Short note: Differential amplifiers

A differential amplifier is a two-input amplifier that amplifies the difference between its two input voltages and rejects any signal common to both. It is the input stage of every op-amp.

          +VCC      +VCC
           |          |
           RC         RC
           |--Vo1  Vo2--|
        C1 |          | C2
  V1 --B Q1            Q2 B-- V2
         E1|          |E2
           +----+-----+
                |
           RE or current source
                |
              -VEE

Output: Vo = Ad·Vd + Acm·Vcm, where Vd = V1 − V2 (difference signal) and Vcm = (V1 + V2)/2 (common-mode signal).

Key results (BJT pair, gm = IC/VT):

• Differential gain, double-ended output: Ad = gm·RC; single-ended: gm·RC/2.
• Common-mode gain (single-ended): Acm ≈ −RC/(2RE), small when RE is large.
• CMRR = |Ad/Acm| ≈ gm·RE (single-ended). A constant-current tail (very large RE) gives very high CMRR.
• Differential input resistance Rid = 2rπ.

Configurations: dual-input balanced output, dual-input unbalanced output, single-input balanced output and single-input unbalanced output.

Features and uses: direct coupling (no capacitors, so it amplifies down to dc), good temperature stability because drifts in both halves cancel, rejection of noise and hum picked up equally by both inputs, and use as the input stage of op-amps, instrumentation amplifiers and comparators.