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BJT differential amplifier collector waveforms

Short answer

A BJT differential pair with matched transistors and equal RC. For differential sinusoidal inputs (v1, v2 out of phase), collector voltages vo1 and vo2 are antiphase, each with amplitude Ad·vd/2; vo1 is inverted relative to v1, vo2 inverted to v2. The differential output between collectors has amplitude Ad·vd.

Draw the circuit diagram of differential amplifier using BJT and sketch the waveform at the collector terminals for sinusoidal differential input.

Circuit

                 +VCC
          +-------+-------+
          |               |
        [RC]            [RC]
          |               |
 vo1 o----+               +----o vo2
          |               |
         C|               |C
 v1 o----B| Q1        Q2  |B----o v2
         E|               |E
          |               |
          +-------+-------+
                  |
                [RE]  (or constant current source)
                  |
                -VEE

Q1 and Q2 are matched transistors with equal collector resistors RC and a common emitter resistor RE (or constant current source). The inputs v1 and v2 are applied at the bases; the outputs are taken at the collectors.

Differential input

Let v1 = (vd/2) sin ωt and v2 = −(vd/2) sin ωt (equal amplitude, 180° out of phase).

  • When v1 rises, IC1 rises, so the voltage drop across RC rises and the collector voltage vo1 falls. At the same time v2 falls, IC2 falls and vo2 rises.
  • The total emitter current stays almost constant (IE1 + IE2 = constant), so the emitter point acts as an ac ground for the differential signal.

Collector waveforms

 v1:      /\    /\         input at base of Q1
         /  \  /  \
        /    \/    \

 v2:    \    /\    /       input at base of Q2
         \  /  \  /
          \/    \/

 vo1:   \    /\    /       collector of Q1: amplified, 180° to v1
         \  /  \  /
          \/    \/

 vo2:     /\    /\         collector of Q2: amplified, in phase with v1
         /  \  /  \
        /    \/    \
  • vo1 is 180° out of phase with v1; vo2 is 180° out of phase with v2 (that is, in phase with v1).
  • vo1 and vo2 are therefore in antiphase with each other, and each has amplitude Ad·vd/2.
  • The output taken between the collectors, vo2 − vo1, has amplitude Ad·vd (twice that of either collector), with differential gain Ad = gm RC. Each single-ended output has a gain of gm RC/2 with respect to vd.
  • A common-mode input (the same signal on both bases) produces a very small output, because the large RE (or current source) gives strong negative feedback.

✓ Answer checked by Claude Opus 5.5 (high effort)

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