C4 · BJT

The Common-Emitter Amplifier: Small In, Large Inverted Out

Drop the small-signal model into a real circuit and make a voltage gain for the first time. Grow the collector resistor yourself and see the output swell to a multiple of the input, and why it flips.

Grow the collector resistor to make gain

The faint curve is the small input vin and the bold curve is the output vout. Grow the collector resistor Rc and the output gets larger and larger. And the output is flipped: it falls when the input rises.

Collector resistor RcRc = 0.10 kΩ

Voltage gain Av

Av = -gm Rc = -19

Rc is small. The voltage the signal current makes across a small resistor is small, so the output is barely larger than the input.

Low gain

Wobble the base and the collector current wobbles

Couple the input signal through a capacitor onto the base, and a small vbe is added on top of the operating point. As seen in C3, this small voltage makes a signal current ic = gm vbe. The transistor has turned the wobble of the input voltage into a proportional wobble of current. Note that this is still a current, not yet a voltage.

That current becomes a voltage across Rc, and flips

This signal current flows through the collector resistor Rc. By Ohm’s law the voltage across Rc wobbles by ic Rc. The output is taken at the collector, whose voltage is Vcc minus Ic Rc. So when the signal current rises, the collector voltage instead falls. The output falls when the input rises: the output is an inverted copy of the input. vout = -ic Rc.

The voltage gain Av = -gm Rc

Substituting ic = gm vbe into vout = -ic Rc gives the voltage gain Av = vout/vin = -gm Rc. Since gm is set by the operating current chosen in C2 and Rc is chosen by the designer, these two fix the gain. The minus sign means a 180-degree inversion. But raising the gain does not make the output grow without limit. The output swing is bound by the headroom of C2, so if gm Rc is too large the peaks hit the supply and clip. Gain and swing trade off.

Observevout = -ic Rc

The output voltage is what the signal current makes across Rc, with opposite sign.

Chooseic = gm ?

The signal current is transconductance times input voltage.

Fill inAv = voutvin = -gm ?

The gain is minus the product of transconductance and collector resistor.

On your ownAv = -(IcVT) ?

Expanding gm, the gain is set by the operating current and Rc.

Back to the first screen

The more you grew the collector resistor, the larger the output became, and each time the input rose the output fell, tracing a flipped shape. The secret has two steps: the small input voltage first becomes a signal current gm vbe through the transistor, and that current, flowing through the collector resistor Rc, becomes a voltage ic Rc that pulls the collector voltage down. Their product, -gm Rc, is the voltage gain. But push too hard and the peaks hit the supply and clip, so the gain is always decided hand in hand with the swing headroom of C2. The small-signal model has at last been completed into the arithmetic of amplification.

A common-emitter amplifier is the small-signal model (C3) placed in a circuit. The input vin wobbles the base to make a signal current ic = gm vbe, and this current flows through the collector resistor Rc to make vout = -ic Rc. Since rising current lowers the collector voltage, the output is inverted. The voltage gain Av = vout/vin = -gm Rc. The larger gm and Rc, the larger the gain, but the output swing is bound by the C2 headroom and clips if pushed too far.

What comes next

You now hold a single voltage gain. But an amplifier never stands alone: a source feeds it in front, and a load receives it behind. The next unit looks at how the amplifier appears to the source and the load, that is, its input and output impedances, and how those trim or set the actual gain.