Common-Collector Current Gain

Ai = β + 1

Quick answer

This calculator solves Ai = β + 1 for Current Gain. With Current Gain β 1.1, the result is 2.1. It solves in 2 directions, so you can enter the values you have and get the one you need.

Calculator

Current Gain
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Formula

Ai = β + 1

Description

A common-collector stage (emitter follower) has a current gain of beta plus one, because the emitter current is the sum of the base and collector currents. This high current gain, combined with near-unity voltage gain, is what lets the follower deliver large load current from a small base current while buffering the previous stage.

Variables

  • Ai — Common-collector current gain
  • β — Common-emitter current gain

Practical Notes

The emitter current Ie = (β+1)·Ib. Together with the input-impedance multiplication (β·RE), this current gain is the basis of the follower’s impedance-transforming action.

Symbols and units

Symbol Meaning Default unit Accepted units
Ai Current Gain — —
beta Current Gain β — —

Step by step

  1. 1. What you know: Current Gain β 1.1
  2. 2. The relation: Ai = β + 1
  3. 3. Substitute: beta = 1.1
  4. 4. Result: Current Gain = 2.1

Worked examples

Minimum range

Given: Current Gain β 0.055

Result: Current Gain = 1.055

Low range

Given: Current Gain β 0.55

Result: Current Gain = 1.55

Typical

Given: Current Gain β 1.1

Result: Current Gain = 2.1

High range

Given: Current Gain β 1.76

Result: Current Gain = 2.76

Maximum range

Given: Current Gain β 17.6

Result: Current Gain = 18.6

Solving for each variable

Solve for Current Gain

Current Gain β 0.055 → 1.055

Solve for Current Gain β

Current Gain 0.025 → -0.975

How Current Gain changes with Current Gain β

Current Gain β (input) Current Gain (result)
0.242 1.242
0.605 1.605
1.21 2.21
1.815 2.815
2.42 3.42
3.63 4.63
4.84 5.84
9.68 10.68
16.94 17.94
24.2 25.2

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Frequently asked questions

How do you calculate Common-Collector Current Gain?

Use Ai = β + 1. With Current Gain β 1.1, Current Gain works out to 2.1.

What is the formula for Common-Collector Current Gain?

The formula is Ai = β + 1. A common-collector stage (emitter follower) has a current gain of beta plus one, because the emitter current is the sum of the base and collector currents.

How do you find Current Gain β when you know the other values?

Rearrange for Current Gain β: with Current Gain 0.025, Current Gain β is -0.975.

Related Concepts

All Discrete Amplifiers formulas →
Thermal Voltage Small-Signal Emitter Resistance Transistor Transconductance Diode Dynamic Resistance Common-Emitter Voltage Gain BJT Alpha–Beta Relationship Darlington Pair Current Gain Emitter-Follower Input Impedance

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