From the given transfer characteristic of a transistor in CE configuration, the value of power gain of this configuration is \(10^{\mathrm{x}}\), for \(\mathrm{R}_{\mathrm{B}}=10 \mathrm{k} \Omega\), and \(\mathrm{R}_{\mathrm{C}}=1 \mathrm{k} \Omega\). The value of x is ______.

JEE Main · 2023 · 13 Apr 2023 · Shift 1 · Semiconductors

From the given transfer characteristic of a transistor in CE configuration, the value of power gain of this configuration is

1 0^{x}

, for

R_{B} = 10 k Ω

, and

R_{C} = 1 k Ω

. The value of x is ______.

Answer: 3

Power gain in a CE configuration is the product of voltage gain and current gain:

Power gain = A_{v} \times A_{i} = β \frac{R _{C}}{R _{B}} \times β = β^{2} \frac{R _{C}}{R _{B}}

From the transfer characteristic graph, the current gain

β

is:

β = \frac{Δ I _{C}}{Δ I _{B}} = \frac{( 20 - 10 ) \times 1 0 ^{- 3}}{( 200 - 100 ) \times 1 0 ^{- 6}} = \frac{10 \times 1 0 ^{- 3}}{100 \times 1 0 ^{- 6}} = 100

Power gain:

β^{2} \frac{R _{C}}{R _{B}} = (100)^{2} \times \frac{1 \times 1 0 ^{3}}{10 \times 1 0 ^{3}} = 1 0^{4} \times \frac{1}{10} = 1 0^{3}

Therefore,

x = 3

JEE Main · 2023 · 13 Apr 2023 · Shift 1 · Integer answer