Question

The Common Emitter amplifier has voltage gain equal to 300 and its input signal is \(0.5 \cos (100 t)\) volt. The output signal will be equal to (A) \(150 \cos (100 \mathrm{t})\) (B) \(300 \cos (100 \mathrm{t})\) (C) \(150 \cos (100 t+\pi)\) (D) \(300 \cos (100 t-\pi)\)

Short answer

The output signal will be equal to (A) \(150 \cos(100t)\).

Step-by-step solution

Write down the given values

We have the following information: - Voltage gain = 300 - Input signal = \(0.5 \cos(100t)\) V

Apply the voltage gain formula

Using the voltage gain formula, we can write: \( V_{output} = \text{voltage gain} \times V_{input} \)

Calculate the output signal

Now, we can plug in the given values to find the output signal: \( V_{output} = 300 \times 0.5 \cos(100t) = 150 \cos(100t) \)

Match the calculated output signal with the given options

The calculated output signal is \(150 \cos(100t)\), which corresponds to option (A). Hence, the output signal will be equal to: (A) \(150 \cos (100 \mathrm{t})\)

Key concepts

Voltage Gain

In an electronic circuit, voltage gain is a crucial concept, especially in amplifiers like the Common Emitter amplifier. Voltage gain represents how much the amplifier increases the amplitude of the input signal. It is simply the ratio of the output voltage to the input voltage.
For a Common Emitter amplifier, the voltage gain is often quite high, which is why it is widely used in applications like radios and other audio devices.
If you have a voltage gain of, say, 300, it means the output voltage will be 300 times the input voltage. This helps boost weak signals for further processing or output.

Input Signal

The input signal is what you initially have before amplification. In the context of the Common Emitter amplifier exercise, the input signal is given by the expression \(0.5 \cos(100t)\) volts.
This is a cosine function, commonly used to represent oscillating signals like sound waves or AC signals in electronics. Here, 0.5 is the amplitude, determining the height of the wave from its center position. The function \(\cos(100t)\) indicates that the signal is oscillating with a specific pattern over time.
Understanding the nature of the input signal ensures better grasp of what happens during amplification.

Output Signal

Once the input signal is amplified through the Common Emitter amplifier, you get the output signal. For this particular case, the amplification results in \(150 \cos(100t)\) volts.
This reflects the voltage gain applied to the input signal, producing a higher amplitude wave, as shown by the amplitude value increasing from 0.5 to 150. The output still maintains its original oscillating pattern denoted by \(\cos(100t)\), meaning the frequency remains unchanged, even though the amplitude has increased.
The result is a much stronger signal suitable for transmission or further processing.

Trigonometric Functions

Trigonometric functions like sine and cosine are pivotal in representing oscillating phenomena in electronics. In the given problem, \(\cos(100t)\) is used to model the periodic nature of the electrical signal.
Cosine functions are used because they describe smooth and continuous oscillations, which make them ideal for signals in circuits. Typical characteristics of trigonometric functions include their width (frequency) and height (amplitude).

• The frequency is determined by the coefficient of \(t\), here 100, which controls how fast the oscillations occur.
• Amplitude is shown by the number in front of the \(\cos\) function and indicates the strength or height of the waveform.

Understanding these functions facilitates the interpretation of how signals change, especially when analyzing amplified signals in electronics.