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The relation between alpha and beta of a...

The relation between `alpha` and `beta` of a transistor is

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The dc common-base current ratio or current gain `(alpha_(dc))` is defined as the ratio of the collector current `(I_(C))` to the emitter current `(I_(E)).`
`alpha_(dc)=(I_(C))/(I_(E))`
The dc common-emitter current ratio or current gain `(beta_(dc))` is defined as the ratio of the collector current to the base current `(I_(B)).`
`beta_(dc)=(I_(C))/(I_(B))`
Since the emitter current `I_(E)=I_(B)+I_(C)`,
`(I_(E))/(I_(C))=(I_(B))/(I_(C))+1`
`therefore (1)/(alpha_(dc))=(1)/(beta_(dc))+1`
Therefore, the common-base current gain in terms of the common-emitter current gain is `alpha_(dc)=(beta_(dc))/(1+beta_(dc))`
Or, the common-emitter gain in terms of the common-base current gain is `beta_(dc)=(alpha_(dc))/(1-alpha_(dc))`
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Knowledge Check

  • The alpha and beta of a transistor are always

    A
    `alpha gt 1, beta lt 1`
    B
    `alpha lt 1, beta gt 1`
    C
    `alpha = beta`
    D
    `alpha beta = 1`

  • The relationship between alpha and beta is given by

    A
    `alpha = beta`
    B
    `alpha = 1/beta`
    C
    `alpha = beta/1+beta`
    D
    `beta = alpha/1+ alpha`

  • The relationship between alpha and beta is given by

    A
    `alpha=beta`
    B
    `alpha=1/(beta)`
    C
    `beta=(alpha)/(1-alpha)`
    D
    `beta=(alpha)/(1+alpha)`

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