Small-Signal Emitter Resistance
re = VT / Ie
Quick answer
This calculator solves re = VT / Ie (≈ 25 mV / Ie) for Emitter Resistance. With Thermal Voltage 0.6 V, Emitter Current 20 mA, the result is 30 Ω. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The intrinsic small-signal emitter resistance of a bipolar transistor is the thermal voltage divided by the DC emitter current. It is not a physical resistor but the dynamic resistance of the base–emitter junction, and it sets the maximum voltage gain of a common-emitter stage (Av = −Rc/re). Higher bias current lowers re and raises gain but also raises power.
Variables
- re — Small-signal emitter resistance (Ω)
- VT — Thermal voltage (≈25–26 mV)
- Ie — DC emitter current (A)
Practical Notes
At 1 mA, re ≈ 25 Ω. Because re depends on bias current, an undegenerated common-emitter stage has gain that varies with operating point and temperature; an external emitter resistor stabilises it.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| re | Emitter Resistance | Ω | mΩ, Ω, kΩ, MΩ |
| Vt | Thermal Voltage | mV | pV, nV, µV, mV, V, kV |
| Ie | Emitter Current | mA | pA, nA, µA, mA, A, kA |
Step by step
- 1. What you know: Thermal Voltage 0.6 V, Emitter Current 20 mA
- 2. The relation: re = VT / Ie (≈ 25 mV / Ie)
- 3. Substitute: Vt = 0.6 V, Ie = 20 mA
- 4. Result: Emitter Resistance = 30 Ω
Related quantities from the same inputs
- P = V × I = 12 mW
Nearest standard component values
| Series | Nearest value | Error |
|---|---|---|
| E12 | 27 Ω | 10% |
| E24 | 30 Ω | 0% |
Worked examples
Minimum range
Given: Thermal Voltage 10 mV, Emitter Current 100 µA
Result: Emitter Resistance = 100 Ω
Low range
Given: Thermal Voltage 100 mV, Emitter Current 1 mA
Result: Emitter Resistance = 100 Ω
Typical
Given: Thermal Voltage 0.6 V, Emitter Current 20 mA
Result: Emitter Resistance = 30 Ω
High range
Given: Thermal Voltage 0.9 V, Emitter Current 0.5 A
Result: Emitter Resistance = 1.8 Ω
Maximum range
Given: Thermal Voltage 9 V, Emitter Current 5 A
Result: Emitter Resistance = 1.8 Ω
Solving for each variable
Solve for Emitter Resistance
Thermal Voltage 10 mV, Emitter Current 100 µA → 100 Ω
Solve for Thermal Voltage
Emitter Resistance 1 Ω, Emitter Current 100 µA → 100 µV
Solve for Emitter Current
Emitter Resistance 1 Ω, Thermal Voltage 10 mV → 10 mA
How Emitter Resistance changes with Thermal Voltage
| Thermal Voltage (input) | Emitter Resistance (result) |
|---|---|
| 60 mV | 3 Ω |
| 150 mV | 7.5 Ω |
| 0.3 V | 15 Ω |
| 0.45 V | 22.5 Ω |
| 0.6 V | 30 Ω |
| 0.9 V | 45 Ω |
| 1.2 V | 60 Ω |
| 2.4 V | 120 Ω |
| 4.2 V | 0.21 kΩ |
| 6 V | 0.3 kΩ |
The same result in other units
| Unit | Value |
|---|---|
| mΩ | 30000 |
| Ω | 30 |
| kΩ | 0.03 |
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<p><a href="https://vbatpower.com/formulas/emitter-resistance-re/">Small-Signal Emitter Resistance</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Small-Signal Emitter Resistance?
Use re = VT / Ie (≈ 25 mV / Ie). With Thermal Voltage 0.6 V, Emitter Current 20 mA, Emitter Resistance works out to 30 Ω.
How do you calculate re = vt / ie small signal emitter resistance calculation?
Rearrange for Emitter Resistance: with Thermal Voltage 100 mV, Emitter Current 1 mA, Emitter Resistance is 100 Ω.
What is the formula for Small-Signal Emitter Resistance?
The formula is re = VT / Ie (≈ 25 mV / Ie). The intrinsic small-signal emitter resistance of a bipolar transistor is the thermal voltage divided by the DC emitter current.
How do you find Thermal Voltage when you know the other values?
Rearrange for Thermal Voltage: with Emitter Resistance 1 Ω, Emitter Current 100 µA, Thermal Voltage is 100 µV.
How do you find Emitter Current when you know the other values?
Rearrange for Emitter Current: with Emitter Resistance 1 Ω, Thermal Voltage 10 mV, Emitter Current is 10 mA.
What units does Small-Signal Emitter Resistance use?
Emitter Resistance is shown in mΩ, Ω, kΩ. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
All Discrete Amplifiers formulas →Need more features?
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