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MOSFETs

The questions below are due on Friday May 08, 2020; 11:59:00 PM.
 
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A particular MOSFET has the measured i_D-v_{DS} characteristic shown below for a gate-source voltage of v_{GS} = 2.5 \text{ V}. Note that in the saturation region the curve is no longer horizontal but instead has a slope, implying some dependence on v_{DS}!

The straight dashed line and the measured data fall on top of one another for v_{DS} \geq 1\text{ V} and i_D \geq 10.8 \text{ mA}.

To better model the measured data, a new MOSFET model is proposed as shown below. This model contains the ideal model used in 6.002 in parallel with a drain-source resistance. You may remember that the ideal model provides iD∗ such that:

i_{D*} = \begin{cases} 0, & \text{for } 0\gt v_{GS}- V_T \\ 0.5K\left(v_{GS}-V_T\right)^2, & \text{for } v_{DS}\geq v_{GS}-V_T\geq 0\\ K\left(v_{GS}-V_T-v_{DS}/2\right)v_{DS}, &\text{for } v_{GS}-V_T\gt v_{DS} \\ \end{cases}

Assume the system has the following equivalent model in its saturation regime:

Given the measured data, determine values for the parameters K, V_T and R_{DS} that best describe the data.

R_{DS} = (in Ohms)

K = (in \text{A/V}^2)

V_T = (in Volts)

For v_{GS} = 2.5\text{ V}, at what value of v_{DS} will the MOSFET dissipate 70 \text{ mW}?

For power dissipation to be 70 mW, v_{DS} = (in Volts)