The input signal given to a CE amplifier having a voltage gain of 150 is `V_(1) = 2cos(15t + pi/3)`. The corresponding output signal will be

Options

A. `300cos(15t + 4pi/3)`
B. `300 co(15t + pi/3)`
C. `75 cos(15t + 2pi/3)`
D. `2cos(15t + 5pi/6)`

Answer

To solve the problem, we need to determine the output signal of a common emitter (CE) amplifier given the input signal and the voltage gain. Let's break it down step by step.

### Step 1: Identify the Input Signal and Voltage Gain
The input signal is given as:
\[ V_{in} = 2 \cos(15t + \frac{\pi}{3}) \]
The voltage gain (A) of the amplifier is given as:
\[ A = 150 \]

### Step 2: Calculate the Maximum Output Voltage
The maximum value of the input voltage, \( V_{in(max)} \), is the amplitude of the input signal, which is 2V. The maximum output voltage can be calculated using the formula:
\[ V_{out(max)} = A \times V_{in(max)} \]
Substituting the values:
\[ V_{out(max)} = 150 \times 2 = 300V \]

### Step 3: Determine the Phase Shift
In a common emitter amplifier, there is a phase shift of \( \pi \) (or 180 degrees) between the input and output signals. Therefore, if the input signal has a phase of \( \frac{\pi}{3} \), the output signal will have a phase of:
\[ \text{Phase of } V_{out} = \text{Phase of } V_{in} + \pi = \frac{\pi}{3} + \pi = \frac{\pi}{3} + \frac{3\pi}{3} = \frac{4\pi}{3} \]

### Step 4: Write the Output Signal
Now, we can express the output signal using the maximum output voltage and the phase shift:
\[ V_{out} = V_{out(max)} \cos(15t + \text{Phase of } V_{out}) \]
Substituting the values we found:
\[ V_{out} = 300 \cos(15t + \frac{4\pi}{3}) \]

### Final Output
Thus, the corresponding output signal is:
\[ V_{out} = 300 \cos(15t + \frac{4\pi}{3}) \]