Emitter-Follower Input Impedance
Zin = β · RE
Quick answer
This calculator solves Zin ≈ β × RE (plus β·re) for Input Impedance. With Current Gain β 0.5, Emitter Resistor 22 kΩ, the result is 11 kΩ. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
An emitter follower (common-collector stage) presents a high input impedance because the emitter resistor is reflected to the base multiplied by the current gain. This lets the stage buffer a high-impedance source to a low-impedance load with near-unity voltage gain. It is the classic impedance-transforming output buffer.
Variables
- Zin — Input impedance looking into the base (Ω)
- β — Current gain
- RE — Emitter resistance / load (Ω)
Practical Notes
The full expression is Zin = β·(re + RE). The output impedance is correspondingly low: Zout ≈ re + Rsource/β. This is why followers drive heavy or capacitive loads well.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| Zin | Input Impedance | kΩ | mΩ, Ω, kΩ, MΩ |
| beta | Current Gain β | — | — |
| RE | Emitter Resistor | kΩ | mΩ, Ω, kΩ, MΩ |
Step by step
- 1. What you know: Current Gain β 0.5, Emitter Resistor 22 kΩ
- 2. The relation: Zin ≈ β × RE (plus β·re)
- 3. Substitute: beta = 0.5, RE = 22 kΩ
- 4. Result: Input Impedance = 11 kΩ
Nearest standard component values
| Series | Nearest value | Error |
|---|---|---|
| E12 | 10 kΩ | 9.1% |
| E24 | 11 kΩ | 0% |
Worked examples
Minimum range
Given: Current Gain β 0.025, Emitter Resistor 0.22 kΩ
Result: Input Impedance = 5.5 Ω
Low range
Given: Current Gain β 0.25, Emitter Resistor 2.2 kΩ
Result: Input Impedance = 0.55 kΩ
Typical
Given: Current Gain β 0.5, Emitter Resistor 22 kΩ
Result: Input Impedance = 11 kΩ
High range
Given: Current Gain β 0.8, Emitter Resistor 0.22 MΩ
Result: Input Impedance = 0.176 MΩ
Maximum range
Given: Current Gain β 8, Emitter Resistor 2.2 MΩ
Result: Input Impedance = 17.6 MΩ
Solving for each variable
Solve for Input Impedance
Current Gain β 0.025, Emitter Resistor 0.22 kΩ → 5.5 Ω
Solve for Current Gain β
Input Impedance 100 Ω, Emitter Resistor 0.22 kΩ → 0.4545
Solve for Emitter Resistor
Input Impedance 100 Ω, Current Gain β 0.025 → 4 kΩ
How Input Impedance changes with Current Gain β
| Current Gain β (input) | Input Impedance (result) |
|---|---|
| 0.05 | 1.1 kΩ |
| 0.125 | 2.75 kΩ |
| 0.25 | 5.5 kΩ |
| 0.375 | 8.25 kΩ |
| 0.5 | 11 kΩ |
| 0.75 | 16.5 kΩ |
| 1 | 22 kΩ |
| 2 | 44 kΩ |
| 3.5 | 77 kΩ |
| 5 | 110 kΩ |
The same result in other units
| Unit | Value |
|---|---|
| Ω | 11000 |
| kΩ | 11 |
| MΩ | 0.011 |
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<p><a href="https://vbatpower.com/formulas/emitter-follower-zin/">Emitter-Follower Input Impedance</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Emitter-Follower Input Impedance?
Use Zin ≈ β × RE (plus β·re). With Current Gain β 0.5, Emitter Resistor 22 kΩ, Input Impedance works out to 11 kΩ.
What is the formula for Emitter-Follower Input Impedance?
The formula is Zin ≈ β × RE (plus β·re). An emitter follower (common-collector stage) presents a high input impedance because the emitter resistor is reflected to the base multiplied by the current gain.
How do you find Current Gain β when you know the other values?
Rearrange for Current Gain β: with Input Impedance 100 Ω, Emitter Resistor 0.22 kΩ, Current Gain β is 0.4545.
How do you find Emitter Resistor when you know the other values?
Rearrange for Emitter Resistor: with Input Impedance 100 Ω, Current Gain β 0.025, Emitter Resistor is 4 kΩ.
What units does Emitter-Follower Input Impedance use?
Input Impedance is shown in Ω, kΩ, MΩ. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
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