The parameters of an n-channel MOSFET are k'n (μCox)=0.6 mA/V^2 and VT=0.8 V. The
drain current is 1 mA with applied voltages of VGS=1.4 V and VDS=4 V. What is the W/L value?

To find the W/L ratio of the n-channel MOSFET, we use the standard equation for the drain current in the saturation region of a MOSFET:

\[
I_D = \frac{k'_n}{2} \cdot \frac{W}{L} \cdot (V_{GS} - V_T)^2
\]

Where:
- \( I_D \) is the drain current,
- \( k'_n \) (or \( \mu C_{ox} \)) is the process transconductance parameter,
- \( V_{GS} \) is the gate-to-source voltage,
- \( V_T \) is the threshold voltage,
- \( W/L \) is the width-to-length ratio of the MOSFET.

Given values:
- \( I_D = 1 \, \text{mA} \),
- \( k'_n = 0.6 \, \text{mA/V}^2 \),
- \( V_{GS} = 1.4 \, \text{V} \),
- \( V_T = 0.8 \, \text{V} \).

### Step 1: Plug in the values into the equation
\[
1 \, \text{mA} = \frac{0.6 \, \text{mA/V}^2}{2} \cdot \frac{W}{L} \cdot (1.4 \, \text{V} - 0.8 \, \text{V})^2
\]
\[
1 \, \text{mA} = \frac{0.6}{2} \cdot \frac{W}{L} \cdot (0.6)^2
\]

### Step 2: Simplify
\[
1 \, \text{mA} = 0.3 \cdot \frac{W}{L} \cdot 0.36
\]
\[
1 \, \text{mA} = 0.108 \cdot \frac{W}{L}
\]

### Step 3: Solve for \( \frac{W}{L} \)
\[
\frac{W}{L} = \frac{1 \, \text{mA}}{0.108} \approx 9.26
\]

Thus, the W/L ratio of the MOSFET is approximately **9.26**.

Do you want further details or have any questions?

Here are 5 related questions to expand this topic:
1. What happens to the MOSFET current if the W/L ratio is increased?
2. How does \( V_{GS} \) affect the operating region of the MOSFET?
3. What are the differences between linear and saturation regions in MOSFET operation?
4. How does changing \( k'_n \) (process parameter) impact the MOSFET's performance?
5. How can one adjust the threshold voltage \( V_T \) in MOSFET design?

**Tip:** In MOSFET design, increasing the W/L ratio improves the drive strength, allowing for higher current at the same gate voltage.

The parameters of an n-channel MOSFET are k'n (μCox)=0.6 mA/V^2 and VT=0.8 V. The drain current is 1 mA with applied voltages of VGS=1.4 V and VDS=4 V. What is the W/L value?

Solve for the W/L ratio of an n-channel MOSFET with parameters k'n = 0.6 mA/V^2, VT = 0.8 V, VGS = 1.4 V, and ID = 1 mA. Learn how to apply the MOSFET drain current equation in the saturation region to determine the transistor's width-to-length ratio.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation