Question

The input resistance of a silicon transistor is \(100 \Omega\). Base current is changed by \(40 \mu \mathrm{A}\) which results in a change in collector current by \(2 \mathrm{~mA}\). This transistor is used as a common emitter amplifier with a load resistance of \(4 \mathrm{~K} \Omega\). The voltage gain of the amplifier is : (1) 2000 (2) 3000 (3) 4000 (4) 1000

Short answer

The voltage gain of the amplifier is 2000.

Step-by-step solution

Determine Current Gain (\beta)

Calculate the current gain using the change in collector current (\triangle I_C = 2 \text{ mA}) and the change in base current (\triangle I_B = 40 \text{ }\text{\textmu A}).\[ \beta = \frac{\triangle I_C}{\triangle I_B} = \frac{2 \times 10^{-3} \text{ A}}{40 \times 10^{-6} \text{ A}} = 50 \]

Calculate Transconductance

Determine the transconductance (g_m) using the formula \[ g_m = \beta \times \frac{1}{R_{in}} \] Given input resistance ( R_{in} = 100 \text{ }\text{\textOmega}) and Beta (\beta = 50), calculate g_m .\[ g_m = 50 \times \frac{1}{100} = 0.5 \text{ } \text{A/V} \]

Calculate Voltage Gain

The voltage gain (A_v) of a common emitter amplifier can be calculated using the formula \[ A_v = g_m \times R_L \] where R_L is the load resistance (R_L = 4 \text{ } \text{k}\text{\textOmega} = 4000 \text{ }\text{\textOmega}). Substituting the values, calculate A_v .\[ A_v = 0.5 \times 4000 = 2000 \]

Key concepts

Transistor Amplifier

A transistor amplifier is an essential circuit in electronics used to amplify signals. Transistor amplifiers operate by taking in a small input signal and producing a larger output signal. They are widely used in audio, radio, and communication systems.

In this example, the transistor is set up in a common emitter configuration. This configuration is popular due to its high voltage gain and moderate input and output impedance. It is important to understand how the different components play a role in amplifying the signal:

• Transistor: Acts as the core amplifying device.
• Input resistance (R_in): Determines the ease with which the input signal can drive the transistor.
• Load resistance (R_L): Connected to the output, it influences the overall voltage gain of the amplifier.

By understanding these elements, you can effectively analyze and design transistor amplifiers for various applications.

Transconductance (g_m)

Transconductance (g_m) is a key parameter in transistor amplifiers, representing the relationship between the input voltage and the output current. It indicates how effectively the input signal controls the output current.

In the solution, transconductance is calculated using the current gain (β) and input resistance (R_in):

For a transistor with a given β and R_in, transconductance is given by:
ewlineewlineewlineewlineThe resulting transconductance indicates the extent to which the input base current can control the collector current. This factor is critical in determining the voltage gain of the amplifier.

Voltage Gain

Voltage gain (A_v) is a measure of how much the input voltage is amplified in a transistor amplifier. It is a crucial parameter for understanding the effectiveness of the amplification process.

In a common-emitter amplifier, the voltage gain is determined by the product of transconductance (g_m) and the load resistance (R_L):

Using these values, we calculate the voltage gain to be 2000. This means the input voltage is amplified 2000 times at the output.

• High Voltage Gain: Such high gain is beneficial in applications where weak signals need to be boosted significantly.
• Applications: These include microphone pre-amplifiers, radio frequency amplifiers, and other low-power signal amplification scenarios.

Understanding voltage gain helps in designing and utilizing amplifiers according to specific signal requirements. It ensures that the amplified signal maintains its integrity while meeting the desired amplification level.