Question
Download Solution PDFTwo n channel MOSFETs are fabricated and biased in saturation region in such a way that the first one has width as well as VGS-VTH double as those of the second one. All other parameters remain the same. What is the ratio of drain currents of the transistors?
Answer (Detailed Solution Below)
Detailed Solution
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- The drain current (ID) of a MOSFET in the saturation region is given by the equation:
ID = (1/2) × μn × Cox × (W/L) × (VGS - VTH)²,
where:- μn: Electron mobility
- Cox: Gate-oxide capacitance per unit area
- W: Width of the MOSFET channel
- L: Length of the MOSFET channel
- VGS: Gate-to-source voltage
- VTH: Threshold voltage
- All other parameters (μn, Cox, and L) are constant in this problem.
- Therefore, the drain current is directly proportional to both the width of the MOSFET (W) and the square of the overdrive voltage (VGS - VTH).
Solution:
Let the parameters of the second MOSFET (MOSFET 2) be:
- Width: W
- Overdrive voltage: (VGS - VTH)
- Drain current: ID2
For the first MOSFET (MOSFET 1), the parameters are:
- Width: 2W (double the width of MOSFET 2)
- Overdrive voltage: 2(VGS - VTH) (double the overdrive voltage of MOSFET 2)
- Drain current: ID1
The drain current for MOSFET 2 is:
ID2 = (1/2) × μn × Cox × (W/L) × (VGS - VTH)²
The drain current for MOSFET 1 is:
ID1 = (1/2) × μn × Cox × (2W/L) × [2(VGS - VTH)]²
Simplifying ID1:
ID1 = (1/2) × μn × Cox × (2W/L) × 4(VGS - VTH)²
ID1 = 4 × (1/2) × μn × Cox × (W/L) × (VGS - VTH)²
ID1 = 8 × ID2
Conclusion:
The ratio of the drain currents of the two MOSFETs is:
ID1 : ID2 = 8 : 1
The correct answer is Option 3.
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