# NMOS Transistor Voltage Range For Specification?

I have a homework question I'm a little confused about. I was hoping for a point in the right direction. I am given the $K_n\prime$ $(400 \cdot 10^{-6} A/V^2)$ and threshold voltage (0.4V) for an NMOS transistor, and told it should operate as a variable resistor (for small $V_{DS}$) between 200 Ohms and 1K Ohms. I need to find the range of $V_{GS}$ (maximum $V_{GS}$ already given as 1.8V) and the required width of the channel, W, knowing the the minimum channel length L is $0.18 \times 10^{-6} m$.

My approach thusfar is as follows: I assume it's a reasonable assumption that small VDS means operation in the triode region, since my given threshold voltage is 0.4V. Also, I could use the given upper limit of $V_{GS}$ in finding the parameters I need. So:

$$I_D = K_n\prime \cdot \frac{W}{L}(V_{GS}-V_t)V_{DS} - \frac{{V_{DS}}^2}{2})$$

But that leaves me stuck. I don't know VDS, or the current. I thought my reasoning for triode operation made sense, but if it is instead in the saturation region, that would spare me finding VDS, but with still two unknowns of the width and the current.

I feel as if I need to use the resistance values given in some way, but as I have not done a similar example before, I'm not sure how to incorporate them.

Any help would be greatly appreciated!

• I've typeset the math with LaTeX to be more readable. Please check my work to be sure I didn't introduce any errors! – Phil Frost Jun 19 '13 at 14:25
• @PhilFrost, I think you dropped an "S" from the subscript of V_DS in the first term of rhs; I've added it in. – The Photon Jun 19 '13 at 16:22
• Sorry - I actually left that out myself in error. Not his fault. :p – Rome_Leader Jun 19 '13 at 16:25

$200 < \dfrac{V_{DS}}{I_D} < 1000$
$200 < \dfrac{\mathrm{d}V_{DS}}{\mathrm{d}I_D} < 1000$