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A common emitter amplifier has a voltage gain of 50, an input impedance of $100\,\Omega$ and an output impedance of $200\,\Omega$. The power gain of the amplifier is
A
1000
B
1250
C
100
D
500
Detailed Solution
Voltage gain $= \beta \times$ impedance (resistance) gain $= \beta \times \dfrac{R_{out}}{R_{in}}$
$50 = \beta \times \dfrac{200}{100} = 2\beta$
$\Rightarrow \beta = 25$ (current gain)
Power gain $= \beta^2 \times \dfrac{R_{out}}{R_{in}}$
$= (25)^2 \times \dfrac{200}{100} = 625 \times 2$
$= 1250$
Check: power gain = voltage gain $\times$ current gain $= 50 \times 25 = 1250$.
$50 = \beta \times \dfrac{200}{100} = 2\beta$
$\Rightarrow \beta = 25$ (current gain)
Power gain $= \beta^2 \times \dfrac{R_{out}}{R_{in}}$
$= (25)^2 \times \dfrac{200}{100} = 625 \times 2$
$= 1250$
Check: power gain = voltage gain $\times$ current gain $= 50 \times 25 = 1250$.