stage sees only the signal. Those caps form high-pass filters, so a common-emitter stage has a low-frequency limit — it amplifies audio happily but ignores DC.
The small-signal model: zoom in on the Q-point
To find the gain, do what physicists always do with a curve: zoom in until it looks straight. The transistor's collector current rises exponentially with base-emitter voltage — a steep, curved relationship — but a tiny signal only nudges the operating point a hair either side of the Q-point, and over that hair the curve is almost a straight line. Replacing the real, curved device with that local straight-line approximation is the small-signal model, and it turns a frightening transistor into ordinary linear circuit math.
The slope of that straight line is the single most important number in the whole guide: the transconductance, gm = Ic / VT, where VT is the thermal voltage, about 25 mV at room temperature. It says how much the collector current changes for a small change in base-emitter voltage: ic = gm times vbe. At a Q-point of Ic = 1 mA, gm = 1 mA / 25 mV = 40 mS (milli-siemens). Notice what gm depends on: the collector current you biased it at — and not, anywhere, on beta. The transistor is at heart a voltage-controlled current source.
Two more quantities fall straight out of gm. Its reciprocal, re' = 1 / gm = VT / Ie, is the transistor's intrinsic emitter resistance — at 1 mA it is 25 mV / 1 mA = 25 ohm, a little resistance that lives inside the emitter whether you want it or not. And looking into the base, the signal sees r_pi = beta times re', the only place beta sneaks into the model. At beta = 100 that is 100 times 25 = 2.5 kohm — and right there is your first warning: anything that leans on r_pi leans on beta, which varies wildly part to part.
The gain, and why it inverts
Now follow the signal through. The input voltage vin appears across the base-emitter (if the emitter is held still at signal frequency), so it produces a collector current ic = gm times vin. That current flows through Rc, and the output is the voltage it drops there: vout = -ic times Rc. The minus sign is real and important — more base voltage means more collector current means a bigger drop across Rc, which pulls the collector voltage down. So the voltage gain is Av = vout / vin = -gm times Rc, which you can equally write as Av = -Rc / re'.
Put numbers in: with Rc = 4.7 kohm and re' = 25 ohm, Av = -4700 / 25 = -188. A small wiggle comes out roughly 190 times bigger and upside-down — that is about 45 dB of voltage gain from one cheap transistor, and it is exactly the result that makes the common-emitter amplifier feel like magic the first time you build it. The inverting part has a nice picture too: as the base voltage rises, the operating point slides down the load line toward the saturation end, and the collector voltage falls; push the base down and the collector climbs back up. Input up, output down — a clean 180-degree inversion.
But here is the honest catch, and it is a big one. That gain of -188 rides entirely on re', and re' = VT / Ie depends on the bias current (which drifts with temperature), on the part you happened to plug in, and — worst of all — it changes across the signal's own swing, because re' is smaller at the top of the swing where current is higher and larger at the bottom. A gain that varies over the waveform is the very definition of distortion. So this textbook -188 is loud, but it is unpredictable, temperature-sensitive, and dirty. You almost never use it as it stands.
Emitter at signal frequency AC emitter R Gain Av = -Rc/(re'+Re_ac) Character --------------------------------------------------------------------------------------- Fully bypassed (Re shorted) re' = 25 -4700 / 25 = -188 big, but drifty + nonlinear Partly bypassed (Re1 = 220) 25 + 220 -4700 / 245 = -19 tunable, set by a ratio Not bypassed (Re = 1.4k) ~ 1400 -4700 / 1400 = -3.4 small, rock-steady, linear Q-point: Ic = 1 mA -> gm = Ic/VT = 1mA / 25mV = 40 mS, re' = 1/gm = 25 ohm, Rc = 4.7k. The more emitter resistance you leave in the AC path, the LOWER the gain -- but the more it becomes a gain you can actually trust.
The honest fix: emitter degeneration
The cure is wonderfully simple: leave a real resistor Re in the emitter's signal path instead of letting re' run the show. This is emitter degeneration, and it changes the gain to Av = -Rc / (re' + Re). Once Re is much bigger than that fickle little re', the re' drops out of the answer and the gain becomes simply Av ≈ -Rc / Re — a ratio of two resistors you chose and trust. With Rc = 4.7 kohm and Re = 1 kohm you get a gain of about -4.7, dead steady, the same on every transistor and at every temperature, and beautifully linear because Re does not change across the swing.
What you have just built is negative feedback — the thermostat forever nudging the output back toward target. The emitter resistor reports the actual output current back to the input (a rising emitter voltage eats into the drive across the base-emitter junction) and opposes any change, whatever caused it. You pay for this by giving up most of the raw gain, but in return you buy predictability, low distortion, wider bandwidth, and immunity to beta and temperature. This is the deepest lesson of transistor design: good design does not rely on beta — it trades away the gain you cannot trust for the gain you can.
Can you have both — steady bias and big gain? Yes, with a clever trick: the emitter bypass capacitor. Keep the full emitter resistor in place for DC, so it still stabilizes the Q-point as the previous guide taught, but park a large capacitor across it (or across part of it). At DC the cap is an open and the whole resistor degenerates the bias; at signal frequency the cap is a near-short that ties the emitter down, restoring the high gain. Split the emitter into a small unbypassed part (say 220 ohm, which sets the AC gain) and a larger bypassed part, and you tune exactly where on the trade-off you want to sit — the middle row of the table above.
Input and output resistance, and what comes next
An amplifier is not just a gain number; it also has terminals that other circuits must drive and be driven by. The input resistance of a common-emitter stage is the bias divider in parallel with the resistance looking into the base, which with degeneration is beta times (re' + Re). In our example that base looks like 100 times 245 ≈ 24 kohm, in parallel with the divider's 8 kohm, giving roughly 6 kohm — moderate, and notably better than the bare stage's low r_pi. The output resistance, meanwhile, is essentially just Rc, about 4.7 kohm here.
That high output resistance is the common-emitter amplifier's Achilles' heel. A 4.7 kohm output cannot drive a low-impedance load — connect an 8 ohm speaker or a 1 kohm next stage straight to the collector and the load forms a voltage divider with Rc that swallows most of your hard-won signal. The common-emitter gives you voltage gain, but it cannot deliver current into a heavy load. The answer, and the whole of the next guide, is to follow it with an emitter follower: a buffer with a gain of about one but a stiff, low output resistance that drives the load while barely loading the stage before it.
The common-emitter stage is also the seed of nearly everything that follows. Tie two of them together at their emitters and you get the differential pair at the heart of every op-amp; load one with a current mirror instead of a plain resistor and the gain soars; stack two transistors into a Darlington for enormous current gain. And the field-effect cousin, the common-source amplifier, works on exactly this logic with gm and a drain resistor in place of re' and Rc — so the intuition you just built transfers straight across. Those building blocks are the next steps up this ladder.