Question

The input signal given to a CE amplifier having a voltage gain of 150 is $v_i = 2 \cos \Bigg(15t+\frac{\pi}{3}\Bigg)$ The corresponding output signal will be

• A. $2 \cos \Bigg(15t+\frac{5\pi}{6}\Bigg)$
• B. $300 \cos \Bigg(15t+\frac{4\pi}{3}\Bigg)$
• C. $300 \cos \Bigg(15t+\frac{\pi}{3}\Bigg)$
• D. $75 \cos \Bigg(15t+\frac{2\pi}{3}\Bigg)$

Answer 1

The Correct Option is B

To solve this problem, we must analyze the input and output signals of a Common Emitter (CE) amplifier.

1. The given input signal is v_i = 2 \cos \Bigg(15t+\frac{\pi}{3}\Bigg). The CE amplifier has a voltage gain of 150. This means that the amplitude of the output voltage will be 150 times the amplitude of the input voltage.

2. Calculate the output voltage amplitude:

   • The amplitude of the input voltage is 2.
   • Using the gain of 150, the amplitude of the output voltage is 150 \times 2 = 300.

3. The phase shift in a CE amplifier is 180 degrees, or \pi\ \text{radians}. Therefore, the phase of the output signal will be the phase of the input signal plus \pi.

4. Calculate the phase of the output signal:

   • The phase of the input signal is \frac{\pi}{3}.
   • Add the phase shift: \frac{\pi}{3} + \pi = \frac{\pi}{3} + \frac{3\pi}{3} = \frac{4\pi}{3}.

5. So the corresponding output signal is:

   • 300 \cos \Bigg(15t+\frac{4\pi}{3}\Bigg)

6. Thus, the correct answer is 300 \cos \Bigg(15t+\frac{4\pi}{3}\Bigg), matching the correct option given in the question.

In conclusion, the output signal is amplified by 300 with a phase shift of \frac{4\pi}{3}, which aligns with how a CE amplifier works.