Transistor Switch Base Resistor

Rb = (Vin − Vbe) · β / Ic

Quick answer

This calculator solves Rb = (Vin − Vbe) × β / Ic for Base Resistor. With Drive Voltage 12 V, Base-Emitter Voltage 26.4 V, Current Gain β 0.5, Collector Current 20 mA, the result is -0.36 kΩ. It solves in 5 directions, so you can enter the values you have and get the one you need.

Calculator

Base Resistor (kΩ)
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Formula

Rb = (Vin − Vbe) × β / Ic

Description

To use a bipolar transistor as a saturated switch, the base resistor must supply enough base current to fully turn it on for the required collector current. This formula sets Rb just at the edge of saturation; in practice designers use a smaller Rb (an overdrive factor of 2–10×) to guarantee hard saturation and a low collector voltage across part tolerances.

Variables

  • Rb — Base resistor (Ω)
  • Vin — Logic/drive high voltage (V)
  • Vbe — Base-emitter drop (~0.7 V)
  • β — Current gain at saturation
  • Ic — Required collector current (A)

Practical Notes

Use the guaranteed minimum (saturation) β, which is far lower than the active-region β. Dividing the computed Rb by an overdrive factor of ~3–5 ensures hard saturation and a low Vce(sat).

Symbols and units

Symbol Meaning Default unit Accepted units
Rb Base Resistor kΩ mΩ, Ω, kΩ, MΩ
Vin Drive Voltage V pV, nV, µV, mV, V, kV
Vbe Base-Emitter Voltage V pV, nV, µV, mV, V, kV
beta Current Gain β — —
Ic Collector Current mA pA, nA, µA, mA, A, kA

Step by step

  1. 1. What you know: Drive Voltage 12 V, Base-Emitter Voltage 26.4 V, Current Gain β 0.5, Collector Current 20 mA
  2. 2. The relation: Rb = (Vin − Vbe) × β / Ic
  3. 3. Substitute: Vin = 12 V, Vbe = 26.4 V, beta = 0.5, Ic = 20 mA
  4. 4. Result: Base Resistor = -0.36 kΩ

Related quantities from the same inputs

  • P = V × I = 0.24 W

Worked examples

Minimum range

Given: Drive Voltage 0.33 V, Base-Emitter Voltage 0.726 V, Current Gain β 0.025, Collector Current 100 µA

Result: Base Resistor = -99 Ω

Low range

Given: Drive Voltage 3.3 V, Base-Emitter Voltage 7.26 V, Current Gain β 0.25, Collector Current 1 mA

Result: Base Resistor = -0.99 kΩ

Typical

Given: Drive Voltage 12 V, Base-Emitter Voltage 26.4 V, Current Gain β 0.5, Collector Current 20 mA

Result: Base Resistor = -0.36 kΩ

High range

Given: Drive Voltage 0.23 kV, Base-Emitter Voltage 0.506 kV, Current Gain β 0.8, Collector Current 0.5 A

Result: Base Resistor = -0.4416 kΩ

Maximum range

Given: Drive Voltage 2.3 kV, Base-Emitter Voltage 5.06 kV, Current Gain β 8, Collector Current 5 A

Result: Base Resistor = -4.416 kΩ

Solving for each variable

Solve for Base Resistor

Drive Voltage 0.33 V, Base-Emitter Voltage 0.726 V, Current Gain β 0.025, Collector Current 100 µA → -99 Ω

Solve for Drive Voltage

Base Resistor 100 Ω, Base-Emitter Voltage 0.726 V, Current Gain β 0.025, Collector Current 100 µA → 1.126 V

Solve for Base-Emitter Voltage

Base Resistor 100 Ω, Drive Voltage 0.33 V, Current Gain β 0.025, Collector Current 100 µA → -70 mV

Solve for Current Gain β

Base Resistor 100 Ω, Drive Voltage 0.33 V, Base-Emitter Voltage 0.726 V, Collector Current 100 µA → -0.02525

Solve for Collector Current

Base Resistor 100 Ω, Drive Voltage 0.33 V, Base-Emitter Voltage 0.726 V, Current Gain β 0.025 → -99 µA

How Base Resistor changes with Drive Voltage

Drive Voltage (input) Base Resistor (result)
1.2 V -0.63 kΩ
3 V -0.585 kΩ
6 V -0.51 kΩ
9 V -0.435 kΩ
12 V -0.36 kΩ
18 V -0.21 kΩ
24 V -60 Ω
48 V 0.54 kΩ
84 V 1.44 kΩ
120 V 2.34 kΩ

The same result in other units

Unit Value
mΩ -360000
Ω -360
kΩ -0.36
MΩ -0.00036

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Frequently asked questions

How do you calculate Transistor Switch Base Resistor?

Use Rb = (Vin − Vbe) × β / Ic. With Drive Voltage 12 V, Base-Emitter Voltage 26.4 V, Current Gain β 0.5, Collector Current 20 mA, Base Resistor works out to -0.36 kΩ.

What is the formula for Transistor Switch Base Resistor?

The formula is Rb = (Vin − Vbe) × β / Ic. To use a bipolar transistor as a saturated switch, the base resistor must supply enough base current to fully turn it on for the required collector current.

How do you find Drive Voltage when you know the other values?

Rearrange for Drive Voltage: with Base Resistor 100 Ω, Base-Emitter Voltage 0.726 V, Current Gain β 0.025, Collector Current 100 µA, Drive Voltage is 1.126 V.

How do you find Base-Emitter Voltage when you know the other values?

Rearrange for Base-Emitter Voltage: with Base Resistor 100 Ω, Drive Voltage 0.33 V, Current Gain β 0.025, Collector Current 100 µA, Base-Emitter Voltage is -70 mV.

What units does Transistor Switch Base Resistor use?

Base Resistor is shown in mΩ, Ω, kΩ, MΩ. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

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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