Common base amplifier circuit and gains

Circuit

Common base amplifier with voltage divider bias: the input vs (through C1 and the source resistance Rs) is applied at the emitter; the output is taken from the collector through C2 to RL; the base is grounded for ac by the capacitor CB.

              C1                              C2
 vs--Rs------||-----+----- E          C ----+----||----+---- vo
                    |        \      /       |          |
                    RE        --------      RC         RL
                    |            |          |          |
                   GND           B         +VCC       GND
                                 |
             R1 to +VCC, R2 to GND, CB to GND (ac ground)

AC equivalent (T-model)

With the base grounded, re is connected from the emitter to ground (through the base), RE is in parallel with it at the input, and the current source α ie feeds the collector load RC || RL. Here ie is the T-model emitter current, flowing from the base through re and out of the emitter terminal.

Input impedance

The input current flows into the emitter, ii = -ie, and the emitter voltage is

vi = -ie re
Zin(emitter) = vi/ii = re
Zin = RE || re ≈ re = VT/IE

It is very low (about 10 to 50 Ω).

Output impedance

Zout = RC || ro  ≈ RC

(The collector looks into a current source, whose resistance is very high, so RC dominates.)

Voltage gain

The collector current α ie flows into the collector, so

vo = -α ie (RC || RL) ,    ie = -vi/re

Av = vo/vi = α (RC || RL) / re  ≈ (RC || RL)/re  = gm (RC || RL)

The gain is positive (no phase shift) and can be large.

Properties