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10 ΜΩ 20 ΜΩ ww +15 V i 2 ΚΩ 2 ΚΩ The NMOS in the circuit shown has the following parameters and is operating in the saturation region: Vtn = 0.5 V and kn' (W/L) = 0.2 mA/V² Determine the value of ID and VDS

10 ΜΩ 20 ΜΩ ww +15 V i 2 ΚΩ 2 ΚΩ The NMOS in the circuit shown has the following parameters and is operating in the saturation region: Vtn = 0.5 V and kn' (W/L) = 0.2 mA/V² Determine the value of ID and VDS

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
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### Circuit Analysis of NMOS Transistor in Saturation **Circuit Description:** The circuit diagram features an NMOS transistor with the following components: - A +15 V power supply connected to the drain through a 2 kΩ resistor. - The gate is connected to a voltage divider composed of a 10 MΩ resistor connected to the +15 V line and a 20 MΩ resistor connected to the ground. - The source terminal is grounded through another 2 kΩ resistor. **Given Parameters:** - Threshold Voltage (\( V_{tn} \)): 0.5 V - Transconductance parameter (\( k'_n \times \frac{W}{L} \)): 0.2 mA/V² **Objective:** Determine the values of: - Drain current (\( I_D \)) - Drain-source voltage (\( V_{DS} \)) **Analysis Approach:** To solve for \( I_D \) and \( V_{DS} \), the NMOS must be in the saturation region, which means: \[ V_{DS} \geq V_{GS} - V_{tn} \] Using the parameters provided, calculate: 1. The gate voltage (\( V_{GS} \)) using the voltage divider rule. 2. Use the NMOS saturation current equation to find \( I_D \): \[ I_D = \frac{1}{2} k'_n \left(\frac{W}{L}\right) (V_{GS} - V_{tn})^2 \] 3. Determine \( V_{DS} \) with the calculated \( I_D \). This analysis will help in understanding the operation and design of NMOS circuits in the saturation region.
Transcribed Image Text:### Circuit Analysis of NMOS Transistor in Saturation **Circuit Description:** The circuit diagram features an NMOS transistor with the following components: - A +15 V power supply connected to the drain through a 2 kΩ resistor. - The gate is connected to a voltage divider composed of a 10 MΩ resistor connected to the +15 V line and a 20 MΩ resistor connected to the ground. - The source terminal is grounded through another 2 kΩ resistor. **Given Parameters:** - Threshold Voltage (\( V_{tn} \)): 0.5 V - Transconductance parameter (\( k'_n \times \frac{W}{L} \)): 0.2 mA/V² **Objective:** Determine the values of: - Drain current (\( I_D \)) - Drain-source voltage (\( V_{DS} \)) **Analysis Approach:** To solve for \( I_D \) and \( V_{DS} \), the NMOS must be in the saturation region, which means: \[ V_{DS} \geq V_{GS} - V_{tn} \] Using the parameters provided, calculate: 1. The gate voltage (\( V_{GS} \)) using the voltage divider rule. 2. Use the NMOS saturation current equation to find \( I_D \): \[ I_D = \frac{1}{2} k'_n \left(\frac{W}{L}\right) (V_{GS} - V_{tn})^2 \] 3. Determine \( V_{DS} \) with the calculated \( I_D \). This analysis will help in understanding the operation and design of NMOS circuits in the saturation region.
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