How a transistor actually amplifies

2026-04-23T00:00:00+00:00

The phrase small-signal gain</em> is one of those engineering expressions that manages to sound both technical and unhelpful at the same time. A transistor amplifies. Fine. How?</p>

The answer, when you work through it, is not that a transistor makes electrons stronger. Nothing in the device multiplies anything in a physical sense. It controls how hard a separate, already-energized current is allowed to flow, and then a nearby resistor turns that variable current back into a variable voltage, and the variable voltage is bigger than the one you started with. That is it. Everything else is details, and the details are where it gets fun.</p>

We'll build this up one scene at a time using an NPN bipolar junction transistor</a>, the sort of thing that still comes in a TO-92 three-legged black lump if you buy a bag from Mouser.</p>

What is a BJT?</h2>
A bipolar junction transistor is a three-terminal semiconductor device: a sandwich of doped silicon with a wire attached to each of its three layers. The NPN kind we'll be using stacks n-type silicon, p-type silicon, and n-type silicon, in that order. The three terminals attached to those layers are called, from outside to middle to outside, the collector</strong>, the base</strong>, and the emitter</strong>.</p>
"N-type" and "p-type" are just two versions of silicon that have been doped with impurities to give them either a surplus of free electrons (n-type) or a surplus of the absence of free electrons, which solid-state physicists call holes</em> and treat like positive charge carriers that move around independently. The bipolar</em> in the name is an admission that both kinds of carriers end up doing useful work inside the device. Most semiconductor designs try to avoid that. The BJT embraces it.</p>
The practical consequence is simple: a small current flowing into the base lets a much larger current flow from the collector to the emitter. That is the whole trick, and once you accept that it happens, the amplifier parts follow.</p>
A transistor is a valve</h2>
Start with the classical way a ham thinks about a BJT. A small current flowing into the base allows a much larger current to flow down through the collector. The ratio between the two is called β, and for most small-signal transistors it sits somewhere between 100 and 300. It is also the one number on the datasheet that is most likely to be wrong about your specific part.</p>
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That's it. Move the base current up, the collector current moves up in lockstep. You have not yet amplified a voltage, because nothing in the picture is a voltage source. All you've done is built a current-controlled current source. Interesting, but not a radio.</p>
The load line: where current meets a resistor</h2>
To get a voltage out, stick a resistor in series with the collector. The supply provides V_CC. The transistor pulls some collector current. The voltage dropped across the resistor is whatever Ohm's law says it has to be, and V_CE is whatever's left over.</p>
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The family of curves shows how I_C depends on V_CE for various base currents. They're nearly flat because an ideal BJT is a current source, not a resistor. The orange line is the load line, the set of all (V_CE, I_C) points compatible with your V_CC and R_C. Wherever the load line meets the base-current curve you chose, that is the operating point (or, more ceremoniously, the Q-point). Turn the base current up, Q-point slides up the load line toward the top-left. Turn it up too far and you hit the saturation wall, where V_CE flattens against the supply rail minus a few tenths of a volt and the transistor gives up on being a current source. Turn it down to zero and you're in cutoff, V_CE sitting at the full V_CC because no current is flowing.</p>
The useful region is the one in the middle. The entire game of building an amplifier is making sure you stay there on purpose.</p>
What's happening as V_BE changes</h2>
The base current is actually controlled by the voltage across the base-emitter junction, V_BE. That junction is a forward-biased diode, and diodes respond exponentially to voltage: small changes near the knee produce large changes in current, until eventually you drop the entire supply across the collector resistor and can't go any further.</p>
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Drag V_in (which is V_BE here) and watch V_out. The three regions of the earlier scene show up as three regions of the curve: a flat portion at the top where nothing happens, a steep diagonal in the middle where a few millivolts of input produce volts of output, and a flat portion at the bottom where you're welded to the rail. The slope of the steep part is the voltage gain. It is not an especially well-behaved function of V_in, but it's enormous, and that's enough.</p>
Notice that the amplifier is upside down. V_in going up makes V_out go down. This is the standard "common-emitter" amplifier</a>, and its inversion is a consequence of the fact that more base drive means more collector current means more voltage dropped across R_C means less voltage left on the collector. The inversion does not bother anyone except people reading their first schematic.</p>
Amplification, live</h2>
Pick a bias near the middle of the steep part. Add a small AC signal on top of the bias. The signal walks V_BE back and forth by a few millivolts. That walks I_C by a few milliamps (multiplied by the exponential). That walks V_CE by a few volts (multiplied by R_C). The result is a bigger, flipped version of the input.</p>
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Crank the input amplitude high enough and the output swing starts slamming into the rails. The peaks clip. A real amplifier design is mostly the art of picking a bias point such that the signal you care about fits cleanly between V_CC and V_CEsat with some margin. Hi-fi engineers and ham radio operators fight about exactly how much margin. The transistor does not have strong opinions on this either way.</p>
Where the number comes from</h2>
All of the above is captured in two small formulas that turn the exponential behavior into linear behavior near a chosen operating point.</p>
The rate at which collector current changes per volt of base drive is called transconductance:</p>

g_m = I_C / V_T</p> </blockquote>
where V_T is the thermal voltage, about 26 mV at room temperature. That is a number that comes directly from the physics of a PN junction and has been the same temperature coefficient since semiconductor devices were invented.</p>
The voltage gain of this common-emitter stage is then:</p>

A_v = -g_m * R_C</p> </blockquote>
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A BJT biased at 2 mA with a 1 kΩ collector resistor has a transconductance of about 77 mA/V and a voltage gain of about 77. Run it at 5 mA and the gain climbs to around 190. Run it at 100 μA and you have a gain of about 4 and should probably consider a different amplifier topology. None of this depends on β, by the way, which is why a well-designed amplifier doesn't care very much that β varies from part to part.</p>
Everything else, and there is a lot of else</em>, is decoration on this core. Bypass capacitors, emitter degeneration, cascode stages, differential pairs, current mirrors, Darlingtons, bootstraps. They all exist to make the basic idea above more linear, more bandwidth-y, more stable with temperature, or less dependent on a specific transistor's specific quirks. But underneath the decoration there's still a valve controlling a current, and a resistor turning that current into a voltage, and the voltage is bigger than the one you started with. The rest is bookkeeping.</p> </div>

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How a transistor actually amplifies