Question

A n-p-n transistor is used in common emitter made in an amplifier it. A change of $40\mu \mathrm{A}$ in the base current changes the output current by $2\mathrm{mA}$ and $0.04\mathrm{V}$ in input voltage. If a load of $6\mathrm{k}\mathrm{\Omega }$ is used, then the voltage gain of the amplifier is (A) 100 (B) 200 (C) 300 (D) 400

Short answer

The voltage gain of the amplifier is 300 (C).

Step-by-step solution

Find the change in output voltage

Given the change in base current and change in output current, we can calculate the change in output voltage. When the load of $6\text{k}\mathrm{\Omega }$ is used, the change in output voltage can be found using Ohm's law, which states that the voltage across a resistor is equal to the product of the current and its resistance: ΔV_output = ΔI_output × R_load, where ΔI_output is the change in output current and R_load is the load.

Calculate the change in output voltage

Given ΔI_output = $2$ mA and R_load = $6$ kΩ, we can compute the change in output voltage: ΔV_output = ($2$ mA) × ($6$ kΩ) = $12$ V.

Determine the voltage gain

The voltage gain of an amplifier (A) is defined as the ratio of the change in output voltage to the change in input voltage: A = ΔV_output / ΔV_input We are given that the change in input voltage, ΔV_input is $0.04$ V. Now we can find the voltage gain: A = ($12$ V) / ($0.04$ V) = $300$. So, the voltage gain of the amplifier is 300 (C).

Key concepts

Voltage Gain

In the context of transistor amplifiers, voltage gain is a critical concept. Simply put, voltage gain is how much an amplifier can increase the amplitude of the input signal. It's a measure of amplification strength. The voltage gain (A) is calculated by taking the ratio of the output voltage change to the input voltage change. In formula terms, this is expressed as:
$$A=\frac{\mathrm{\Delta }{V}_{\text{output}}}{\mathrm{\Delta }{V}_{\text{input}}}.$$This formula shows that a higher gain means more amplification of the input voltage.

For example, if a small change in input voltage is greatly amplified at the output, the amplifier has high voltage gain. In the given exercise, applying this formula allowed us to determine that the amplifier had a voltage gain of 300. This indicates that the output voltage was increased 300 times the size of the input voltage change.

• This calculation is fundamental when designing or analyzing amplifier circuits.
• Understanding voltage gain helps in improving the performance and efficiency of electronic circuits.

Ohm's Law

Ohm's Law is a foundational principle in electronics and electrical engineering. It describes the relationship between voltage, current, and resistance in an electrical circuit:
$$V=I\times R,$$where $V$ is the voltage across the resistor, $I$ is the current flowing through the resistor, and $R$ is the resistance of the resistor.

In the context of this exercise, Ohm's Law was crucial for calculating the change in output voltage across a load resistor. Given the change in output current (ΔI_output = 2 \text{ mA}), and the load resistance (6 \text{k}Ω), we used Ohm's Law to find that the change in output voltage (ΔV_output) was 12 V:
$$\Delta V_{\text{output}}=\Delta I_{\text{output}}\times R_{\text{load}}=(2\text{ mA})\times (6\text{k}\mathrm{\Omega })=12\text{ V}.$$This step is essential for understanding how amplifiers work and how they can manipulate electrical signals.

• Ohm’s Law simplifies the analysis and design of circuits.
• It provides the necessary framework to calculate how different parameters change when others are modified.

Common Emitter Configuration

The common emitter configuration is one of the most widely used transistor amplifier settings. It offers a good balance of voltage gain and current gain, making it ideal for amplification purposes.

When an n-p-n transistor operates in the common emitter mode, the input signal is applied to the base-emitter junction, while the output is taken from the collector-emitter junction. This setup allows for significant amplification of the input signal.

Key advantages include:

• High voltage gain: A common emitter circuit can efficiently amplify small input signals to much larger output voltages.
• Good input-output phase relationship: The output voltage signal is inverted compared to the input, which can be beneficial in certain design scenarios.

This configuration is favored across various applications, from audio amplifiers to RF transmitters, owing to its flexibility and efficiency.
Understanding the common emitter configuration is pivotal for anyone looking to design or troubleshoot amplifiers in active electronic circuits.