Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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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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