Common-Emitter Voltage Gain
Av = −Rc / re
Quick answer
This calculator solves Av = −Rc / re for Voltage Gain. With Collector Resistor 10 kΩ, Emitter Resistance 0.47 kΩ, the result is -21.28. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The voltage gain of an undegenerated common-emitter amplifier is the collector load resistance divided by the small-signal emitter resistance, with a minus sign because the stage inverts. Since re is set by bias current, the gain rises with collector resistance and bias current. Adding an external emitter resistor RE changes this to −Rc/(re+RE), trading gain for stability and linearity.
Variables
- Av — Voltage gain (negative = inverting)
- Rc — Collector load resistance (Ω)
- re — Small-signal emitter resistance (Ω)
Practical Notes
With an emitter degeneration resistor RE, Av ≈ −Rc/RE, which is stable and bias-independent. The undegenerated gain here is the maximum achievable but varies with temperature and current.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| Av | Voltage Gain | — | — |
| Rc | Collector Resistor | kΩ | mΩ, Ω, kΩ, MΩ |
| re | Emitter Resistance | Ω | mΩ, Ω, kΩ, MΩ |
Step by step
- 1. What you know: Collector Resistor 10 kΩ, Emitter Resistance 0.47 kΩ
- 2. The relation: Av = −Rc / re
- 3. Substitute: Rc = 10 kΩ, re = 0.47 kΩ
- 4. Result: Voltage Gain = -21.28
Worked examples
Minimum range
Given: Collector Resistor 100 Ω, Emitter Resistance 1 Ω
Result: Voltage Gain = -100
Low range
Given: Collector Resistor 1 kΩ, Emitter Resistance 10 Ω
Result: Voltage Gain = -100
Typical
Given: Collector Resistor 10 kΩ, Emitter Resistance 0.47 kΩ
Result: Voltage Gain = -21.28
High range
Given: Collector Resistor 100 kΩ, Emitter Resistance 4.7 kΩ
Result: Voltage Gain = -21.28
Maximum range
Given: Collector Resistor 1 MΩ, Emitter Resistance 47 kΩ
Result: Voltage Gain = -21.28
Solving for each variable
Solve for Voltage Gain
Collector Resistor 100 Ω, Emitter Resistance 1 Ω → -100
Solve for Collector Resistor
Voltage Gain -0.025, Emitter Resistance 1 Ω → 25 mΩ
Solve for Emitter Resistance
Voltage Gain -0.025, Collector Resistor 100 Ω → 4 kΩ
How Voltage Gain changes with Collector Resistor
| Collector Resistor (input) | Voltage Gain (result) |
|---|---|
| 1 kΩ | -2.128 |
| 2.5 kΩ | -5.319 |
| 5 kΩ | -10.64 |
| 7.5 kΩ | -15.96 |
| 10 kΩ | -21.28 |
| 15 kΩ | -31.91 |
| 20 kΩ | -42.55 |
| 40 kΩ | -85.11 |
| 70 kΩ | -148.9 |
| 100 kΩ | -212.8 |
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<p><a href="https://vbatpower.com/formulas/ce-voltage-gain/">Common-Emitter Voltage Gain</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Common-Emitter Voltage Gain?
Use Av = −Rc / re. With Collector Resistor 10 kΩ, Emitter Resistance 0.47 kΩ, Voltage Gain works out to -21.28.
What is the formula for Common-Emitter Voltage Gain?
The formula is Av = −Rc / re. The voltage gain of an undegenerated common-emitter amplifier is the collector load resistance divided by the small-signal emitter resistance, with a minus sign because the stage inverts.
How do you find Collector Resistor when you know the other values?
Rearrange for Collector Resistor: with Voltage Gain -0.025, Emitter Resistance 1 Ω, Collector Resistor is 25 mΩ.
How do you find Emitter Resistance when you know the other values?
Rearrange for Emitter Resistance: with Voltage Gain -0.025, Collector Resistor 100 Ω, Emitter Resistance is 4 kΩ.
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