How to Calculate the Transistor Gain From VCE & VBE

The gain of a transistor can be determined using the Alpha and Beta parameters of the transistor.

In order to calculate the gain of a transistor, it must be used as an amplifier in a circuit. The gain of a transistor is determined by its configuration. The Common Base Configuration results in a voltage gain but no current gain. The Common Collector configuration has a current gain but no voltage gain. The Common Emitter configuration has both a current gain and the voltage gain. When determining the voltage or the current gain of a transistor, the voltage across the Base and Emitter (VBE) of the transistor as well as the voltage across the Collector and the Emitter (VCE) are used.

Instructions

1. Determine the ratio of the Collector current (Ic) to the Base current (Ib) using the formula below:

   Ic / Ib

   This ratio is designated using the Beta sign ( β). The Base and Collector currents can be determined by use of the base resistor (Rb) and the load resistors (RL) respectively, and the Ohm's Law below:

   V = I / R

   Ib = Vb / Rb

   Ic = Vcc / RL

   Where:

   Vb = Voltage supplied across the Base Emitter junction

   Vcc = Supply voltage across the load resistor and the Emitter terminal

2. Determine the current gain of the transistor using the Collector current (Ic) and the Emitter current (Ie) using the formula below:

   Ic / Ie

   This ratio is designated with the Alpha symbol (α) and is usually a function of the transistor itself. The large collector current and the small base current usually results in a value of the alpha α being very close to unity and will generally lie close to 0.99.

3. Combine the α and the β parameters to determine the current flow and gain of the transistor as shown below:

   Alpha α = β / β + 1 β = α / α + 1

   If α = 0.99 then β = 0.99 / 0.01 = 99

Tips & Warnings

• Notice that the Beta β value has no units and is usually taken as a ratio.

• Theoretically, in a non-resistive circuit, the Emitter current can also be found using the formula below:

• Ie = Ib + Ic

• In an NPN transistor, the Base Emitter voltage (Vbe) is positive to the Base and the Collector Emitter voltage ( Vce) is positive with respect to the Emitter.

• For standard transistors, the Beta gain is generally between 50-200 and for high current power transistors, the range varies anywhere from 20-1000.

References

• Electronics-Tutorials: Bipolar Transistor
• Electronics-Tutorials: The NPN Transistor

Resources

• Read this Article in Spanish
• VicPhysics; VCE Physics -- Electronics and Photonics; The NPN Transistor Voltage Amplifier