Problem Breakdown:

The MOSFET is operating in saturation, with the drain current ($I_D$) given by:

$I_D = K \cdot (V_{GS} - V_t)^2$

where:

• $K = 3.25 \, \text{mA/V}^2$,
• $V_t = 1 \, \text{V}$,
• $V_{GS} = 1.5 \, \text{V}$.

The transconductance ($g_m$) for a MOSFET in saturation is calculated as:

$g_m = \frac{\partial I_D}{\partial V_{GS}} = 2K \cdot (V_{GS} - V_t)$

Solution:

Step 1: Substitute the given values into the equation for $g_m$.

Using:

• $K = 3.25 \, \text{mA/V}^2$,
• $V_{GS} = 1.5 \, \text{V}$,
• $V_t = 1.0 \, \text{V}$,

we calculate:

$g_m = 2 \cdot 3.25 \cdot (1.5 - 1.0)$

$g_m = 2 \cdot 3.25 \cdot 0.5$

$g_m = 3.25 \, \text{mA/V}$

Final Answer:

$\boxed{g_m = 3.25 \, \text{mA/V}}$

Would you like me to provide further details or discuss related topics?

Related Questions:

1. How is transconductance used in determining amplifier performance?
2. What conditions are necessary for a MOSFET to operate in the saturation region?
3. Can $g_m$ change with varying $V_{GS}$? If so, how?
4. How does the value of $K$ influence the operation of the MOSFET?
5. What are the implications of a higher $g_m$ on circuit behavior?

Tip:

When working with MOSFETs in the saturation region, always verify the operating point (e.g., $V_{GS}$ and $V_t$) to ensure that the device is correctly biased.