C4 · BJT

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

Put the small-signal model into a real circuit and you make a voltage gain for the first time. In this unit you enlarge the collector resistor yourself and see how many times larger the output grows than the input, and why it is inverted.

Enlarge the collector resistor to make gain

The faint curve is the small input and the bold curve is the output. Enlarge the collector resistor and the output grows, but it is upside down: when the input rises, the output falls. Enlarge the resistor to see the output grow well beyond the input, and watch too for the point where the peaks start to hit the top and bottom limits and get cut off.

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 too, so the output is not much larger than the input.

Low gain

Wobble the base and the collector current wobbles

Feed 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 swing of the input voltage into a proportional swing of current; note that at this stage it is still a current, not yet a voltage.

That current becomes a voltage across Rc, and flips

This signal current passes through the collector resistor Rc, and by Ohm's law the voltage across Rc swings by ic Rc. The output is taken at the collector, and since the collector voltage is Vcc minus Ic Rc, an increase in signal current actually pulls the collector voltage down. The output falls as the input rises, so the output is an inverted, enlarged copy of the input: vout = -ic Rc.

The voltage gain Av = -gm Rc

Substitute ic = gm vbe into vout = -ic Rc and the voltage gain comes out as Av = vout/vin = -gm Rc. gm is set by the operating-point current chosen in C2 and Rc is chosen by the designer, so the two together set the gain. The minus sign means the phase is inverted by 180 degrees. Even so, the output cannot grow without limit. How far it can swing is tied to the operating-point margin of C2, so if gm Rc is too large, the peaks hit the supply and are cut off. Gain and swing are a 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 the transconductance times the input voltage.

Fill inAv = voutvin = -gm ?

The gain is the transconductance times the collector resistance, with a minus sign.

On your ownAv = -(IcVT) ?

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

Back to the first screen

The larger you made the collector resistor, the larger the output grew, and each time the input rose the output fell, tracing an inverted shape. Two steps lie behind it. The small input voltage first becomes a signal current gm vbe through the transistor, and that current, passing through the collector resistor, becomes a voltage of ic Rc that pulls the collector voltage down. Multiplied together, -gm Rc is the voltage gain. But push it too far and the peaks hit the supply and were cut off, so the gain is always settled together with the swing margin of C2. The small-signal model is finally completed as the arithmetic of amplification.

A common-emitter amplifier puts the small-signal model (C3) into a circuit. The input vin swings the base and makes a signal current ic = gm vbe, and this current flows through the collector resistor Rc to make vout = -ic Rc. As the current rises the collector voltage falls, so the output is inverted. The voltage gain is Av = vout/vin = -gm Rc. The larger gm and Rc, the larger the gain, but the output swing is tied to the operating-point margin of C2 and is clipped if pushed too far.

What comes next

Now you hold one voltage gain in hand. But an amplifier never stands alone: in front is a source that supplies the signal, and behind is a load that receives it. The next unit covers how the amplifier looks to the source and the load, that is, its input impedance and output impedance, and how they trim or set the actual gain.