The working of a transistor as an amplifier is one of the most important aspects to study because as an amplifier it can manipulate the electrical signals.

Introduction

Transistors are fundamental building blocks in modern electronics, serving diverse roles, including switching and amplification. Their ability to amplify weak input signals into stronger output signals makes them crucial in circuits such as radios, audio systems, and communication devices.

Understanding how transistors operate as amplifiers is critical for anyone delving into electronic circuit design or analysis.

Transistors as Amplifiers

Transistors are essential components in many electronic circuits, acting primarily as amplifiers. They receive a weaker electronic signal and convert that into a stronger phase-shifted electronic signal.

Circuit Analysis

A basic transistor voltage amplifier circuit, as shown in the figure, operates as follows:

Biasing

In the transistor, there are two types of junctions between the three terminals.

1. Base-Emitter Junction: This junction is forward-biased by the battery $V_{BB}$ .

2. Collector-Base Junction: This junction is reverse-biased by the battery $V_{CC}$ .

Input and Output

The circuit, typically, is provided with an input signal at the base side for a common base or emitter amplifier, and an amplified output is obtained at the collector side. These are represented as,

Input Voltage = $V_{\text{in}}$
Output Voltage = $V_{\text{out}}$

Key Parameters

Some key parameters need to be discussed to understand the functioning of the transistor.

Base Current $\left( I_B \right)$

There is a small current that flows from the base to the emitter of the transistor and is given as,

$I_B = \frac{V_{BE}}{r_e}$ … (1)

Here,

$r_e$ = base-emitter resistance
$V_{BE}$ = potential drop across $r_e$

Base-Emitter Resistance $\left( r_e \right)$

It is defined as,

“the dynamic resistance of the base-emitter junction of a transistor when operating in the active region.”

It represents the change in base-emitter voltage $\left( V_{BE} \right)$ for a small change in emitter current $\left( I_E \right)$ .

Mathematical Formulation

Mathematically, it is given as,

$r_e = \frac{\Delta V_{BE}}{\Delta I_E}$

In small-signal analysis, $\left( r_e \right)$ is given as an approximate value,

$r_e = \frac{kT}{qI_E}$

Here,

$k = \text{Boltzmann's constant } \left( 1.38 \times 10^{-23} J\cdotK^{-1} \right)$
$T = \text{absolute temperature in kelvins } \left( K \right)$
$q = \text{charge of an electron } \left( 1.6 \times 10^{-19} C \right)$
$I_E = \text{DC emitter current in amperes}$

This resistance arises due to the exponential nature of the current-voltage relationship of the base-emitter junction. It is a key parameter in determining the gain and impedance of transistor amplifiers.

Collector Current $\left( I_C \right)$

A large amount of current is drawn into the collector of the transistor and is given as,

$I_C = \beta \cdot I_B$ … (1)

Here, $\beta$ is the current gain of the transistor.

Output Voltage ( $V_out$ )

The magnitude of the output voltage can be found using Kirchhoff’s Voltage Law (KVL) in the output loop. It is given as,

$V_{\text{CC}} = V_C + V_\text{CE}$

$V_{\text{CC}} = I_C \cdot R_C + V_\text{CE}$

$V_{CE} = V_{CC} - I_C \cdot R_C$

$V_{\text{out}} = V_{CC} - I_C \cdot R_C$ … (1)

Substitute the value of $I_C$ ,

$V_{\text{out}} = V_{CC} - \beta \cdot I_B \cdot R_C$

Now, substituting the value of $I_B$ ,

$V_{\text{out}} = V_{CC} - \beta \cdot \frac{V_{BE}}{r_e} \cdot R_C$

$V_{\text{out}} = V_{CC} - \beta \cdot V_{BE} \cdot \left( \frac{R_C}{r_e} \right)$ … (2)

Small-Signal Analysis

When a small input signal ( $\Delta V_{\text{in}}$ ) is applied, the following incremental changes take place.

