GATE EC 2015 Set 1 — Question 44
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Electronic Devices → MOS Capacitor & MOSFET → Body Effect & Channel Modulation
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Question
A MOSFET in saturation has a drain current of 1 mA for = 0.5 V. If the channel length modulation coefficient is 0.05 , the output resistance (in k) of the MOSFET is _____.
Correct answer
19 to 21
Solution
For a MOSFET in saturation, the drain current with channel length modulation is given by:
where is the drain current without channel length modulation, and is the channel length modulation coefficient.The output resistance is defined as .First, let's find the derivative of with respect to :
So, the output resistance is:
We are given = 1 mA at = 0.5 V and = 0.05 .
We need to find first using the given and :
Now, calculate :
The output resistance is approximately 20.49 k. This value falls within the range of 19 to 21 k.Alternatively, we can approximate if is small. In this case, , which is small.
So,
This approximation gives 20 k, which is within the specified range.
where is the drain current without channel length modulation, and is the channel length modulation coefficient.The output resistance is defined as .First, let's find the derivative of with respect to :
So, the output resistance is:
We are given = 1 mA at = 0.5 V and = 0.05 .
We need to find first using the given and :
Now, calculate :
The output resistance is approximately 20.49 k. This value falls within the range of 19 to 21 k.Alternatively, we can approximate if is small. In this case, , which is small.
So,
This approximation gives 20 k, which is within the specified range.
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