Common Collector Amplifier

The common collector amplifier, also called an emitter follower, delivers a voltage gain just below 1 but provides very high input impedance and very low output impedance. It is the standard buffer stage between a high-impedance sensor and a low-impedance load such as a loudspeaker or ADC input.

Core Concept

In a common collector stage, the collector is tied directly to the supply rail (AC ground). The input goes to the base, and the output is taken from the emitter. Because the emitter voltage tracks VBE below the base voltage, the output follows the input almost exactly, giving the circuit the name emitter follower.

The voltage gain is slightly less than 1, typically 0.95 to 0.99. Despite this, the circuit provides substantial power gain because of its impedance transformation: a 1 MΩ source can drive a 50 Ω load without voltage loss. This is the same principle used in the BC547-based output stage of a multimeter input buffer.

Current gain equals beta + 1. The output current is (beta+1) times the base current. The input impedance is therefore (beta+1) times RE, which can be hundreds of kilohms. The output impedance is approximately re + Rs/(beta+1), which falls to tens of ohms even with a 10 kΩ source resistance.

Key Equations

Voltage gain: AV = RE / (RE + re) where re = VT/IE = 26mV/IE. For RE >> re, AV ≈ 1.

Current gain: AI = beta + 1. Output current at emitter is (beta+1) times the input base current.

Input impedance: Rin = RB || [(beta+1)*(RE + re)] where RB is the parallel combination of the bias resistors R1 and R2.

Output impedance: Rout = RE || (re + Rs/(beta+1)) where Rs is the Thevenin source resistance driving the base.

Given:
  BC547, VCC = 12V
  R1 = 47 kΩ, R2 = 10 kΩ
  RE = 2.2 kΩ, beta = 100, VT = 26 mV
  Source resistance Rs = 10 kΩ

Why this formula:
  Find IE from DC bias, then re, then AV and Rout.

Step 1 - DC bias:
  VB = VCC * R2/(R1+R2) = 12 * 10/(47+10) = 120/57 = 2.105 V
  VE = VB - VBE = 2.105 - 0.7 = 1.405 V
  IE = VE / RE = 1.405 / 2200 = 0.639 mA

Step 2 - re:
  re = VT / IE = 26 mV / 0.639 mA = 40.7 Ω

Step 3 - Voltage gain:
  Formula: AV = RE / (RE + re)
  AV = 2200 / (2200 + 40.7) = 2200 / 2240.7 = 0.982

Step 4 - Output impedance:
  Formula: Rout = RE || (re + Rs/(beta+1))
  = 2200 || (40.7 + 10000/101)
  = 2200 || (40.7 + 99.0)
  = 2200 || 139.7
  = (2200 * 139.7) / (2200 + 139.7)
  = 307340 / 2339.7

Calculation:
  Rout = 131.4 Ω

Final Answer:
  AV = 0.982 (~1), Rout = 131.4 Ω
  Compare: source impedance 10 kΩ reduced to 131 Ω at output.

Exam Tip: GATE often gives a common collector circuit and asks for output impedance. The trap is forgetting to divide Rs by (beta+1) before adding re. The formula is Rout = RE || (re + Rs/(beta+1)), not RE || (re + Rs). Also note: AV is always less than 1 for emitter follower; if your calculation gives AV > 1, you have made an error in the formula.

Key Properties

• Voltage gain is slightly less than 1 (non-inverting). Emitter follows base voltage with a fixed 0.7V offset.
• Current gain = beta + 1. For BC547 with beta=100, AI = 101.
• Input impedance is very high: tens to hundreds of kilohms depending on bias resistors.
• Output impedance is very low: tens of ohms, ideal for driving low-impedance loads.
• No phase inversion: output is in phase with input (0° phase shift).
• Used as a buffer between stages, at the output of a voltage divider, or at the ADC driver in a 5V microcontroller circuit.
• Bandwidth is wide because there is no voltage gain, so the Miller effect on CBC is negligible.

Quick Revision

• Input: base. Output: emitter. Reference: collector (tied to VCC).
• Voltage gain: AV = RE/(RE + re), always less than 1.
• Current gain: beta + 1.
• Input impedance: high. Output impedance: low.
• Phase shift: 0° (non-inverting).
• Primary use: impedance matching, buffering, driving low-impedance loads.
• Exam trap: Students write AV = RC/re (common emitter formula) for this circuit. The emitter follower has no RC in the signal path; the gain formula uses RE, not RC.