BJT Modelling

Introduction

BJT Modelling is an essential concept in the field of Electronic Devices and Circuits. It involves the representation of Bipolar Junction Transistors (BJTs) using mathematical models, which allows engineers to analyze and design circuits with these devices. This topic explores the key concepts and principles of BJT Modelling, including the hybrid model, simplified model, common emitter with emitter resistor, high input impedance circuits, emitter follower, comparison of CB, CE, CC configurations, Darlington pair, bootstrapping, and cascode amplifier.

Key Concepts and Principles

Hybrid Model

The hybrid model is a commonly used model for BJT analysis. It represents the BJT as a combination of two-port networks, with input and output terminals. The hybrid parameters, also known as h-parameters, are used to describe the BJT's behavior in the hybrid model. These parameters include hfe (current gain), hie (input impedance), hre (output impedance), and hoe (reverse voltage gain).

The hybrid model can be derived by considering the small-signal equivalent circuit of the BJT and applying linear approximations. It is particularly useful for analyzing small-signal amplifiers and determining their voltage gain, input impedance, and output impedance.

Simplified Model

The simplified model is another commonly used model for BJT analysis. It simplifies the hybrid model by neglecting certain parameters that have minimal impact on circuit performance. The simplified model parameters include hfe (current gain), hie (input impedance), hre (output impedance), and hoe (reverse voltage gain).

The simplified model is easier to work with compared to the hybrid model, as it requires fewer calculations. It is often used in introductory circuit analysis and design.

Common Emitter with Emitter Resistor

The common emitter configuration with an emitter resistor is a widely used BJT amplifier circuit. It provides high voltage gain and good input-output isolation. The emitter resistor plays a crucial role in stabilizing the circuit by providing negative feedback.

To analyze the common emitter with emitter resistor circuit, the hybrid or simplified model can be used. The voltage gain, input impedance, and output impedance can be calculated using the appropriate model. The emitter resistor also affects the frequency response of the circuit.

High Input Impedance Circuits

BJTs can be used to design circuits with high input impedance, which is desirable in many applications. The common base and common gate configurations are commonly used for this purpose. These circuits provide high input impedance and low output impedance, making them suitable for impedance matching and buffering.

When compared to other configurations such as common emitter and common collector, high input impedance circuits have different voltage gain characteristics and input/output impedance values. The choice of configuration depends on the specific requirements of the circuit.

Emitter Follower

The emitter follower, also known as the common collector configuration, is a BJT amplifier circuit that provides unity voltage gain. It has high input impedance and low output impedance, making it suitable for impedance matching and buffering.

The voltage gain of the emitter follower is approximately 1, but it provides high current gain. It is commonly used as a buffer stage between high impedance sources and low impedance loads.

Comparison of CB, CE, CC Configurations

The common base (CB), common emitter (CE), and common collector (CC) configurations are three basic BJT amplifier configurations. Each configuration has different voltage gain characteristics, input impedance, and output impedance.

The CB configuration provides high voltage gain and low input impedance, making it suitable for impedance matching. The CE configuration provides moderate voltage gain and high input impedance, making it suitable for general-purpose amplification. The CC configuration provides low voltage gain and high output impedance, making it suitable for impedance matching and buffering.

The choice of configuration depends on the specific requirements of the circuit, such as voltage gain, input impedance, and output impedance.

Darlington Pair

The Darlington pair is a configuration that combines two BJTs to achieve high current gain. It is commonly used in applications where high gain amplification is required, such as audio amplifiers and power amplifiers.

The Darlington pair configuration provides high current gain and moderate voltage gain. It has high input impedance and low output impedance, making it suitable for impedance matching and buffering.

Bootstrapping

Bootstrapping is a technique used in BJT circuits to increase the input impedance of an amplifier. It involves using a capacitor to feed back a portion of the output signal to the input, effectively bootstrapping the input impedance.

Bootstrapping can be used to increase the input impedance of audio amplifiers and oscillators, allowing for better signal fidelity and stability.