1. Input Voltage

$V_{BE} \to V_{BE} + \Delta V_{\text{BE}}$

Since,

$\Delta V_{\text{in}} \approx \Delta V_{\text{BE}}$

So,

$V_{BE} \to V_{BE} + \Delta V_{\text{in}}$

2. Base Current

$I_B \to I_B + \Delta I_B$

3. Collector Current

$I_C \to I_C + \Delta I_C$

4. Output Voltage

$V_{\text{out}} \to V_{\text{out}} + \Delta V_{\text{out}}$

Voltage Gain $\left( A_V \right)$

It is defined as,

“the ratio between output voltage to the input voltage of a transistor.”

Mathematically, it is given as,

$A_v = \frac{\Delta V_{\text{out}}}{\Delta V_{\text{in}}}$ … (i)

Determination of Voltage Gain in Terms of Current Gain

To derive the voltage gain, relationships between small-signal changes are also analysed.

METHOD I

Considering the incremental changes, the equation (2) can be transformed as,

$V_{\text{out}} + \Delta V_{\text{out}} = V_{CC} - \beta \cdot \left( V_{BE} + \Delta V_{\text{in}} \right) \cdot \left( \frac{R_C}{r_e} \right)$

$V_{\text{out}} + \Delta V_{\text{out}} = V_{CC} - \beta \cdot \left( \frac{R_C}{r_e} \right) \cdot V_{BE} - \beta \cdot \left( \frac{R_C}{r_e} \right) \cdot \Delta V_{\text{in}}$ … (3)

Subtracting equation (2) from equation (3) we get,

$\Delta V_{\text{out}} = - \beta \cdot \left( \frac{R_C}{r_e} \right) \cdot \Delta V_{\text{in}}$ … (4)

Here, the negative sign indicates a voltage drop across the resistor $R_C$ . Now, rearranging the equation (4) we get,

$\frac{\Delta V_{\text{out}}}{\Delta V_{\text{in}}} = - \beta \cdot \left( \frac{R_C}{r_e} \right)$

$A_V = - \beta \cdot \left( \frac{R_C}{r_e} \right)$ … (5)

Deduction

The value of $A_V$ is of the order of hundreds, indicating that the input voltage has been amplified. Additionally, a negative sign indicates that the output voltage has $180^\circ$ phase shift as compared to the input voltage.

METHOD II

1. Relationship between $\Delta V_{\text{in}}$ and $\Delta I_B$

For a small change in $\Delta V_{\text{BE}}$ , there is a corresponding small change in $\Delta I_B$ . It is given as,

$\Delta V_{\text{BE}} = \Delta I_B \cdot r_e$

$\Delta I_B = \frac{\Delta V_{\text{BE}}}{r_e}$

We can also write it as,

$\Delta I_B = \frac{\Delta V_{\text{in}}}{r_e}$

2. Relationship Between $\Delta I_B$ and $\Delta I_C$

From the definition of current gain, we know that $\Delta I_B$ and $\Delta I_C$ can be related as follows,

$\Delta I_C = \beta \cdot \Delta I_B$

3. Relationship Between $\Delta I_C[latex] and [latex]\Delta V_{\text{out}}$

Due to an incremental increase in input voltage, there is an incremental increase in output voltage which results in an incremental increase in collector current. It is given by,

$\Delta V_{\text{out}} = -R_C \cdot \Delta I_C$

Here, the negative sign indicates a voltage drop across the resistor.

