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For the small signal circuit below, use Thevenin analysis to determine an expression for the input resistance (R). Note that "g" represents the gain for the current source.

For the small signal circuit below, use Thevenin analysis to determine an expression for the input resistance (R). Note that "g" represents the gain for the current source.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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**Determining Input Resistance Using Thevenin Analysis** **Objective:** For the small signal circuit shown, use Thevenin analysis to determine an expression for the input resistance (\(R_{in}\)). **Key Note:** - The variable “g” represents the gain for the current source. **Circuit Description:** - The circuit includes: - A resistor labeled \(R_{in}\), connected at the input. - A resistor \(R_C\) in series with a branch containing a parallel combination of: - A resistor \(R_B\) - A voltage source \(v_B\) - A dependent current source represented as \(g v_B\), connected in series with the parallel combination, where \(g\) is the gain factor. **Instructions:** Thevenin analysis is used to simplify a complex circuit into a simple equivalent circuit with a single voltage source and series resistance. In this context, it will help derive the expression for \(R_{in}\). To carry out Thevenin analysis: 1. **Identify the portion of the circuit to be analyzed** for finding \(R_{in}\). 2. **Remove the load** from the output if present. 3. **Determine the open-circuit voltage (Thevenin voltage)** at the terminals of interest. 4. **Find the equivalent resistance (Thevenin resistance)** by deactivating all independent sources and calculating the resistance between the terminals. By following these steps, you will deduce the expression for \(R_{in}\) in terms of the given components and the gain \(g\).
Transcribed Image Text:**Determining Input Resistance Using Thevenin Analysis** **Objective:** For the small signal circuit shown, use Thevenin analysis to determine an expression for the input resistance (\(R_{in}\)). **Key Note:** - The variable “g” represents the gain for the current source. **Circuit Description:** - The circuit includes: - A resistor labeled \(R_{in}\), connected at the input. - A resistor \(R_C\) in series with a branch containing a parallel combination of: - A resistor \(R_B\) - A voltage source \(v_B\) - A dependent current source represented as \(g v_B\), connected in series with the parallel combination, where \(g\) is the gain factor. **Instructions:** Thevenin analysis is used to simplify a complex circuit into a simple equivalent circuit with a single voltage source and series resistance. In this context, it will help derive the expression for \(R_{in}\). To carry out Thevenin analysis: 1. **Identify the portion of the circuit to be analyzed** for finding \(R_{in}\). 2. **Remove the load** from the output if present. 3. **Determine the open-circuit voltage (Thevenin voltage)** at the terminals of interest. 4. **Find the equivalent resistance (Thevenin resistance)** by deactivating all independent sources and calculating the resistance between the terminals. By following these steps, you will deduce the expression for \(R_{in}\) in terms of the given components and the gain \(g\).
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