Cascode Amplifier

The cascode amplifier is a configuration that combines two BJTs to achieve high voltage gain and high input impedance. It is commonly used in high frequency circuits, such as radio frequency amplifiers and mixers.

The cascode amplifier configuration provides high voltage gain and high input impedance. It has low output impedance, making it suitable for driving low impedance loads.

Step-by-Step Problem Solving

To understand the application of BJT modelling in circuit analysis, let's consider an example problem:

Problem: Design a common emitter amplifier with a voltage gain of 100 and an input impedance of 10 kΩ. The BJT has a current gain (hfe) of 100 and an input impedance (hie) of 1 kΩ.

Solution:

1. Determine the emitter resistor value (Re) using the desired voltage gain and the BJT's current gain:

Re = (hfe / (hfe + 1)) * (Rc / Av)

where Rc is the collector resistor and Av is the desired voltage gain.

1. Calculate the base resistor value (Rb) using the desired input impedance and the BJT's input impedance:

Rb = (hie / (hie + 1)) * (Re / Zi)

where Zi is the desired input impedance.

1. Choose appropriate values for Rc, Re, and Rb based on standard resistor values.

2. Analyze the circuit using the hybrid or simplified model to determine the voltage gain and input impedance.

Real-World Applications

BJT modelling is used in various real-world applications, including:

• Audio amplifiers: BJT amplifiers are commonly used in audio systems to amplify low-level audio signals.

• Power amplifiers: BJT amplifiers are used in power amplifiers to amplify high-power signals for driving loudspeakers.

• RF amplifiers: BJT amplifiers are used in radio frequency (RF) circuits to amplify RF signals for wireless communication.

• Oscillators: BJT circuits are used in oscillator circuits to generate continuous waveforms for various applications.

• Switching circuits: BJTs can be used as switches in digital circuits, where they can control the flow of current.

BJT modelling allows engineers to design and analyze these circuits, ensuring optimal performance and reliability.

Advantages and Disadvantages of BJT Modelling

Advantages of BJT modelling include:

• Accurate representation: BJT models provide an accurate representation of the transistor's behavior, allowing for precise circuit analysis and design.

• Versatility: BJT models can be used to analyze a wide range of circuit configurations and applications.

• Simplified analysis: BJT models simplify the analysis process by reducing complex transistor behavior to a set of parameters.

Disadvantages or limitations of BJT modelling include:

• Nonlinear behavior: BJTs exhibit nonlinear behavior, which can make circuit analysis and design more challenging.

• Temperature dependence: BJT parameters can vary with temperature, requiring additional considerations in circuit design.

• Limited frequency range: BJT models are typically valid within a certain frequency range, beyond which more complex models may be required.

Conclusion

BJT modelling is a fundamental concept in Electronic Devices and Circuits. It allows engineers to analyze and design circuits with BJTs, enabling the development of various electronic systems. By understanding the hybrid model, simplified model, common emitter with emitter resistor, high input impedance circuits, emitter follower, comparison of CB, CE, CC configurations, Darlington pair, bootstrapping, and cascode amplifier, engineers can effectively utilize BJTs in their designs and achieve desired circuit performance.

Summary

BJT Modelling is an essential concept in the field of Electronic Devices and Circuits. It involves the representation of Bipolar Junction Transistors (BJTs) using mathematical models, which allows engineers to analyze and design circuits with these devices. This topic explores the key concepts and principles of BJT Modelling, including the hybrid model, simplified model, common emitter with emitter resistor, high input impedance circuits, emitter follower, comparison of CB, CE, CC configurations, Darlington pair, bootstrapping, and cascode amplifier.

Analogy

An analogy to understand BJT Modelling is to think of BJTs as actors in a play. The BJT models are like scripts that describe the behavior and characteristics of the actors. Just as a director uses scripts to analyze and design the play, engineers use BJT models to analyze and design circuits. The hybrid model is like a detailed script that includes all the nuances and interactions between the actors, while the simplified model is like a summarized script that focuses on the main plot points. The different BJT configurations and techniques, such as common emitter with emitter resistor, high input impedance circuits, and bootstrapping, are like different acting techniques and stage setups that can be used to enhance the performance of the play.