4. Complete Voltage Gain Derivation

Substitute $\Delta I_B$ into $\Delta I_C$ ,

$\Delta I_C = \beta \cdot \left( \frac{\Delta V_{\text{in}}}{r_e} \right)$

Substitute $\Delta I_C$ into $\Delta V_{\text{out}}$ ,

$\Delta V_{\text{out}} = -R_C \cdot \left( \beta \cdot \frac{\Delta V_{\text{in}}}{r_e} \right)$

Substitute $\Delta V_{\text{out}}}$ into equation (i),

$A_v = \frac{-R_C \cdot \left( \beta \cdot \frac{\Delta V_{\text{in}}}{r_e} \right)}{\Delta V_{\text{in}}}$

$A_v = - \beta \cdot \frac{R_C}{r_e}$

Deduction

This expression shows that the voltage gain is directly proportional to the current gain of the transistor $\left( \beta \right)$ and the collector resistance $\left( R_C \right)$ , while being inversely proportional to the base-emitter resistance $\left( r_e \right)$ .

Conclusion

Transistors enable the manipulation of weak signals into powerful outputs. By understanding the underlying principles of biasing, small-signal analysis, and voltage gain, engineers can design efficient circuits tailored to specific applications.

The precision with which transistors amplify signals demonstrates their versatility and importance in the world of electronics. As technology advances, the fundamental concepts of transistor amplifiers continue to play a vital role in driving innovation across industries, from communications to computing and beyond.

Frequently Asked Questions (FAQs)

Write the working of a transistor as an amplifier.

A transistor as an amplifier can increase the strength of a weak input electrical signal into a stronger output electrical signal.

How does biasing affect transistor amplifiers?

Biasing ensures the transistor operates in the active region, allowing it to amplify signals effectively without distortion.

What is the role of base-emitter resistance $\left( r_e \right)$ in amplification?

Base-emitter resistance determines the relationship between small changes in input voltage and emitter current, affecting the transistor’s gain.

What does the current gain $\left( \beta \right)$ signify in a transistor amplifier?

The current gain represents the ratio of collector current to base current, showing how much the input current is amplified.

Why is there a phase shift in the output of a transistor amplifier?

The negative sign in the voltage gain equation indicates a $180^\circ$ phase shift between the input and output signals.

What is the formula for voltage gain in a transistor amplifier?

Voltage gain is given by $A_V = - \beta \cdot \left( \frac{R_C}{r_e} \right)$ , showing its dependence on current gain, collector resistance, and base-emitter resistance.

How does temperature affect transistor amplifiers?

Temperature changes can alter the base-emitter resistance $\left( r_e \right)$ and current flow, impacting the performance of the amplifier.

How is output voltage calculated in a transistor amplifier?

The output voltage is derived using Kirchhoff’s Voltage Law, accounting for the collector resistance and current.

What are the common applications of transistor amplifiers?

Transistor amplifiers are widely used in audio systems, radio frequency circuits, communication devices, and signal processing systems.

Working of a Transistor as an Amplifier | 101 Easy Guide

Table of Contents

Introduction

Transistors as Amplifiers

Circuit Analysis

Biasing

Input and Output

Key Parameters

Base Current $\left( I_B \right)$

Base-Emitter Resistance $\left( r_e \right)$

Mathematical Formulation

Collector Current $\left( I_C \right)$

Output Voltage ( $V_out$ )

Small-Signal Analysis

Voltage Gain $\left( A_V \right)$

Determination of Voltage Gain in Terms of Current Gain

Deduction

1. Relationship between $\Delta V_{\text{in}}$ and $\Delta I_B$

2. Relationship Between $\Delta I_B$ and $\Delta I_C$

3. Relationship Between $\Delta I_C[latex] and [latex]\Delta V_{\text{out}}$

4. Complete Voltage Gain Derivation

Deduction

Conclusion

Frequently Asked Questions (FAQs)

Write the working of a transistor as an amplifier.

How does biasing affect transistor amplifiers?

What is the role of base-emitter resistance $\left( r_e \right)$ in amplification?

What does the current gain $\left( \beta \right)$ signify in a transistor amplifier?

Why is there a phase shift in the output of a transistor amplifier?

What is the formula for voltage gain in a transistor amplifier?

How does temperature affect transistor amplifiers?

How is output voltage calculated in a transistor amplifier?

What are the common applications of transistor amplifiers?

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