### BJT Common Emitter Amplifier Analysis**Problem Statement:**A BJT common emitter amplifier is analyzed using the small-signal T model with parameters \( \alpha \) and \( r_e \). Given:- \( \beta = 105 \)- \( R_e = 80 \, \Omega \)- \( g_m = 200 \, \text{mA/V} \)Determine the value of the small signal input resistance, \( R_{\text{in}} \), expressed in ohms.**Circuit Diagram:**The circuit consists of:- A transistor base at point B.- An input voltage \( v_i \).- An input current \( i_b \).- The main loop through the transistor is characterized by \(\alpha i_e \).- Emitter resistance \( r_e \).- An additional emitter resistor \( R_e \) connected to ground.- A collector current \( i_c \) flowing through a 4 kΩ resistor.**Analysis and Explanation:**To solve for \( R_{\text{in}} \), the following relationships and parameters will be essential:- \( \beta \), the current gain, relates the base current \( i_b \) to the collector current \( i_c \).- Transconductance \( g_m \), which is given as 200 mA/V, relates changes in emitter current to changes in base-emitter voltage.- The emitter resistor \( R_e \) influences the input resistance perceived at the base, especially when considering the feedback through the transistor.**Steps:**1. Use the small-signal model to express the base-emitter voltage in terms of the base current and resistances.2. Use relationships among \( \beta \), \( g_m \), and other given values to calculate \( R_{\text{in}} \).By understanding these relationships within a BJT common emitter amplifier and given parameters, the small signal input resistance can be accurately determined.

Answered: Image /qna-images/answer/a40e8175-bcf9-4973-8496-bbc1560fdd1b.jpg

A BJT common emitter amplifier is shown below using the small-signal T model with parameters x and little re. If beta = 105, big Re = 80 ohms, and gm = 200 mA/V, what is the value of the small signal input resistance, Rin, expressed in ohms? Rin 2) OE ai Re 4 ΚΩΣ

A BJT common emitter amplifier is shown below using the small-signal T model with parameters x and little re. If beta = 105, big Re = 80 ohms, and gm = 200 mA/V, what is the value of the small signal input resistance, Rin, expressed in ohms? Rin 2) OE ai Re 4 ΚΩΣ

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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### BJT Common Emitter Amplifier Analysis

**Problem Statement:**
A BJT common emitter amplifier is analyzed using the small-signal T model with parameters \( \alpha \) and \( r_e \). Given:
- \( \beta = 105 \)
- \( R_e = 80 \, \Omega \)
- \( g_m = 200 \, \text{mA/V} \)

Determine the value of the small signal input resistance, \( R_{\text{in}} \), expressed in ohms.

**Circuit Diagram:**

The circuit consists of:
- A transistor base at point B.
- An input voltage \( v_i \).
- An input current \( i_b \).
- The main loop through the transistor is characterized by \(\alpha i_e \).
- Emitter resistance \( r_e \).
- An additional emitter resistor \( R_e \) connected to ground.
- A collector current \( i_c \) flowing through a 4 kΩ resistor.

**Analysis and Explanation:**

To solve for \( R_{\text{in}} \), the following relationships and parameters will be essential:
- \( \beta \), the current gain, relates the base current \( i_b \) to the collector current \( i_c \).
- Transconductance \( g_m \), which is given as 200 mA/V, relates changes in emitter current to changes in base-emitter voltage.
- The emitter resistor \( R_e \) influences the input resistance perceived at the base, especially when considering the feedback through the transistor.

**Steps:**
1. Use the small-signal model to express the base-emitter voltage in terms of the base current and resistances.
2. Use relationships among \( \beta \), \( g_m \), and other given values to calculate \( R_{\text{in}} \).

By understanding these relationships within a BJT common emitter amplifier and given parameters, the small signal input resistance can be accurately determined.

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