Overview

We will calculate the value of Rb based on the following circuit:

Questions to Ask when Sizing

• Can your transistor handle the load through the collector? Does it exceed Ic(max)?
• Can the transistor handle supply voltage? Vcc > Vce (max) ?
• Find the worst case current gain during saturation. Ic
• Calculate the minimum base current. Ib
• Compare base current Ib max current your micro controller can deliver.
• Find worst case (highest) Vbe
• Calculate voltage drop across base resistor using Vbe and micro controller output
• Calculate required base resistor Rb.
• Calculate collector power dissipation.

Calculating the Rb Value

Calculations for Ic:

Ic = (Vcc-Vce)/RL = 11.3v/155Ω = 73 mA

Calculation for Vb

Vb = Vi - Vbe(sat) = 3.3 - 1.2 = 2.1v

Calculating using Ib=Ic/10 (*** Best Approach)

It is common to assume that base current is 1/10 of the collector current.

Ib = Ic/10 = 73/10 = 7.3mA  

Rb = Vb/Ib = 2.1/0.0073 = 288 Ω

Confirm: Can the micro controller deliver Ib current required?

Tested with 220 Ω and it worked.

Calculating using hFE

To guarantee that the transistor operates in the saturation region, we multiply the base current by a factor of three.

hFE=100 (@100mA)

Ib = Ic/Hfe = 73/100 = 0.73mA

Rb = Vb/Ibx3 = 2.1/(0.00073x3) =  959 Ω

This would be the max value for Rb.

Calculating using the online calculator

hFE=100

Rb = 960 Ω 

This would be the max value for Rb.

Formulas

Ic=(V-Vce)/RL

Ib=Ic/hFE

Rb=(Vi-Vbe)/(3*Ib)

References