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Chapter 10: Problem 11

If the \(f_{1}\) of the trimsistor used in a certain amplifier is 75 MHz and the bendwidth is \(10 \mathrm{MHz}\). the voltage gain must be (a) 750 (b) \(7.5\) (c) 10 (d) 1

Short Answer

Expert verified
The voltage gain of the given transistor used in this amplifier is 75. Therefore, the correct answer is (b).

Step by step solution

01

Gain-Bandwidth Product Formula

The gain-bandwidth product (GBP) formula relates the voltage gain (A_v), the current gain, and the bandwidth (BW) of an amplifier. The formula is given by: \[A_v * BW = GBP\] With the given values, we can find the voltage gain (A_v).
02

Calculate the Gain-Bandwidth Product

We are given the frequency at which the current gain is unity (\(f_{1}\)) as 75 MHz and the bandwidth as 10 MHz. Using these values, we can find the GBP: \[GBP = f_{1} * BW = 75 * 10^6 * 10 * 10^6 = 750 * 10^{12}\]
03

Calculate the Voltage Gain using GBP

We know that: \[A_v * BW = GBP\] Now, we can find the voltage gain (A_v) by dividing the GBP by the bandwidth: \[A_v = \frac{GBP}{BW} = \frac{750 * 10^{12}}{10 * 10^6}\] \[A_v = 75\] So, the voltage gain of the given transistor used in this amplifier is 75. Therefore, the correct answer is (b).

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