An n-channel MOSFET is connected as shown in the Figure.
Assume $V_{TH} = 1\text{ V}$, $V_{DD} = 5\text{ V}$, and $\mu C_{ox}\left(\frac{W}{L}\right) = 2\text{ mA V}^{-2}$ and neglect channel length modulation effects.
The gate voltage ($V_G$) of the n-channel MOSFET (in Volt) is __.
(rounded off to two decimal places)
To find the gate voltage \( V_G \) of the n-channel MOSFET, we start by analyzing the circuit. The MOSFET is in saturation since it's connected as a source follower with \( V_{DD} > V_{TH} \). The current equation in saturation is:
\[ I_D = \frac{1}{2}\mu C_{ox}\left(\frac{W}{L}\right)(V_{GS} - V_{TH})^2 \]
Here, the drain current (\( I_D \)) through the 1 kΩ resistor can be calculated as:
\[ I_D = \frac{V_{DD} - V_G}{1 \, \text{k}\Omega} \]
Equating both expressions for \( I_D \):
\[\frac{V_{DD} - V_G}{1 \, \text{k}\Omega} = \frac{1}{2} \cdot 2 \, \text{mA/V}^2 \cdot (V_G - V_{TH})^2\]
\[V_{DD} - V_G = (V_G - V_{TH})^2\]
Substitute \( V_{DD} = 5 \, \text{V} \) and \( V_{TH} = 1 \, \text{V} \):
\[5 - V_G = (V_G - 1)^2\]
Expanding and simplifying:
\[5 - V_G = V_G^2 - 2V_G + 1\]
\[V_G^2 - V_G - 4 = 0\]
Using the quadratic formula \( V_G = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 1 \), \( b = -1 \), \( c = -4 \):
\[V_G = \frac{1 \pm \sqrt{1 + 16}}{2}\]
\[V_G = \frac{1 \pm \sqrt{17}}{2}\]
Since \( \sqrt{17} \approx 4.12 \):
\[V_G = \frac{1 \pm 4.12}{2}\]
Calculating the positive root (ensures \( V_{GS} > V_{TH} \)):
\[V_G = \frac{5.12}{2} = 2.56 \, \text{V}\]
Thus, the computed \( V_G \) of 2.56 V falls within the expected range of 2.5 to 2.6 V.
Important Questions from MOSFET
- A semiconductor uses P-type substrates with $N_A = 5 \times 10^{15}cm^{-3}$ in an n-MOS device having depletion region width of 0.415 $\mu$m. What is the depletion charge in magnitude?
- MOSFETs exhibit a non-linear relationship between input voltage and output current due to the device construction. The non-linear relationship is connected through the device parameter 'K'. Calculate 'K' for a specific MOSFET operating with an input voltage of 6 V and output current of 10 mA. The Threshold voltage of the chosen MOSFET is 4 V.
- Given below are two statements: one is labelled as Assertion (a) and the other is labelled as Reason (r).
Assertion (a): In a ratioless logic, the transistors can be of minimum size.
Reason (r): In a ratioless logic, the logic levels are not dependent upon the relative device size. - What are the effects of increasing temperature in the I-V characteristics of the NMOS transistor ?
MOSFET can be used as a ____________.
