To calculate the ratio $\frac{V_{t(sat)}}{V_{t(lin)}}$, where $V_{t(sat)}$ refers to the threshold voltage in the saturation region and $V_{t(lin)}$ refers to the threshold voltage in the linear region, we need to identify both values from the graph.

Key characteristics to note from the MOSFET curve:

• Linear Region: The MOSFET operates in the linear region when $V_D$ (Drain voltage) is low and the drain current ($I_D$) increases almost linearly with $V_D$.
• Saturation Region: The MOSFET enters saturation when $V_D$ becomes sufficiently large, beyond a certain point where $I_D$ becomes nearly constant for a fixed $V_G$ (Gate voltage).

Step-by-step approach:

1. Locate $V_{t(lin)}$: The linear region threshold voltage occurs at the point where the current starts to increase significantly with a small increase in $V_D$.
2. Locate $V_{t(sat)}$: The saturation region threshold voltage occurs at the point where the MOSFET transitions from the linear region to the saturation region. This can be approximated by the value of $V_D$ at which the curve flattens for each $V_G$.

From the graph:

• For $V_G = 3V$, $4V$, and $5V$, observe where the transition from the linear region to saturation occurs, i.e., where the current starts to plateau.

Let me analyze these regions and compute the ratio for you.The ratio of $\frac{V_{t(sat)}}{V_{t(lin)}}$ is approximately 15.0.

This means that the threshold voltage in the saturation region is 15 times larger than the threshold voltage in the linear region for this MOSFET.

Do you want more details or have any questions? Here are some related questions:

1. What is the role of threshold voltage in MOSFET operation?
2. How does the gate voltage affect MOSFET performance?
3. Can you explain the difference between the linear and saturation regions of a MOSFET?
4. How do different gate voltages influence the $I_D$-$V_D$ characteristics?
5. What factors affect the threshold voltage of a MOSFET?

Tip: The saturation region is typically used in amplification applications, while the linear region is more common in switching.