Given \(I_{E}(\mathrm{dc})=1.2 \mathrm{~mA}, \beta=120\), and \(r_{o}=40 \mathrm{k} \Omega\), sketch the following: a. Common-emitter hybrid equivalent model. b. Common-emitter \(r_{e}\) equivalent model. c. Common-base hybrid equivalent model. d. Common-base \(r_{e}\) equivalent model.

The common-emitter hybrid model is a representation of a transistor that helps in understanding and analyzing its behavior in a circuit. This model comprises a few key components, notably a controlled current source and output resistance.
In circuit analysis, the current source is defined by \( \beta i_{b} \), with \( \beta \) representing the transistor's current gain. The current source essentially replicates the transistor's capability to amplify the input current. Additionally, the model includes an output resistance, labeled as \( r_{o} \), which accounts for the output characteristics of the transistor, affecting how it interacts with the rest of the circuit.

• To determine the base current \( i_{b} \) in the model, one must divide the DC emitter current, \( I_{E}(\mathrm{dc}) \), by \( \beta+1 \) due to the relationship between the base, emitter, and collector currents in a transistor.
• The given parameters, such as \( I_{E}(\mathrm{dc}) \) and \( r_{o} \) are plugged into the model to fully depict the transistor's behavior in a common-emitter configuration.

This model is essential for students as it provides a visual and conceptual tool to predict the performance of the common-emitter amplifier, which is a fundamental configuration in electronics.

Moving onto the common-emitter \( r_{e} \) equivalent model, it's a simplified approach that uses a resistor and a voltage source to mimic the transistor's operation. This model focuses on the transistor's input characteristics and is particularly helpful in low-frequency analysis.

• The resistance \( r_{e} \) signifies the dynamic resistance at the emitter junction, calculated as \( 26mV/I_{E_{(ma)}} \)—with 26mV being the thermal voltage at room temperature.
• For this exercise, given the emitter current \( I_{E}(\mathrm{dc}) \) is 1.2 mA, you would use this value to find \( r_{e} \) by dividing 26mV by the current in mA.

Understanding the \( r_{e} \) model is vital because it simplifies the analysis and design of transistor circuits, particularly when exploring the input impedance or voltage gain. It allows students to connect real transistor behavior to a manageable figure of merit.

Shifting our focus to the common-base hybrid equivalent model, we encounter a modified version of the common-emitter hybrid model. This configuration is less common but insightful for specific circuit applications.

• It typically involves a current source based on \( I_{C} = \beta I_{B} \), reflecting the relationship between collector and base currents.
• The common-base model is characterized by a different kind of current amplification, one that compares the collector current to the input base current.

In transistor circuit analysis, selecting the common-base configuration might be advantageous for certain performance aspects, such as input-output isolation or high-frequency operation. Students can benefit from understanding the common-base model, as it rounds out their grasp of how transistors can be employed within electronic circuits.

Lastly, transistor circuit analysis is a culmination of understanding and applying various transistor models to solve and design electronic circuits. It involves a multitude of considerations, from DC biasing to signal amplification, and how these functionalities are affected by different transistor parameters and configurations.

• Analyzing a transistor circuit might require calculating values such as input and output impedances, current and voltage gains, and frequency response.
• Tools like the common-emitter \( r_{e} \) model or common-base hybrid model offer a structured path to extract these values by replacing the transistor with an equivalent circuit.

For students, grasping transistor circuit analysis is crucial as it integrates theoretical knowledge with practical application. It enables them to predict circuit behavior, troubleshoot issues, and innovate designs, forming the bedrock of electronic engineering and related fields.