Darlington Pair Current Gain
βtotal = β1 · β2
Quick answer
This calculator solves βtotal ≈ β1 × β2 for Total Gain. With Gain β1 1.1, Gain β2 2.35, the result is 2.585. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
A Darlington pair connects two transistors so the first one’s emitter current drives the second’s base, multiplying their current gains. The result is an extremely high effective beta, allowing a tiny base current to control a large load current—useful for power switching, relay and motor drivers, and high-input-impedance buffers.
Variables
- βtotal — Combined current gain
- β1 — First (driver) transistor gain
- β2 — Second (output) transistor gain
Practical Notes
Two β=100 transistors give β≈10000. The cost is a doubled base–emitter drop (~1.2–1.4 V) and slower switching; a Baker clamp or speed-up components help turn-off.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| betaTot | Total Gain | — | — |
| beta1 | Gain β1 | — | — |
| beta2 | Gain β2 | — | — |
Step by step
- 1. What you know: Gain β1 1.1, Gain β2 2.35
- 2. The relation: βtotal ≈ β1 × β2
- 3. Substitute: beta1 = 1.1, beta2 = 2.35
- 4. Result: Total Gain = 2.585
Worked examples
Minimum range
Given: Gain β1 0.055, Gain β2 0.118
Result: Total Gain = 0.00649
Low range
Given: Gain β1 0.55, Gain β2 1.18
Result: Total Gain = 0.649
Typical
Given: Gain β1 1.1, Gain β2 2.35
Result: Total Gain = 2.585
High range
Given: Gain β1 1.76, Gain β2 3.76
Result: Total Gain = 6.618
Maximum range
Given: Gain β1 17.6, Gain β2 37.6
Result: Total Gain = 661.8
Solving for each variable
Solve for Total Gain
Gain β1 0.055, Gain β2 0.118 → 0.00649
Solve for Gain β1
Total Gain 0.025, Gain β2 0.118 → 0.2119
Solve for Gain β2
Total Gain 0.025, Gain β1 0.055 → 0.4545
How Total Gain changes with Gain β1
| Gain β1 (input) | Total Gain (result) |
|---|---|
| 0.11 | 0.2585 |
| 0.275 | 0.6463 |
| 0.55 | 1.293 |
| 0.825 | 1.939 |
| 1.1 | 2.585 |
| 1.65 | 3.878 |
| 2.2 | 5.17 |
| 4.4 | 10.34 |
| 7.7 | 18.1 |
| 11 | 25.85 |
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<p><a href="https://vbatpower.com/formulas/darlington-gain/">Darlington Pair Current Gain</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Darlington Pair Current Gain?
Use βtotal ≈ β1 × β2. With Gain β1 1.1, Gain β2 2.35, Total Gain works out to 2.585.
What is the formula for Darlington Pair Current Gain?
The formula is βtotal ≈ β1 × β2. A Darlington pair connects two transistors so the first one’s emitter current drives the second’s base, multiplying their current gains.
How do you find Gain β1 when you know the other values?
Rearrange for Gain β1: with Total Gain 0.025, Gain β2 0.118, Gain β1 is 0.2119.
How do you find Gain β2 when you know the other values?
Rearrange for Gain β2: with Total Gain 0.025, Gain β1 0.055, Gain β2 is 0.4545.
Related Concepts
All Discrete Amplifiers formulas →Need more features?
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