How to calculate the transistor gain from vce & vbe

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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. (Hemera Technologies/Photos.com/Getty Images)

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.

Skill level:
Easy

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Instructions

  1. 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. 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. 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 and 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.

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