To calculate the drain current ($I_D$) of an MOSFET, we use the following formula for the saturation region of operation, neglecting the body effect and channel-length modulation (i.e., assuming that $\lambda = 0$):

$I_D = \frac{1}{2} K' \left( \frac{W}{L} \right) \left( V_{GS} - V_{th} \right)^2$

Where:

• $I_D$ is the drain current
• $K'$ is the process transconductance parameter ($K' = K_p$ for NMOS or PMOS, as given in your problem)
• $W$ is the width of the MOSFET
• $L$ is the length of the MOSFET
• $V_{GS}$ is the gate-source voltage
• $V_{th}$ is the threshold voltage of the MOSFET

Given:

• $W = 1.8 \, \mu m$
• $L = 0.6 \, \mu m$
• $K_p = 50 \, \mu A/V^2$ (This is the process transconductance parameter)

Step 1: Find the effective $K'$ for the MOSFET

Since $K_p = 50 \, \mu A/V^2$, this is the process transconductance parameter for the given MOSFET.

Step 2: Substitute the values in the drain current formula

We can substitute the values for $W$, $L$, $K_p$, $V_{GS}$, and $V_{th}$ into the equation to calculate the drain current. However, the values of $V_{GS}$ and $V_{th}$ are not provided in the problem. Typically, for such a question, if these values were provided, we could plug them into the formula to solve for $I_D$.

If you have values for $V_{GS}$ and $V_{th}$, please provide them, and I can continue the calculation. Alternatively, if this is a theoretical question and you want to see the steps with symbolic values, I can proceed accordingly.

Example:

Let’s assume some values for illustration:

• $V_{GS} = 2.0 \, V$
• $V_{th} = 0.5 \, V$

Step 3: Calculate the drain current

Substituting these values into the formula:

$I_D = \frac{1}{2} \times 50 \, \mu A/V^2 \times \left( \frac{1.8 \, \mu m}{0.6 \, \mu m} \right) \times (2.0 \, V - 0.5 \, V)^2$

$I_D = \frac{1}{2} \times 50 \times 3 \times (1.5)^2$

$I_D = 25 \times 3 \times 2.25$

$I_D = 168.75 \, \mu A$

So, the drain current is $I_D = 168.75 \, \mu A$ for this example.

Do you need more clarification on this, or would you like to discuss the role of each parameter in more detail?

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5 Related Questions:

1. How does the threshold voltage ($V_{th}$) affect the drain current in an MOSFET?
2. What happens if the MOSFET is operating in the linear region instead of saturation?
3. How does the channel length $L$ influence the drain current?
4. How do temperature and process variations affect the value of $K_p$ in MOSFETs?
5. What is the effect of body effect on the drain current in an MOSFET?

Tip: Always ensure that the MOSFET is in saturation mode before using the saturation current formula, as the behavior changes in different regions of operation.