Differential amplifier

The differential amplifier — also called the difference amplifier or emitter-coupled amplifier — is the main building block of IC amplifiers and is the basic input stage of an integrated op-amp. It is a direct-coupled amplifier that, as its name implies, amplifies the difference between its two input signals.

Basic circuit. The basic differential amplifier (Figure 5.2.1) uses two identical transistors $Q_1$ and $Q_2$, two collector resistors $R_{C1}$ and $R_{C2}$, and a common emitter resistor $R_E$. The two input signals $V_{i1}$ and $V_{i2}$ are applied to the bases of the two transistors, and the two outputs $V_{o1}$ and $V_{o2}$ are taken from the collectors. Two power supplies $V_{CC}$ and $V_{EE}$ bias the circuit.

Four modes. Depending on how many inputs are driven and how many outputs are taken, a differential amplifier can be operated in four modes:

1. Double-ended input and double-ended output (dual input, balanced output) — Figure 5.2.2a.
2. Single-ended input and single-ended output (single input, balanced output) — Figure 5.2.2b.
3. Double-ended input and single output (dual input, unbalanced output) — Figure 5.2.2d.
4. Single-ended input and double-ended output (single input, balanced output) — Figure 5.2.2c.

Working of the dual-input balanced-output amplifier. The operation is analysed using the superposition theorem by taking one input at a time (Figure 5.2.3, phases shown in Figure 5.2.4):

• Condition 1 — apply $V_{i1}$, ground $V_{i2}$: $V_{i1}$ is the base input of $Q_1$ and its output $V_{o1}$ is taken at the $Q_1$ collector, so $Q_1$ works as a common-emitter (CE) amplifier and $V_{o1}$ is out of phase with $V_{i1}$. At the same time $V_{i1}$ appears at the emitter of $Q_2$, so $Q_2$ works as a common-base (CB) amplifier whose collector output $V_{o2}$ is in phase with $V_{i1}$.
• Condition 2 — apply $V_{i2}$, ground $V_{i1}$: now $Q_2$ acts as a CE amplifier and $V_{o2}$ is out of phase with $V_{i2}$; $Q_1$ acts as a CB amplifier, and $V_{i2}$ reaching its emitter appears amplified and in phase at the $Q_1$ collector as $V_{o1}$.

When both inputs are applied together, the output $V_O$ is measured between the two collectors, and the voltage gain is

(The textbook writes the difference of the two inputs using a tilde, $V_{i1} \sim V_{i2}$; it simply means the difference between the two input voltages.)

Common-mode operation. When the same (common) input is applied to both terminals, the amplifier is in common-mode operation. A good differential amplifier refuses to amplify common-mode signals: the equal inputs drive both identical transistors equally, and the resulting output contributions are opposite in polarity and cancel. By superposition, if $V_{i1} = V_{i2}$ then $V_{o1} = 0$ and $V_{o2} = 0$, so for a dual-input single-output amplifier $V_O = 0$, i.e. the common-mode gain is ideally zero. The common-mode gain is

Differential-mode operation. When two opposite-polarity signals are applied to the two inputs, the amplifier is in differential mode: the difference of the two signals is amplified and appears at the output. The gain for this input is the differential-mode voltage gain $A_d$. By superposition, if $V_{i1} \neq V_{i2}$ then $V_{o1} = A_d(V_{i1} - V_{i2})$ and $V_{o2} = A_d(V_{i1} - V_{i2})$, and

where $r'_e$ is the AC emitter resistance of the transistors. …