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C5 · BJT

Gain and Impedance: An Amplifier Feels Its Neighbors

An amplifier sits between a source and a load. In this unit you connect loads both heavy and light yourself and see how the ideal gain of the last unit is trimmed in practice, and what decides that trimming.

Change the load and watch the gain shrink

The dashed peaks are the ideal output with no load, and the bold curve is the actual output. Lower the load resistance to make the load heavier and the actual output shrinks inside the dashed line; raise it and the output comes back close to the ideal. Use the slider to compare how much the output differs between a light load and a heavy one.

Load resistor RLRL = 0.20 kΩ
Actual voltage gain Av
Av = -gm (Rc || RL) = -32
Rout = Rc = 1 kΩ · |Av|max = 192
The load resistance is smaller than Rc. In parallel with Rc it cuts the effective resistance a lot, and the actual gain drops to a fraction of the ideal.
Heavy load · gain cut

Input impedance, what the source sees

Look into the amplifier from the side of the source that supplies the signal and it appears as a single resistance. In a common-emitter stage this input impedance is the small-signal input resistance rπ in parallel with the bias resistors. The source always has its own internal resistance Rs, which forms a voltage divider with the input impedance, so if the input impedance is small, only part of the source voltage reaches the base and signal is lost from the start.

Output impedance, what the load sees

Conversely, look into the amplifier from the output side, at the collector, and the load sees another resistance. The transistor's output is ideally a current source with infinite internal resistance, so the output impedance the load sees is practically the collector resistor Rc. Connect a load resistor RL and it sits alongside Rc, that is, in parallel. The smaller the output impedance, the less the voltage is trimmed by the same load.

The load trims the gain

Because the load RL is in parallel with the collector resistor Rc, the effective resistance the signal current sees is Rc || RL. So the actual voltage gain is Av = -gm (Rc || RL), which is always smaller than the no-load -gm Rc. The heavier the load, that is, the smaller RL, the smaller the parallel value and the more the gain is trimmed. To get a large gain by chaining stages, each stage's output impedance must be well below the next stage's input impedance so that no signal is lost, which is why amplifier design weighs impedance as much as gain.

ObserveRout = Rc
The output impedance is the collector resistance.
Choosevbe = vs · rπ / (rπ + ?)
The input enters in the ratio of the input resistance over the source resistance plus it.
Fill inAv = -gm (Rc || ?)
The actual gain follows the parallel of Rc and the load.
On your ownRc || RL = Rc RL / (Rc + ?)
The parallel value is the product over the sum.

Back to the first screen

The heavier the load, the more the actual output shrank inside the dashed line, and lightening the load brought it back close to the dashed line. That dashed line is the ideal gain with no load, -gm Rc, and the actual output was always the smaller -gm (Rc || RL). What decided the trimming was the parallel combination of the output impedance Rc and the load RL. In the same way, on the input side the input impedance and the source resistance form a divider that splits the signal. An amplifier never stands alone, and its gain is always settled together with the neighboring impedances; with this, the BJT amplifier has come full circle.

An amplifier never stands alone. The input impedance Rin(≈ rπ) is the resistance the source sees, forming a divider with the source resistance Rs that trims the input, and the output impedance Rout(= Rc) is the resistance the load sees, with the load RL attaching to Rc in parallel. So the actual voltage gain Av = -gm (Rc || RL) is always smaller than the no-load -gm Rc, and the heavier the load, the more it is trimmed. To chain stages without losing signal, each stage's Rout must be well below the next stage's Rin.

What comes next

The BJT governed a large current with a small one. In the next set you meet another transistor, the MOSFET, which opens and closes its channel not with current but with voltage, that is, with the electric field applied at the gate alone. Its first unit looks at its structure and threshold voltage, starting from the fact that almost no current flows into the gate, which makes its input impedance very high.